AND A

BASE STATION IN A HETEROGENEOUS NETWORK

TECHNICAL FIELD

The present disclosure relates generally to uplink transmission in heterogeneous networks and, more particularly, to uplink transmission in heterogeneous networks with quantized forward relaying with massive multiple-input, multiple output (M IMO) .

BACKGROUND

Compared to Fourth Generation (4G) systems, the Fifth Generation (5G) cellular standard aims to improve the spectral efficiency by 3 to 10 times, and data rates by 50 times to serve the escalating growth of connected devices. Some key enabling technologies to achieve these goals include Heterogeneous Networks (HetNet) with small cell densification and wireless backhaul, Full-Duplex (FD) transmission, and M IMO transmission schemes.

Heterogeneous networks comprise a mixture of macro cells and small cells. Small cells are compact, low-powered cells with limited range as compared to macro cells. Small cell densification refers to the deployment of many small cells in the coverage area of a macro cