TECHNICAL FIELD

The embodiments herein relate to nodes and methods for transmission of downlink radio signals in a Distributed Multiple Input Multiple Output system. A corresponding computer program and a computer program carrier are also disclosed.

BACKGROUND

In a typical wireless communication network, wireless devices, also known as wireless communication devices, mobile stations, stations (STA) and/or User Equipments (UE), communicate via a Local Area Network (LAN) such as a Wi-Fi network or a Radio Access Network (RAN) to one or more core networks (CN). The RAN covers a geographical area which is divided into service areas or cell areas. Each service area or cell area may provide radio coverage via a beam or a beam group. Each service area or cell area is typically served by a radio access node such as a radio access node e.g., a Wi-Fi access point or a radio base station (RBS), which in some networks may also be denoted, for example, a NodeB, eNodeB (eNB), or gNB as denoted in 5G. A service area or cell area is a geographical area where radio coverage is provided by the radio access node. The radio access node communicates over an air interface operating on radio frequencies with the wireless device within range of the radio access node.

Specifications for the Evolved Packet System (EPS), also called a Fourth Generation (4G) network, have been completed within the 3rd Generation Partnership Project (3GPP). A Fifth Generation (5G) network also referred to as 5G New Radio (NR) has also been specified and work is now directed to further specifications of the 5G network. This work will continue in the coming 3GPP releases.

To increase the capacity of wireless communication systems, it may be preferred to be as close as possible to a wireless communications device in an unobstructed environment. To achieve this, a network topology that is distributed in space may be needed.

A Distributed Multiple-Input Multiple-Output (D-MIMO) communications system is a system where a base station’s antennas are distributed over a cell in contrast to traditional deployments where the antennas are co-located in a single array in a cell center. From a performance standpoint, D-MIMO typically performs better than traditional co-located massive MIMO.

D-MIMO systems should be highly scalable and flexible to be able to provide true ubiquitous connectivity.

The probability of achieving a Line-of-Sight (LoS) channel between a wireless communications device, such as a User Equipment (UE), and one network Access Point (AP) is significantly larger for a D-MIMO system than for a centralized MIMO system. This makes D-MIMO a promising technique for building wireless communications systems with high performance and reliable coverage.

Non-coherent and Coherent Joint Transmission from D-MIMO system

Joint transmission schemes are used for the simultaneous transmission from multiple access points to the same UE. One of the schemes used in coordinated multipoint (CoMP) technology is joint processing including joint transmission (JT) and reception. JT may include two approaches: non-coherent (NCJT) and coherent joint transmission (CJT).

In NCJT, the network does not use detailed channel information in the joint transmission and in the majority of cases no radio frequency (RF) phase coherency is achieved. Therefore, a main gain that may be eventually achieved by NCJT is that the power of several APs is used to serve the same UE, i.e., a power gain. The use of distributed APs may still provide a significant macro diversity gain also when NCJT is used.

Conversely, in CJT, the detailed channel information between the UE and two or more APs involved in the JT is used to calculate the transmission precoding weights of all APs. In principle, by means of CJT the greatest MIMO gains can be realized, i.e., diversity and power gains. On the other hand, CJT requires stringent requirements on the time synchronization and relative phase coherency of the cooperating APs which may increase the complexity of its implementation. It is noted that in communication systems where channel reciprocity holds (e.g., TDD), calibration and precoding schemes to achieve CJT may be relaxed.

Distributed MIMO, also known as "cell-free massive MIMO", Radio Stripes, RadioWeaves, etc., is a key technology candidate for the 6G physical layer. As mentioned above, a basic idea is to distribute service antennas geographically and have them operate phase-coherently together. In an example architecture multiple antenna panels, also known as access points, or APs, are interconnected and configured in such a way that more than one panel may cooperate in coherent decoding of data from a given UE, and more than one panel may cooperate in coherent transmission of data to a UE. Each panel in turn may comprise multiple antenna elements that are configured to operate phase-coherently together. The preferred way of operation is in time-division duplexing (TDD), relying on reciprocity of the propagation channel, whereby uplink pilots transmitted by the UEs are used to obtain both the uplink and downlink channel responses simultaneously. Various research projects, for example H2020-REINDEER, are addressing aspects relating to this architecture, including the design of beamforming methods, random access signaling and procedures, etcetera.

Figure 1 illustrates a wireless communications network 100 comprising a D- MIMO network 101 which comprises L geographically distributed radio-heads APi, AP2, ... APL, such as APs (Access Points), each equipped with N antenna elements, although only one antenna element 11, 12 is depicted per radio-head in Figure 1. The total number of antennas in the network is N x L. The radio-heads AP1, AP2, ... APL may for example be remote radio-heads.

The D-MIMO network 101 further comprises a Processing Unit (PU) 130, which may be located in a Central Unit 110. The PU 130 may be a central processing unit. In some other embodiments the PU 130 may be located in one of the radio-heads AP1, AP2, ... AP _L or in another network node not shown in Figure 1.

The radio-heads AP1, AP2, ... APL may be connected via fronthaul links to the PU 130, which facilitate the coordination among APs. Note that fronthaul links connecting the APs with the PU 130 may be serial or parallel, as well as wired or wireless.

The APs are cooperating to serve K UEs in a coverage area jointly by phase coherent transmission in the downlink and phase coherent reception in the uplink.

In the downlink (as shown in Figure 1) a data symbol S/< to a wireless communications device 121 , also referred to as UEt, k e {1, . is transmitted from the PU 130 via a number of serving APs, AP _1; ... AP _L . The transmitted signals from APs, e.g. AP ₍ I e {1, use transmission weights (w _{; fc} is the transmission weight from AP, towards UE _k ) which are typically calculated based on channel state information derived from uplink pilots, e.g., by assuming downlink and uplink channel are reciprocal. There may also be a further wireless communications device 122, also referred to as UE/<. k' e {1, Interference components from the transmission to the wireless communications device 121 may reach the further wireless communications device 122 as illustrated in Figure 1.

Note that the transmission weight vector (w _{; fc} ) may equally well be expressed as an amplitude multiplied with a pre-coding vector (v _{; fc} ) with unit norm (i.e. w _{l k} = consequently ||w _{( fc} || = p _lik ).

In an ideal case the transmission weight vectors are designed so that signals from different APs are coherently and constructively added at the desired receiver (UE/<) and destructively combined (cancelled out) at interfered receivers (UER). At other locations the signals from different APs add up non-coherently, i.e., with random phase.

Figure 1 also introduces some of the notation that will be used below. A downlink channel between UE/< and AP/ is denoted b _{( k} and in case the UE has a single antenna element this is a row vector of size N. The receiver noise at UE/< is denoted nk, which is a scalar value in case the UE has a single antenna element. In the text below h _{( k} will be used to denote the uplink channel and b _{( fc} to denote the downlink channel. Uplink and downlink channel estimates are denoted h _{( k} and b _{( fc} , respectively. If the uplink channel and downlink channel are reciprocal, then it is known that b _{( k} = h" _fe and consequently

SUMMARY

The performance of D-MIMO downlink transmission relies on phase alignment. Signals transmitted from different APs use transmission weights which may be based on the uplink pilots assuming that downlink and uplink channels are reciprocal.

In all realistic scenarios, there will be some level of phase misalignment between APs. The phase misalignment may be due to differences in local AP clock references, and these time differences show up as phase differences at the receivers. For multiple serving APs, since APs are distributed, there will therefore be phase errors even after calibration of the phases since all calibration measurements are noisy. The different APs cannot transmit at exactly the same time, i.e. , with the same phase, which causes a phase misalignment at the receive side when UEs are served by several serving APs. If the downlink transmission weight vectors are designed based on the uplink channel, the gains with D-MIMO will quickly vanish when there are large phase misalignments between APs. The consequence is that D-MIMO will not perform as good as expected since signal components from different APs are not coherently added and the interference components are not perfectly suppressed when received at the UE side.

In Figure 2 a reference procedure used for downlink D-MIMO transmission is presented.

A phase alignment procedure is executed. This may e.g. involve transmitting several reference signals between the APs, which is well-known. However, the phase alignment procedure is not perfect and there will always be some residual phase misalignment that cannot be accounted for.

A downlink D-MIMO transmission may require channel state information (CSI) at the transmitter side, and this may e.g. be obtained by instructing the UE to transmit a pilot signal in the uplink (uplink pilot assignment in Figure 2). In the example in Figure 2 the CSI for UE/< obtained at AP/ is denoted CSI/,/<. Examples of CSI information is channel estimation, the covariance of the channel estimation error, the noise and interference covariance, delay spread, Doppler, etc. Note that in the example the CSI is obtained in the APs, but it is also possible to forward the received signals to the PU and obtain the CSI there.

Once the CSI is determined the transmission parameters, e.g., the transmission weight vectors for all UEs, for each AP may be determined. This may be done using standard methods like maximum ratio transmission (MRT), minimum mean square error (MMSE), zero-forcing (ZF), etc. In this context the transmission weight vectors w _{l k} (or equivalently, the pre-coding vector v _{l k} and transmission power parameters p _{l k} ) are considered to be the transmission parameters for each AP/ and UE/<, i.e. w _{i k} = [p^y _{i k} . Sometimes the problem of determining precoders (v _{; fc} ) and power control parameters (jO _{; fc} ) are treated separately, but for the purpose of simplifying the description this is considered to be a joint problem of determining the transmission weights (w _{; fc} ).

The PU obtains the data symbol s _k to be transmitted to UE/<, e.g. from higher protocol layers, and forwards this to the APs via the fronthaul. The APs may then generate the signals to be transmitted for each UE/< e.g. as w _{( k} s _k from AP/.

In real scenarios, the downlink and uplink are not perfectly reciprocal, there will be differences in downlink and uplink, especially related to timing. In D-MIMO networks, since APs are distributed, there is a need to calibrate the phases of APs to achieve coherent phase addition and suppression of the interference, which are the D-MIMO gains. However, measurements used to calibrate phases will be noisy, and even after the calibration there are still residual phase alignment errors. Moreover, some calibration methods require defining a phase reference AP so that non-phase-aligned serving APs may be aligned with the reference AP. Such calibration methods become difficult when the number of serving APs increase. For example, calibration may become more difficult as each UE may have several APs in a subset and a reference AP for the respective UE may be different.

Thus, a problem is that the signals from different APs cannot be transmitted at exactly the same time, i.e. the signals from different APs are transmitted with misaligned phases.

These timing errors cannot be observed, but may still be defined mathematically by assuming that there exists a global clock. The global clock is unobservable for the APs and they have to rely on their own local clocks to determine when to transmit the signals. The difference between the global unobservable clock and the local clock of AP/ is denoted <p _L . The UE will receive a composite signal where these local clock errors appear as phase errors. The absolute values do not matter, but the relative difference between the local clocks does.

When transmission parameters are designed by ignoring the phase misalignment, the consequence is a degradation in performance.

An object of embodiments herein may be to obviate some of the problems related to phase misalignment of DL transmissions in D-MIMO systems.

According to an aspect of embodiments herein, the object is achieved by a method, performed by a Processing Unit, PU, for determining transmission weights for transmission of DownLink, DL, radio signals from a Distributed Multiple Input Multiple Output, D-MIMO, system. The D-MIMO system comprises the PU, a first radio-head and a second radio-head.

The method comprises obtaining first channel state information associated with transmissions between the wireless communications device and the first radio-head and second channel state information associated with transmissions between the wireless communications device and the second radio-head. The method further comprises obtaining an estimation of a variability in a distribution of a difference in phase between DL transmissions from the first radiohead and DL transmissions from the second radio-head.

The method further comprises determining respective first and second transmission weights for transmission of DL radio signals from the first radio-head and from the second radio-head to the wireless communications device based on the first and second channel state information and further based on the obtained estimation of the variability in the distribution of the difference in phase.

According to a second aspect of embodiments herein, the object is achieved by a PU configured to determine transmission weights for transmission of DownLink, DL, radio signals from a D-MIMO system. The D-MIMO system comprises the PU, a first radio-head and a second radio-head.

The PU is configured to obtain first channel state information associated with transmissions between the wireless communications device and the first radio-head and second channel state information associated with transmissions between the wireless communications device and the second radio-head.

The PU is further configured to obtain an estimation of a variability in a distribution of a difference in phase between DL transmissions from the first radiohead and DL transmissions from the second radio-head.

The PU is further configured to determine respective first and second transmission weights for transmission of DL radio signals from the first radio-head and from the second radio-head to the wireless communications device based on the first and second channel state information and further based on the obtained estimation of the variability in the distribution of the difference in phase.

According to a third aspect of embodiments herein, the object is achieved by a network node comprising the PU.

According to a further aspect, the object is achieved by a computer program comprising instructions, such as computer readable code units, which when executed by a processor of the PU causes the PU to perform actions according to any of the aspects above. According to a further aspect, the object is achieved by a carrier comprising the computer program of the aspect above, wherein the carrier is one of an electronic signal, an optical signal, an electromagnetic signal, a magnetic signal, an electric signal, a radio signal, a microwave signal, or a computer-readable storage medium.

An advantage of embodiments herein is that they enable calculating downlink transmission weights that are robust against phase alignment errors between radioheads, such as APs, in the D-MIMO network.

A further advantage of embodiments herein is that they enable the use of a numerically efficient and numerically stable Linear Quadratic Regulator (LQR) optimization algorithm to calculate the transmission weights. The transmission weights may be calculated by optimizing an LQR cost function which balances both estimation errors and transmitting power.

Balancing both errors and transmitting power means that it is desired to minimize the estimation errors (the first term in the cost function) at the same time as the power needed to minimize the estimation errors is also minimized or at least restricted.

Furthermore, the optimization may be performed for one AP or multiple serving APs, which allows to use a scalable decentralized sub-set method, e.g., a number of serving APs for each UE may be selected based on a trade-off between complexity and performance.

A further advantage of some embodiments herein is that a resulting performance may be optimal in terms of minimum mean square error and optimal power distribution.

BRIEF DESCRIPTION OF THE DRAWINGS

In the figures, features that appear in some embodiments are indicated by dashed lines.

The various aspects of embodiments disclosed herein, including particular features and advantages thereof, will be readily understood from the following detailed description and the accompanying drawings, in which:

Figure 1 illustrates a simplified illustrates a wireless communications network comprising a D-MIMO network,

Figure 2 is a combined flow chart and signalling diagram schematically illustrating a reference procedure used for downlink D-MIMO transmission,

Figure 3 is a graph illustrating an impact of the residual phase error on D-MIMO performance, Figure 4 is a signaling diagram schematically illustrating methods according to embodiments herein,

Figure 5a is a flowchart illustrating methods according to embodiments herein,

Figure 5b is a graph illustrating quantification of performance gains obtained by embodiments disclosed herein,

Figure 6 is a schematic block diagram illustrating an example implementation of a network node of the wireless communications network,

Figure 7 schematically illustrates a telecommunication network connected via an intermediate network to a host computer.

Figure 8 is a generalized block diagram of a host computer communicating via a base station with a user equipment over a partially wireless connection.

Figures 9 to 12 are flowcharts illustrating methods implemented in a communication system including a host computer, a base station and a user equipment.

DETAILED DESCRIPTION

As mentioned above, a problem of prior art D-MIMO systems is that even if a calibration of the transmissions is performed there is still a residual phase error between the APs.

An object of embodiments herein is therefore to improve the transmissions from D- MIMO system by taking into account the residual phase error between the APs, e.g., a difference in transmission phase, when determining the transmission weights, such that the impact of the residual phase error on the received signal is reduced.

Thus, embodiments herein disclose methods for determining robust D-MIMO downlink transmission weight parameters. The methods are designed to take the phase misalignment uncertainty into account for each AP.

The phase misalignment uncertainty may be included when determining the transmission weight parameters for example by adding a model of the phase error in the channel covariance matrix. For example, the transmission weight calculation may include the phase uncertainty when minimizing a linear mean-square error expression.

A further advantage of embodiments herein is that they are compatible with existing methods. For example, in some embodiments herein a channel estimation uncertainty may also be included in the channel covariance matrix when determining the transmission weights. As the channel itself is also random, it changes randomly depending on the environment and UE locations and speed, which means that there is uncertainty when the mean and variance of the channel is used. Embodiments herein are very generic since the channel covariance matrix may be included when determining the transmission weights embodiments herein become generic.

Embodiments herein may use a Linear Quadratic Regulator (LQR) solution for calculating the downlink transmission weights. The transmission weights may be obtained by minimizing a linear quadratic cost function, where phase uncertainties are included.

From an implementation point of view, the algorithm for solving the LQR problem is similar to the implementation of the Kalman filter for uplink combining. This means that a standard square-root implementation of Kalman filters is applicable. The Kalman filter square-root implementation always assures that the covariance matrix is symmetric and positive semi-definite, which avoids the singularity problem when inverting the covariance matrix.

In order to better understand embodiments herein a method for D-MIMO downlink precoding using the LQR solution will first be presented.

D-MIMO downlink precoding using LQR solution

In a D-MIMO network, a duality principle in optimization theory may be applied to solve the downlink precoding using the uplink Kalman filtering method when the downlink and uplink channels are reciprocal.

The downlink signal to all K UEs may be expressed as a vector s = [Si ••• This vector of data symbols is to be transmitted from the PU to the UEs via a subset of the serving APs in the D-MIMO network. To simplify the analysis, it will be assumed that the data symbols are normally distributed complex random variables with zero mean and variance 1 In case they are selected from a QAM signal constellation this assumption is still a good approximation.

The signal u ₍ transmitted from AP/ to all UEs may now be expressed in vector notation as u ₍ = W ₍ s

Since each AP has N antenna elements u ₍ is a vector of length N. The transmission weight matrix of size (N x K) comprises the transmission weight vectors for each UE as columns, i.e. W ₍ = [M'I.I •" ^w t,x], (W _; e C ^Nx ). Using an LQR optimal solution the transmission weight W ₍ , may be calculated for the signal at each antenna. The downlink channel from AP/ to UE/< is denoted b _{( fc} . The signal received at each UE is a weighted sum of transmitted signals from the serving APs. This signal will consist of both the desired signal, the interference from all other transmissions, and receiver noise. If all L APs are serving APs we may write the received signal as y _fc = Zf=i fcU ₍ + n _k .

If only a sub-set of the APs are used to serve each UE, which is known as a subset precoding method, the number of serving APs in the subset of UEs may be varied and aggregated from sub-1 to sub-L In general, let L, 1 < L < L be the number of serving APs for the UE/<, then the received signal may be written as

Here it may be assumed that the UE only has a single antenna and hence both y _k and n _k (receiver noise) are scalar complex values. The generalization to multi-antenna UEs is straightforward and will not be described here. To simplify these expressions further the number of serving APs is assumed to be L and a channel matrix for all serving APs is defined as which is of a size K x NL, and a transmitted signal vector from all serving APs and a vector of noises at receiver: n = [n ••• n _K ] ^T of a size K x 1. This gives y = Bu + n.

The received signals for all UE _fc , k = 1, ... K are then used to define the vector of received signal vector: y = [yi ••• VK] ⁷ .

To determine the transmission parameters (in this example the precoding vectors and the power scaling parameter for all APs and all UEs) the following linear quadratic equation may be minimized as function of the transmission parameters:

E((y ^_ s) ^H P(y - s) + U ^H EU)

This linear quadratic function is called the LQR cost function. The cost function has two weighting matrices, P and E. The weighting matrices may be tuned to prioritize minimization of the estimation error (y - s) for individual UE and the power (defined by r ^w ii the transmission weights in u = Ws, where W = for individual antenna elements.

W _L

Both weighting matrices are diagonal matrices. P is used to penalize the estimation errors

(y - s), one for each UE, and E is used to penalize the power to be used, one for each antenna element. In a normal deployment (e.g., where APs and UEs are well distributed in an area) the same values for diagonal elements in these weighting matrices may be used (e.g., to make it easier for the implementation). When necessary, it is possible to set individual diagonal elements for the respective matrices.

A problem to find transmission parameters that minimize this linear quadratic function may be formulated as a “Linear Quadratic Regulator” problem, or LQR problem, the term regulator comes from control theory. The solution to the LQR problem is sometimes denoted an LQR solution.

The LQR problem here is to find u given the signal s so that the linear quadratic cost function is minimized for the given weighting matrices P and E. And since u ₍ = W ₍ s, and W ₍ = [W{,i ••• W( ] the optimum weights w _{l k} from APi to UE/< are to be found (that is the transmission weights (or transmission parameters) to be used in AP, to send the data signal to UE/<) for all / = 1, ... , L and all k = 1, ... , K.

One advantage of using the LQR solution for calculating the transmission weights is that the optimization may be performed in any number of serving APs in the sub-set. The transmission weights for all APs in a sub-set, sub-L, (for AP, with indexes I e imply denoted by W. If a sub-set, sub-L, which has £ serving APs is has a size N£ x K. If the downlink channel B is known, applying

LQR to minimizing the cost function, the optimal solution is given by u = Ws where W is the downlink transmission weight matrix, which may be expressed as

W = R ^-1 B ^H P, where R is the channel covariance matrix

R = B ^H PB + E ² . As an example, to explain the sizes of matrices in the above, considering a sub-set

Wi consists of L serving APs, W = has a size NL x K', the channel matrix B has a size

LW

K x NL, hence B ^H has a size NL x K P is of size K x K and E is of size NL x NL, thus the covariance matrix R has a size NL x NL.

The implementation complexity of solving the LQR is dominated by the calculation of the inverse of the covariance matrix R. The more serving APs in the subset the larger size of the covariance matrix, hence the more sensitive when inverting the covariance matrix. The square-root implementation for solving the Kalman filter and/or the LQR problem may be used since the square-root implementation is shown to be numerically sound when inverting the covariance matrix.

In order to further explain the relevance of embodiments herein several precoding methods, which will be called “cell-free-book” methods and decentralized subset method will now be presented as a reference.

The impact of the residual phase error on D-MIMO performance is illustrated in Figure 3. In Figure 3 precoding methods are shown on the x-axis and performance in terms of the 10 ^th percentile of spectral efficiency, which is equivalent to SI NR, on the y- axis. The first four precoding methods from the left, marked with “cell-free-book”, include both centralized methods (C-AII, P-DCC) and decentralized methods (L-AII, LP-DCC). The “subset methods” use a subset of APs for each UE as serving APs. The selection of the serving APs may be based on the path-gain between APs and UE. The number of serving APs to form the subset is a trade-off between the complexity and performance. Sub-1 has a single serving AP, which turns D-MIMO into “small cell”. The number of serving APs may be aggregated depending on the fronthaul and performance requirement, from two serving APs, sub-2, and all the way up to include all APs, say L, in the D-MIMO network, sub-L.

Figure 3 shows simulation results for the above-mentioned “cell-free-book” methods and the decentralized subset method when transmission precoding weights are calculated assuming perfect phase alignment by ignoring the existence of phase errors (this represents the performance of the reference methods). In this example, there are 36 APs, L = 36, hence sub-36 gives the upper bound of the performance in the ideal case.

In the non-ideal case, there are phase errors. Since phase errors are unknown and random, the phase error p is modelled as a random process with a zero-mean Gaussian distribution p e J\T(0, o- ² ), where a is the standard deviation. The standard deviation a was varied from 1° to 45°, and compared with a = 0, i.e., the ideal case without phase error. From the simulation results it may be seen that the performance degrades when the standard deviation of phase error a increases, the larger phase errors, the more performance degradation. In the ideal case (o = 0), the more APs we use, the better performance is obtained. However, in the non-ideal case, the D-MIMO gains vanish when more APs are added, and the “small-cell” becomes the best alternative when a = 45°.

Exemplifying methods according to embodiments herein will now be described with reference to a signaling diagram in Figure 4. The signaling diagram illustrates a method for determining transmission weights for transmission of radio signals from the D-MIMO system 101 for wireless communication with the wireless communications device 121. The transmissions may be DL transmissions. As mentioned above, the D-MIMO system 101 comprises the Pll 130, the first radio-head APi and the second radio-head AP2. The method may be performed by the D-MIMO system 101 , more specifically by the different nodes of the D-MIMO system 101 , and the wireless communications device 121.

In action 401 the radio-heads, such as the first radio-head AP1 and the second radio-head AP ₂ , of the D-MIMO network 101 may perform a “phase alignment procedure”.

Since the actual residual phase error may be difficult to obtain, in action 402 the Pll 130 obtains an estimate of a variability of a residual phase error, such as a standard deviation and/or variance, after phase alignment (here denoted a ² ). The estimate of the variability of the residual phase error after phase alignment may be obtained in several different ways. For example, noise of measurements used during phase alignment may be estimated for each AP and using standard estimation theory the Pll 130 may then obtain an expression of the variability of the phase alignment error for each APi (here denoted The standard estimation theory may for example, using Maximum likelihood estimation, assume that measured data is random with a probability distribution which is dependent on some parameters, such as the phase alignment error. See for example action 402a in which the first radio-head APi transmits an estimate of a first phase error variance a ² ₁ representing the uncertainty of a first phase of first DL transmissions from the first radio-head APi. Likewise, in action 402b the second radio-head AP ₂ transmits an estimate of a second phase error variance o- ² ₂ representing the uncertainty of a second phase of second DL transmissions from the second radio-head AP ₂ . The phase alignment errors may also depend on ambient temperature, and they may then be obtained e.g. from a look-up-table. However, for embodiments herein the estimate of the variability of the residual phase error after phase alignment may also be obtained in other ways.

In action 403 the wireless communications device UEk is instructed, e.g., by the Pll 130, to transmit a pilot signal in the uplink.

In action 404 the wireless communications device UE _k transmits the pilot signal in the uplink to the radio-heads, such as the first radio-head APi and the second radio-head AP ₂ .

In action 405a the first radio-head APi obtains first CSI for a first channel associated with the the wireless communications device UE _k and the first radio-head APi.

In action 405b the second radio-head AP ₂ obtains second CSI for a second channel associated with the wireless communications device UE _k and the second radiohead AP ₂ .

In action 406a the first radio-head APi transmits the first CSI to the Pll 130.

In action 406b the second radio-head AP ₂ transmits the second CSI to the Pll 130.

In action 407 the Pll 130 determines DL transmission weights based on the first CSI, the second CSI and the estimate of the variability of the residual phase error after phase alignment.

A model of the residual phase alignment error may then be used when determining the transmission parameters. As will be showed below, this results in transmission parameters that provide significant performance gains. Note that the phase misalignment errors will still be present and that they are just as large as before. However, the transmission weights derived using embodiments herein are much more robust to these phase alignment errors.

In action 408a the Pll 130 transmits, to the first radio-head APi, a first DL transmission weight w _{l fe} to be used by the first radio-head APi. In action 408b the Pll 130 transmits, to the second radio-head AP2, a second DL transmission weight w _{2 fe} to be used by the second radio-head AP2.

In action 409 the Pll 130 obtains a data symbol s _k for the wireless communications device UE _k .

In action 410a the Pll 130 transmits, to the first radio-head AP1 data symbol s _k to be used in DL transmissions by the first radio-head AP1.

In action 410b the Pll 130 transmits, to the second radio-head AP ₂ , data symbol s _k to be used in DL transmissions by the second radio-head AP2.

In action 411a the first radio-head AP1 generates a first DL TX signal w _{l k} s _k .

In action 411b the second radio-head AP2 generates a second DL TX signal W ₂ ,fcSfc.

In action 412a the first radio-head AP1 transmits the first DL TX signal w _{l k} s _k when a first local clock of the first radio-head AP1 fulfils a first time criterion, such as when the first local clock is zero.

In action 412b the second radio-head AP2 transmits the second DL TX signal w _{2 k} s _fe when a second local clock of the second radio-head AP2 fulfils a second time criterion, such as when the second local clock is zero.

In action 413a and 413b the wireless communications device UE _k receives the transmitted signals with a phase difference corresponding to the difference in transmission times due to the difference in local clocks of the radio-heads.

Exemplifying methods according to embodiments herein will now be described with reference to a flow chart in Figure 5a and with continued reference to Figure 1. The flow chart illustrates a method, performed by the PU 130 for determining transmission weights for transmission of DL radio signals from the D-MIMO system 101 for wireless communication with the wireless communications device 121. As mentioned above, the D-MIMO system 101 comprises the Pll 130, a first radiohead APi and a second radio-head AP2.

In action 501 , the Pll 130 obtains first channel state information associated with transmissions between the wireless communications device 121 and the first radio-head AP1 and second channel state information associated with transmissions between the wireless communications device 121 and the second radio-head AP2.

In action 502, the Pll 130 obtains an estimation of a variability in a distribution of a difference in phase between DL transmissions from the first radio-head AP1 and DL transmissions from the second radio-head AP2.

In some embodiments herein the Pll 130 obtains one estimation of the variability ^1-9)2 in th® distribution of the difference in phase between DL transmissions from the first radio-head AP1 and DL transmissions from the second radio-head AP2.

In some other embodiments the PU 130 obtains the estimation of the variability in the distribution of the difference in phase between DL transmissions from the first radio-head AP1 and DL transmissions from the second radio-head AP2 by: obtaining an estimation of a first variability in a first distribution of a first phase alignment error associated with DL transmissions from the first radio-head AP1 to the wireless communications device 121 ; and obtaining an estimation of a second variability in a second distribution of a second phase alignment error associated with DL transmissions from the second radio-head AP2 to the wireless communications device 121 .

In general, when there are N APs N-1 variance estimates may be required as input to the determination of the transmission weights. However, N (one per AP) variance estimates may also be used to determine the transmission weights.

In some embodiments herein the PU 130 obtains the estimation of the variability ^1-9)2 ' ⁿ the distribution of the difference in phase based on obtaining an estimation of noise of measurements performed during phase alignment of the first radio-head AP1 and the second radio-head AP ₂ for the respective radio-head AP1, AP ₂ .

Obtaining the estimation of the variability in the distribution of the difference in phase may be based on a maximum-likelihood estimation of a phase alignment error between the first radio-head AP1 and the second radio-head AP2. The maximum- likelihood estimation of the phase alignment error may be based on the obtained estimation of noise of measurements performed during phase alignment.

A difference between the first phase alignment error and the second phase alignment error may correspond to a phase error between transmitted DL signals from the first radio-head (APi) and the second radio-head (AP2) to the wireless communications device (121).

In action 503, the Pll 130 determines respective first and second transmission weights, for transmission of DL radio signals from the first radio-head AP1 and from the second radio-head AP ₂ to the wireless communications device 121 based on the first and second channel state information and further based on the obtained estimation of the variability in the distribution of the difference in phase.

In some embodiments determining the first and second transmission weights is based on a Linear Quadratic Regulator optimization algorithm. The LQR optimization algorithm may minimize both mean-square error and power to use.

The respective transmission weight may comprise or be equivalent to a precoding vector and a power scaling parameter.

In some embodiments determining the first and second transmission weights is based on minimizing a linear quadratic cost function comprising: a first quadratic term dependent on an estimation error of received DL signals associated with the obtained first and second channel state information with respect to a transmitted signal, wherein the estimation error is based on the obtained first and second channel state information and the obtained estimation of the variability in the distribution of the difference in phase, and a second quadratic term dependent on the transmitted signal, and wherein the transmitted signal is dependent on the first and second transmission weights.

For example, the linear quadratic cost function may comprise a parameter representing an effective channel which may be based on the CSI. The linear quadratic cost function may further comprise a parameter representing a total uncertainty which may be based on the obtained estimation of the variability in the distribution of the difference in phase.

The estimation of the variability in the distribution of the difference in phase may in turn be based on a variance or standard deviation of a relative phase error between transmissions from the first radio-head AP1 and the second radio-head AP ₂ . Minimizing the linear quadratic cost function may further be based on prioritizing the first quadratic term or the second quadratic term based on multiplying the first quadratic term with a first weighting matrix and/or based on multiplying the second quadratic term with a second weighting matrix.

The first weighting matrix may be used to penalize the estimation errors (y-s). The second weighting matrix may be used to penalize the power to be used, one for each antenna element. In the normal deployment (APs and UEs are well distributed in an area) the same values may be used for diagonal elements in the first and the second weighting matrices (e.g. to make it easier for the implementation). However, induvial diagonal elements may be set when it is necessary.

In some embodiments minimizing the linear quadratic cost function comprises calculating an effective channel based on the obtained first and second channel state information and the obtained estimation of the variability in the distribution of the difference in phase.

Minimizing the linear quadratic cost function may comprise calculating a channel covariance matrix based on the obtained estimation of the variability in the distribution of the difference in phase.

The covariance is the mean value of estimation errors. The estimation errors are the differences between the real and estimated values. In embodiments herein, the estimation errors may include the channel estimation errors and phase estimation errors. It is on the DL channels that signals are going to be transmitted. However, the estimation of the DL channel may be based on uplink channel measurements.

Thus, the covariance matrix is a measure of the uncertainty. It may be used to decide weights on the signals when transmitting in DL. The weights may be complex values that provide both a direction and a power to transmit the signal. The weights may be calculated depending on how much uncertainty that there is in the estimations. Generally speaking, with a larger uncertainty, the more careful the method should be when the weights are selected.

The weighting matrices represents weights (or so-called knobs in the automatic control processes) in the LQR cost function that are possible to tune so that an optimal solution (e.g. a minimum value) of an LQR problem may be tuned and balanced. Note that the optimal solution may be a matrix and provides the weights for all antennas of APs to all UEs at once. These weights may be balanced to maximize signal energy and to minimize the interference. In some embodiments determining the respective first and second transmission weights comprise scaling the transmission weights equally by a constant p for antenna elements 11, 12 of the first radio-head APi and the second radio-head AP2 when a transmission power of an antenna element 11, 12 of the antenna elements 11, 12 exceeds the maximum power budget of the antenna element 11, 12.

In some scenarios it may happen that some weights (amplitudes) exceed a maximum power budget of the antenna elements. For example, the antennas’ maximum power budget may be restricted by a maximum power budget of the radio-heads, e.g., limited by a size of a battery powering the radio-head. (Antenna has power limit as all APs). In that case, the antenna cannot transmit the signal with weights given by the LQR optimal solution. However, this may be solved in different ways. One way is to scale down the power with a constant (p) for all antenna elements even for those that do not exceed the maximum limit. A reason to scale all the antenna elements may be to maintain the optimization.

Another way of controlling the power below the power budget may be to determine the respective first and second transmission weights by further adjusting the second weighting matrix to penalize the power of each antenna element 11, 12 of the first radio-head AP1 and the second radio-head AP2 individually before minimizing the linear quadratic cost function.

In action 504, the Pll 130 transmits the respective determined transmission weight to the associated radio-head of the first radio-head AP1 and the second radio-head AP2.

Further detailed example embodiments

Here embodiments will now be described in further detail. For example, it will be described how the residual phase alignment error is used to derive robust transmission parameters. Although the LQR implementation is used as an example, please note that some embodiments herein may also be applied to other methods for determining D-MIMO transmission parameters such as minimum mean square error (MMSE) and zero-forcing (ZF) methods. An advantage of using an LQR method is that there exist very effective algorithms for LQR.

Performance gains obtained by embodiments disclosed herein are quantified in Figure 5b. In Figure 5b a gain of embodiments disclosed herein is larger for the methods that lost the most using only the reference method, for example when the phase error variance is the largest (45 degrees here). It is not possible to regain all performance loss, after all the phase alignment errors are still present. But accounting for the phase misalignment errors when determining transmission parameters result in gains in the range of 20% to 70%.

In Figure 5b embodiments herein have only been applied to the “Subset methods”, but it is expected that similar gains also will be present in the “Cell-free book methods”. Solid lines represent performance with the reference methods and dashed lines represent the performance with embodiments herein. Different phase alignment errors, ranging from o = 0 to o = 45 degrees are plotted using different data point markers.

Note that the dashed lines use an LQR (linear quadratic regulator) method, that will be further explained below.

Figure 4 illustrate how the phase error may be included in the downlink channel chain, exemplified by any two APs, APi and AP2 that are involved. The phase error for AP1 is <p ₁ and for AP2 is <p ₂ . Note that it is the differences <p _± - <p ₂ that causes phase misalignment. This may be compared to Figure 2 where the phase error is ignored when determining the transmission parameters.

The effective downlink channel, including phase misalignment errors, for UE/< may be expressed as

And the effective channel for all UEs is b ^f

B ^eff = b °K ^eff .

The effective channel may also be written as B ^eff = B + 8 _tot C _tot ) with mean B and covariance C _tot . Note that 8 _tot = B ^eff - B and hence 8 _tot e JV' _C (O, C _tot ) where C _tot = C _ch + (1 - e ^_ff2 )B ^H B and C _ch is the covariance matrix of the channel estimation error.

To show how to calculate the downlink transmission weights with all uncertainty 8 _tot , this is exemplified by calculating transmission weights based on the optimal LQR solution. However, embodiments herein work with any other optimization methods, such as MMSE and ZF.

To include the total uncertainty 8 _tot in the LQR problem, the cost function described above is modified as: The LQR optimal solution may be calculated by minimizing this cost function. The optimal solution is u = Ws where W is the robust downlink transmission weight matrix which may be expressed as

W = R ^-1 B ^H P, and the total uncertainty 8 _tot is included in the covariance matrix R as

The phase uncertainty is considered as a part of total uncertainty which is given by E{8 _tot P8^ _ot } = k Pk,k ^c k,k ^ar| d ^c k,k ^are diagonal elements of the channel covariance C _tot and p _{k k} are the diagonal elements of P. In this way the phase alignment uncertainty is included in the covariance matrix when LQR minimizes the cost function and when calculating the robust transmission weights W.

As mentioned above, with a larger uncertainty, the more careful the method should be when the weights are selected. For example, when the term E{8 _tot P8^ _t } of the covariance matrix R is large, the covariance matrix R becomes large. Hence the precoding weight matrix W becomes small since it is dependent on an inverse of R. When the weights are small, the transmission power is lower. Thus, the power may be a regulator. With a lower power, regulation of the power level needs to be more careful.

Additional power control, per-antenna element or per-AP

After optimal transmission weights have been obtained, there is no need to do individual power control. The optimal transmission amplitudes are already included in the transmission weights. Any additional power control may destroy the optimization that balances the distribution of transmission power among the antenna elements. However, there may be the situation where some transmission powers of antenna elements exceed the maximum power budget of the antenna elements. In that case there are different alternatives to keep the maximum power limit. One way is to scale the weights by a constant p equally for all antenna elements. In this way the optimal balance of the transmission power given by the transmission weights is kept. This power scaling method works as long as the difference between the maximum and rest of the weighted signal power is relatively small. In the case when the differences of weighted signal power between antenna elements are large, the weighting matrix E in the LQR cost function may also be adjusted to penalize the power of the antenna element individually before solving the optimization of the LQR problem to obtain transmission weights.

Figure 6 shows an example implementation of a network node 600 of the wireless communications network 100.

The network node 600 may be configured to perform the method actions of Figure 5a and some of the method actions of Figure 4. The network node 600 may for example be the central unit 110 or any of the radio-heads APi , AP2.

The network node 600 may comprise the Pll 130 for performing the above method actions. The Pll 130 may comprise further sub-units which will be described below.

In some embodiments disclosed herein the Pll 130 may be distributed over several nodes, such as over several radio-heads. Thus, the Pll 130 may comprise multiple Plls, such as a first Pll located in the first radio-head AP1 and a second Pll located in the second radio-head AP2.

The network node 600 may comprise an input and output interface, IF, 606 configured to communicate with for example other network nodes, such as radio-heads or central units, or even core network nodes, and the wireless communications devices 121, 122, see Figure 6. The input and output interface 606 may comprise a wireless receiver (not shown) and a wireless transmitter (not shown).

The network node 600 may further comprise an obtaining unit 610 for obtaining CSI and one or more estimations of the variability in the distribution of the difference in phase between DL transmissions from the first radio-head and DL transmissions from the second radio-head.

The network node 602 may further comprise a determining unit 620 for determining respective first and second transmission weights.

The network node 600 may further comprise a transmitting unit 630, which may transmit the respective determined transmission weight to the associated radio-head and further messages and/or signals.

The embodiments herein may be implemented through a respective processor or one or more processors, such as the respective processor 604, of a processing circuitry in the network node 600, and depicted in Figure 6 together with computer program code for performing the functions and actions of the embodiments herein. The program code mentioned above may also be provided as a computer program product, for instance in the form of a data carrier carrying computer program code for performing the embodiments herein when being loaded into the respective network node 600. One such carrier may be in the form of a CD ROM disc. It is however feasible with other data carriers such as a memory stick. The computer program code may furthermore be provided as pure program code on a server and downloaded to the respective network node 600.

The Pll 130 is configured to determine transmission weights for transmission of DL radio signals from the D-MIMO system 101 for wireless communication with the wireless communications device 121. As mentioned above, the D-MIMO system 101 comprises the Pll, 130, the first radio-head APi and the second radio-head AP2.

The Pll 130 is further configured to obtain first channel state information associated with transmissions between the wireless communications device 121 and the first radio-head AP1 and second channel state information associated with transmissions between the wireless communications device 121 and the second radio-head AP2.

The Pll 130 is further configured to obtain an estimation of the variability in the distribution of the difference in phase between DL transmissions from the first radiohead AP1 and DL transmissions from the second radio-head AP2.

The PU 130 is further configured to determine respective first and second transmission weights for transmission of DL radio signals from the first radio-head AP1 and from the second radio-head AP ₂ to the wireless communications device 121 based on the first and second channel state information and further based on the obtained estimation of the variability in the distribution of the difference in phase.

In some embodiments herein the PU 130 is configured to determine the first and second transmission weights based on the Linear Quadratic Regulator optimization algorithm.

The PU 130 may be configured to determine the first and second transmission weights by being configured to minimize the linear quadratic cost function.

As mentioned above, the linear quadratic cost function may comprise the first quadratic term dependent on an estimation error of received DL signals associated with the obtained first and second channel state information with respect to the transmitted signal. The estimation error may be based on the obtained first and second channel state information and the obtained estimation of the variability in the distribution of the difference in phase.

The linear quadratic cost function may further comprise the second quadratic term dependent on the transmitted signal, and wherein the transmitted signal is dependent on the first and second transmission weights.

In some embodiments herein the Pll 130 is configured to minimize the linear quadratic cost function further by being configured to prioritize the first quadratic term or the second quadratic term based on multiplying the first quadratic term with the first weighting matrix and/or based on multiplying the second quadratic term with the second weighting matrix.

The Pll 130 may be configured to minimize the linear quadratic cost function by being configured to calculate an effective channel based on the obtained first and second channel state information and the obtained estimation of the variability in the distribution of the difference in phase.

In some embodiments herein the Pll 130 is configured to minimize the linear quadratic cost function by being configured to calculate the channel covariance matrix based on the obtained estimation of the variability in the distribution of the difference in phase.

The Pll 130 may be further configured to determine the respective first and second transmission weights by being configured to scale the transmission weights equally by the constant p for antenna elements 11, 12 of the first radio-head APi and the second radio-head AP ₂ when the transmission power of an antenna element 11, 12 of the antenna elements 11 , 12 exceeds the maximum power budget of the antenna element 11, 12.

In some embodiments herein the Pll 130 is configured to determine the respective first and second transmission weights by being further configured to adjust the second weighting matrix to penalize the power of each antenna element 11, 12 of the first radiohead APi and the second radio-head AP ₂ individually before minimizing the linear quadratic cost function.

The Pll 130 may be further configured to obtain the estimation of the variability

' ⁿ the distribution of the difference in phase by being configured to obtain an estimation of noise of measurements performed during phase alignment of the first radiohead APi and the second radio-head AP2 for the respective radio-head AP1, AP2.

In some embodiments herein the Pll 130 is configured to obtain the estimation of the variability in the distribution of the difference in phase based on the maximumlikelihood estimation of the phase alignment error between the first radio-head AP1 and the second radio-head AP2. The maximum-likelihood estimation of the phase alignment error may be based on the obtained estimation of noise of measurements performed during phase alignment.

The Pll 130 may be configured to obtain the estimation of the variability in the distribution of the difference in phase between DL transmissions from the first radiohead AP1 and DL transmissions from the second radio-head AP2 by being configured to: obtain an estimation of the first variability in the first distribution of the first phase alignment error associated with DL transmissions from the first radio-head AP1 to the wireless communications device 121 ; and obtain an estimation of the second variability in the second distribution of the second phase alignment error associated with DL transmissions from the second radiohead AP2 to the wireless communications device 121.

When the PU 130 comprises the first PU located in the first radio-head AP1 and the second PU located in the second radio-head AP2, then the first PU may be configured to: obtain first channel state information associated with transmissions between the wireless communications device 121 and the first radio-head AP1; obtain the estimation of the variability in the distribution of the difference in phase between DL transmissions from the first radio-head AP1 and DL transmissions from the second radio-head AP2; and determine the first transmission weight for transmission of DL radio signals from the first radio-head AP1 to the wireless communications device 121 based on the first channel state information and further based on the obtained estimation of the variability

' ⁿ the distribution of the difference in phase; and then the second Pll may be configured to: obtain second channel state information associated with transmissions between the wireless communications device 121 and the second radio-head AP ₂ ; obtain the estimation of the variability in the distribution of the difference in phase between DL transmissions from the first radio-head APi and DL transmissions from the second radio-head AP ₂ ; and determine second transmission weights for transmission of DL radio signals from the second radio-head AP ₂ to the wireless communications device 121 based on the second channel state information and further based on the obtained estimation of the variability in the distribution of the difference in phase.

The network node 600 may further comprise a memory 602 comprising one or more memory units. The memory comprises instructions executable by the processor in the network node 600.

The memory 602 is arranged to be used to store e.g. information, data, configurations, and applications to perform the methods herein when being executed in the respective network node 600 and network node 602.

In some embodiments, a computer program 603 comprises instructions, which when executed by the at least one processor, cause the at least one processor of the network node 600 to perform the actions above. The computer program 603 may be loaded into the memory 602.

In some embodiments, a carrier 605 comprises the respective computer program, wherein the carrier is one of an electronic signal, an optical signal, an electromagnetic signal, a magnetic signal, an electric signal, a radio signal, a microwave signal, or a computer-readable storage medium.

Those skilled in the art will also appreciate that the units described above may refer to a combination of analog and digital circuits, and/or one or more processors configured with software and/or firmware, e.g. stored in the respective network node 600, that when executed by the respective one or more processors such as the processors described above. One or more of these processors, as well as the other digital hardware, may be included in a single Application-Specific Integrated Circuitry (ASIC), or several processors and various digital hardware may be distributed among several separate components, whether individually packaged or assembled into a system-on-a-chip (SoC).

Abbreviation Explanation

MIMO Multiple input multiple output

D-MIMO Distributed MIMO

LQR Linear quadratic regulator

AP Access point

UE User equipment

TDD Time division duplex

PU Processing unit

CSI Channel state information

MRT Maximum ratio transmission

MMSE Minimum mean square error

ZF Zero forcing

QAM Quadrature amplitude modulation

SI NR Signal to interference and noise ratio

With reference to Figure 7, in accordance with an embodiment, a communication system includes a telecommunication network 3210, such as a 3GPP-type cellular network, which comprises an access network 3211, such as a radio access network, and a core network 3214. The access network 3211 comprises a plurality of base stations 3212a, 3212b, 3212c, such as the source and target access node 111, 112, AP STAs NBs, eNBs, gNBs or other types of wireless access points, each defining a corresponding coverage area 3213a, 3213b, 3213c. Each base station 3212a, 3212b, 3212c is connectable to the core network 3214 over a wired or wireless connection 3215. A first user equipment (UE) such as a Non-AP STA 3291 located in coverage area 3213c is configured to wirelessly connect to, or be paged by, the corresponding base station 3212c. A second UE 3292 such as a Non-AP STA in coverage area 3213a is wirelessly connectable to the corresponding base station 3212a. While a plurality of UEs 3291, 3292 are illustrated in this example, the disclosed embodiments are equally applicable to a situation where a sole UE is in the coverage area or where a sole UE is connecting to the corresponding base station 3212.

The telecommunication network 3210 is itself connected to a host computer 3230, which may be embodied in the hardware and/or software of a standalone server, a cloud-implemented server, a distributed server or as processing resources in a server farm. The host computer 3230 may be under the ownership or control of a service provider, or may be operated by the service provider or on behalf of the service provider. The connections 3221 , 3222 between the telecommunication network 3210 and the host computer 3230 may extend directly from the core network 3214 to the host computer 3230 or may go via an optional intermediate network 3220. The intermediate network 3220 may be one of, or a combination of more than one of, a public, private or hosted network; the intermediate network 3220, if any, may be a backbone network or the Internet; in particular, the intermediate network 3220 may comprise two or more subnetworks (not shown).

The communication system of Figure 7 as a whole enables connectivity between one of the connected UEs 3291 , 3292 such as e.g. the UE 121 , and the host computer 3230. The connectivity may be described as an over-the-top (OTT) connection 3250. The host computer 3230 and the connected UEs 3291 , 3292 are configured to communicate data and/or signaling via the OTT connection 3250, using the access network 3211 , the core network 3214, any intermediate network 3220 and possible further infrastructure (not shown) as intermediaries. The OTT connection 3250 may be transparent in the sense that the participating communication devices through which the OTT connection 3250 passes are unaware of routing of uplink and downlink communications. For example, a base station 3212 may not or need not be informed about the past routing of an incoming downlink communication with data originating from a host computer 3230 to be forwarded (e.g., handed over) to a connected UE 3291. Similarly, the base station 3212 need not be aware of the future routing of an outgoing uplink communication originating from the UE 3291 towards the host computer 3230. Example implementations, in accordance with an embodiment, of the UE, base station and host computer discussed in the preceding paragraphs will now be described with reference to Figure 8. In a communication system 3300, a host computer 3310 comprises hardware 3315 including a communication interface 3316 configured to set up and maintain a wired or wireless connection with an interface of a different communication device of the communication system 3300. The host computer 3310 further comprises processing circuitry 3318, which may have storage and/or processing capabilities. In particular, the processing circuitry 3318 may comprise one or more programmable processors, application-specific integrated circuits, field programmable gate arrays or combinations of these (not shown) adapted to execute instructions. The host computer 3310 further comprises software 3311, which is stored in or accessible by the host computer 3310 and executable by the processing circuitry 3318. The software 3311 includes a host application 3312. The host application 3312 may be operable to provide a service to a remote user, such as a UE 3330 connecting via an OTT connection 3350 terminating at the UE 3330 and the host computer 3310. In providing the service to the remote user, the host application 3312 may provide user data which is transmitted using the OTT connection 3350.

The communication system 3300 further includes a base station 3320 provided in a telecommunication system and comprising hardware 3325 enabling it to communicate with the host computer 3310 and with the UE 3330. The hardware 3325 may include a communication interface 3326 for setting up and maintaining a wired or wireless connection with an interface of a different communication device of the communication system 3300, as well as a radio interface 3327 for setting up and maintaining at least a wireless connection 3370 with a UE 3330 located in a coverage area (not shown in Figure 8) served by the base station 3320. The communication interface 3326 may be configured to facilitate a connection 3360 to the host computer 3310. The connection 3360 may be direct or it may pass through a core network (not shown in Figure 8) of the telecommunication system and/or through one or more intermediate networks outside the telecommunication system. In the embodiment shown, the hardware 3325 of the base station 3320 further includes processing circuitry 3328, which may comprise one or more programmable processors, application-specific integrated circuits, field programmable gate arrays or combinations of these (not shown) adapted to execute instructions. The base station 3320 further has software 3321 stored internally or accessible via an external connection.

The communication system 3300 further includes the UE 3330 already referred to. Its hardware 3335 may include a radio interface 3337 configured to set up and maintain a wireless connection 3370 with a base station serving a coverage area in which the UE 3330 is currently located. The hardware 3335 of the UE 3330 further includes processing circuitry 3338, which may comprise one or more programmable processors, applicationspecific integrated circuits, field programmable gate arrays or combinations of these (not shown) adapted to execute instructions. The UE 3330 further comprises software 3331 , which is stored in or accessible by the UE 3330 and executable by the processing circuitry 3338. The software 3331 includes a client application 3332. The client application 3332 may be operable to provide a service to a human or non-human user via the UE 3330, with the support of the host computer 3310. In the host computer 3310, an executing host application 3312 may communicate with the executing client application 3332 via the OTT connection 3350 terminating at the UE 3330 and the host computer 3310. In providing the service to the user, the client application 3332 may receive request data from the host application 3312 and provide user data in response to the request data. The OTT connection 3350 may transfer both the request data and the user data. The client application 3332 may interact with the user to generate the user data that it provides. It is noted that the host computer 3310, base station 3320 and UE 3330 illustrated in Figure 8 may be identical to the host computer 3230, one of the base stations 3212a, 3212b, 3212c and one of the UEs 3291, 3292 of Figure 7, respectively. This is to say, the inner workings of these entities may be as shown in Figure 8 and independently, the surrounding network topology may be that of Figure 7.

In Figure 8, the OTT connection 3350 has been drawn abstractly to illustrate the communication between the host computer 3310 and the use equipment 3330 via the base station 3320, without explicit reference to any intermediary devices and the precise routing of messages via these devices. Network infrastructure may determine the routing, which it may be configured to hide from the UE 3330 or from the service provider operating the host computer 3310, or both. While the OTT connection 3350 is active, the network infrastructure may further take decisions by which it dynamically changes the routing (e.g., on the basis of load balancing consideration or reconfiguration of the network).

The wireless connection 3370 between the UE 3330 and the base station 3320 is in accordance with the teachings of the embodiments described throughout this disclosure. One or more of the various embodiments improve the performance of OTT services provided to the UE 3330 using the OTT connection 3350, in which the wireless connection 3370 forms the last segment. More precisely, the teachings of these embodiments may improve the data rate, latency, power consumption and thereby provide benefits such as reduced user waiting time, relaxed restriction on file size, better responsiveness, extended battery lifetime.

A measurement procedure may be provided for the purpose of monitoring data rate, latency and other factors on which the one or more embodiments improve. There may further be an optional network functionality for reconfiguring the OTT connection 3350 between the host computer 3310 and UE 3330, in response to variations in the measurement results. The measurement procedure and/or the network functionality for reconfiguring the OTT connection 3350 may be implemented in the software 3311 of the host computer 3310 or in the software 3331 of the UE 3330, or both. In embodiments, sensors (not shown) may be deployed in or in association with communication devices through which the OTT connection 3350 passes; the sensors may participate in the measurement procedure by supplying values of the monitored quantities exemplified above, or supplying values of other physical quantities from which software 3311 , 3331 may compute or estimate the monitored quantities. The reconfiguring of the OTT connection 3350 may include message format, retransmission settings, preferred routing etc.; the reconfiguring need not affect the base station 3320, and it may be unknown or imperceptible to the base station 3320. Such procedures and functionalities may be known and practiced in the art. In certain embodiments, measurements may involve proprietary UE signaling facilitating the host computer’s 3310 measurements of throughput, propagation times, latency and the like. The measurements may be implemented in that the software 3311, 3331 causes messages to be transmitted, in particular empty or ‘dummy’ messages, using the OTT connection 3350 while it monitors propagation times, errors etc.

FIGURE 9 is a flowchart illustrating a method implemented in a communication system, in accordance with one embodiment. The communication system includes a host computer, a base station such as a AP STA, and a UE such as a Non-AP STA which may be those described with reference to Figure 7 and Figure 8. For simplicity of the present disclosure, only drawing references to Figure 9 will be included in this section. In a first action 3410 of the method, the host computer provides user data. In an optional subaction 3411 of the first action 3410, the host computer provides the user data by executing a host application. In a second action 3420, the host computer initiates a transmission carrying the user data to the UE. In an optional third action 3430, the base station transmits to the UE the user data which was carried in the transmission that the host computer initiated, in accordance with the teachings of the embodiments described throughout this disclosure. In an optional fourth action 3440, the UE executes a client application associated with the host application executed by the host computer.

FIGURE 10 is a flowchart illustrating a method implemented in a communication system, in accordance with one embodiment. The communication system includes a host computer, a base station such as a AP STA, and a UE such as a Non-AP STA which may be those described with reference to Figure 7 and Figure 8. For simplicity of the present disclosure, only drawing references to Figure 10 will be included in this section. In a first action 3510 of the method, the host computer provides user data. In an optional subaction (not shown) the host computer provides the user data by executing a host application. In a second action 3520, the host computer initiates a transmission carrying the user data to the UE. The transmission may pass via the base station, in accordance with the teachings of the embodiments described throughout this disclosure. In an optional third action 3530, the UE receives the user data carried in the transmission.

FIGURE 11 is a flowchart illustrating a method implemented in a communication system, in accordance with one embodiment. The communication system includes a host computer, a base station such as a AP STA, and a UE such as a Non-AP STA which may be those described with reference to Figure 7 and Figure 8. For simplicity of the present disclosure, only drawing references to Figure 11 will be included in this section. In an optional first action 3610 of the method, the UE receives input data provided by the host computer. Additionally, or alternatively, in an optional second action 3620, the UE provides user data. In an optional subaction 3621 of the second action 3620, the UE provides the user data by executing a client application. In a further optional subaction 3611 of the first action 3610, the UE executes a client application which provides the user data in reaction to the received input data provided by the host computer. In providing the user data, the executed client application may further consider user input received from the user. Regardless of the specific manner in which the user data was provided, the UE initiates, in an optional third subaction 3630, transmission of the user data to the host computer. In a fourth action 3640 of the method, the host computer receives the user data transmitted from the UE, in accordance with the teachings of the embodiments described throughout this disclosure.

FIGURE 12 is a flowchart illustrating a method implemented in a communication system, in accordance with one embodiment. The communication system includes a host computer, a base station such as a AP STA, and a UE such as a Non-AP STA which may be those described with reference to Figures 32 and 33. For simplicity of the present disclosure, only drawing references to Figure 12 will be included in this section. In an optional first action 3710 of the method, in accordance with the teachings of the embodiments described throughout this disclosure, the base station receives user data from the UE. In an optional second action 3720, the base station initiates transmission of the received user data to the host computer. In a third action 3730, the host computer receives the user data carried in the transmission initiated by the base station. When using the word "comprise" or “comprising” it shall be interpreted as nonlimiting, i.e. meaning "consist at least of".

The embodiments herein are not limited to the above described preferred embodiments. Various alternatives, modifications and equivalents may be used.

NUMBERED EMBODIMENTS

1. A method, performed by a Processing Unit, PU, (130), for determining transmission weights for transmission of DownLink, DL, radio signals from a Distributed Multiple Input Multiple Output, D-MIMO, system (101) for wireless communication with a wireless communications device (121), wherein the D-MIMO system (101) comprises the PU, (130), a first radio-head (APi) and a second radio-head (AP2), the method comprising: obtaining (501) first channel state information associated with transmissions between the wireless communications device (121) and the first radio-head (AP1) and second channel state information associated with transmissions between the wireless communications device (121) and the second radio-head (AP2); obtaining (502) an estimation of a variability (o^i-^) in ^a distribution of a difference in phase between DL transmissions from the first radio-head (AP1) and DL transmissions from the second radio-head (AP2); and determining (503) respective first and second transmission weights for transmission of DL radio signals from the first radio-head (AP1) and from the second radio-head (AP2) to the wireless communications device (121) based on the first and second channel state information and further based on the obtained estimation of the variability (o^i-^) in the distribution of the difference in phase.

2. The method according to embodiment 1 , wherein determining the first and second transmission weights is based on a Linear Quadratic Regulator optimization algorithm.

3. The method according to embodiment 2, wherein determining the first and second transmission weights is based on minimizing a linear quadratic cost function comprising: a first quadratic term dependent on an estimation error of received DL signals associated with the obtained first and second channel state information with respect to a transmitted signal, wherein the estimation error is based on the obtained first and second channel state information and the obtained estimation of the variability (^1-^2) in th® distribution of the difference in phase, and a second quadratic term dependent on the transmitted signal, and wherein the transmitted signal is dependent on the first and second transmission weights. The method according to embodiment 3, wherein minimizing the linear quadratic cost function is further based on prioritizing the first quadratic term or the second quadratic term based on multiplying the first quadratic term with a first weighting matrix and/or based on multiplying the second quadratic term with a second weighting matrix. The method according to any of the embodiments 1-4, wherein minimizing the linear quadratic cost function comprises calculating an effective channel based on the obtained first and second channel state information and the obtained estimation of the variability (o^i-^) in the distribution of the difference in phase. The method according to any of the embodiments 1-5, wherein minimizing the linear quadratic cost function comprises calculating a channel covariance matrix based on the obtained estimation of the variability (o^i-^) in the distribution of the difference in phase. The method according to any of the embodiments 1-6, wherein determining the respective first and second transmission weights comprises scaling the transmission weights equally by a constant (p) for antenna elements (11, 12) of the first radio-head (APi) and the second radio-head (AP ₂ ) when a transmission power of an antenna element (11 , 12) of the antenna elements (11, 12) exceeds the maximum power budget of the antenna element (11, 12). The method according to any of the embodiments 1-7, wherein determining the respective first and second transmission weights further comprises adjusting the second weighting matrix to penalize the power of each antenna element (11 , 12) of the first radio-head (APi) and the second radio-head (AP ₂ ) individually before minimizing the linear quadratic cost function. The method according to any of the embodiments 1-8, wherein obtaining the estimation of the variability (o^i-^) in the distribution of the difference in phase is based on obtaining an estimation of noise of measurements performed during phase alignment of the first radio-head (AP _X ) and the second radio-head (AP ₂ ) for the respective radio-head (APi, AP ₂ ). The method according to embodiment 9, wherein obtaining the estimation of the variability (o^i-^) in the distribution of the difference in phase is based on a maximum-likelihood estimation of a phase alignment error between the first radiohead (APi) and the second radio-head (AP ₂ ), and wherein the maximum-likelihood estimation of the phase alignment error is based on the obtained estimation of noise of measurements performed during phase alignment. The method according to any of the embodiments 1-10, wherein obtaining (502) the estimation of the variability in the distribution of the difference in phase between DL transmissions from the first radio-head (APi) and DL transmissions from the second radio-head (AP ₂ ) comprises: obtaining (502a) an estimation of a first variability in a first distribution of a first phase alignment error associated with DL transmissions from the first radiohead (APi) to the wireless communications device (121); and obtaining (502b) an estimation of a second variability in a second distribution of a second phase alignment error associated with DL transmissions from the second radio-head (AP ₂ ) to the wireless communications device (121). A Processing Unit, PU, (130), configured to determine transmission weights for transmission of DownLink, DL, radio signals from a Distributed Multiple Input Multiple Output, D-MIMO, system (101) for wireless communication with a wireless communications device (121), wherein the D-MIMO system (101) comprises the PU, (130), a first radio-head (APi) and a second radio-head (AP ₂ ), the PU (130) being further configured to: obtain first channel state information associated with transmissions between the wireless communications device (121) and the first radio-head (APi) and second channel state information associated with transmissions between the wireless communications device (121) and the second radio-head (AP ₂ ); obtain an estimation of a variability (o^i-^) in ^a distribution of a difference in phase between DL transmissions from the first radio-head (APi) and DL transmissions from the second radio-head (AP ₂ ); and determine respective first and second transmission weights for transmission of DL radio signals from the first radio-head (APi) and from the second radio-head (AP ₂ ) to the wireless communications device (121) based on the first and second channel state information and further based on the obtained estimation of the variability distribution of the difference in phase.

13. The Pll (130) according to embodiment 12, wherein the Pll (130) is configured to determine the first and second transmission weights based on a Linear Quadratic Regulator optimization algorithm.

14. The Pll (130) according to embodiment 13, wherein the Pll (130) is configured to determine the first and second transmission weights by being configured to minimize a linear quadratic cost function comprising: a first quadratic term dependent on an estimation error of received DL signals associated with the obtained first and second channel state information with respect to a transmitted signal, wherein the estimation error is based on the obtained first and second channel state information and the obtained estimation of the variability distribution of the difference in phase, and a second quadratic term dependent on the transmitted signal, and wherein the transmitted signal is dependent on the first and second transmission weights.

15. The Pll (130) according to embodiment 14, wherein the Pll (130) is configured to minimize the linear quadratic cost function further by being configured to prioritize the first quadratic term or the second quadratic term based on multiplying the first quadratic term with a first weighting matrix and/or based on multiplying the second quadratic term with a second weighting matrix.

16. The Pll (130) according to any of the embodiments 12-15, wherein the Pll (130) is configured to minimize the linear quadratic cost function by being configured to calculate an effective channel based on the obtained first and second channel state information and the obtained estimation of the variability (o^i-^) in the distribution of the difference in phase.

17. The Pll (130) according to any of the embodiments 12-16, wherein the Pll (130) is configured minimize the linear quadratic cost function by being configured to calculate a channel covariance matrix based on the obtained estimation of the variability (^1-^2) ' ⁿ the distribution of the difference in phase. 18. The Pll (130) according to any of the embodiments 12-17, wherein the Pll (130) is configured to determine the respective first and second transmission weights by being configured to scale the transmission weights equally by a constant (p) for antenna elements (11 , 12) of the first radio-head (APi) and the second radio-head (AP ₂ ) when a transmission power of an antenna element (11 , 12) of the antenna elements (11 , 12) exceeds the maximum power budget of the antenna element (11 , 12).

19. The Pll (130) according to any of the embodiments 12-18, wherein the Pll (130) is configured to determine the respective first and second transmission weights by being further configured to adjust the second weighting matrix to penalize the power of each antenna element (11 , 12) of the first radio-head (APi) and the second radio-head (AP ₂ ) individually before minimizing the linear quadratic cost function.

20. The Pll (130) according to any of the embodiments 12-19, wherein the Pll (130) is configured to obtain the estimation of the variability (o^i-^) in the distribution of the difference in phase by being configured to obtain an estimation of noise of measurements performed during phase alignment of the first radio-head (APi) and the second radio-head (AP ₂ ) for the respective radio-head (APi, AP ₂ ).

21. The Pll (130) according to embodiment 20, wherein the Pll (130) is configured to obtain the estimation of the variability (o^i-^) in the distribution of the difference in phase based on a maximum-likelihood estimation of a phase alignment error between the first radio-head (APi) and the second radio-head (AP ₂ ), and wherein the maximumlikelihood estimation of the phase alignment error is based on the obtained estimation of noise of measurements performed during phase alignment.

22. The Pll (130) according to any of the embodiments 12-21 , wherein the Pll (130) is configured to obtain the estimation of the variability in the distribution of the difference in phase between DL transmissions from the first radio-head (APi) and DL transmissions from the second radio-head (AP ₂ ) by being configured to: obtain an estimation of a first variability _a f j _rs t distribution of a first phase alignment error associated with DL transmissions from the first radio-head (APi) to the wireless communications device (121); and obtain an estimation of a second variability in a second distribution of a second phase alignment error associated with DL transmissions from the second radio-head (AP ₂ ) to the wireless communications device (121). 23. A network node (600) comprising the Pll (130) according to any of the embodiments 12-22.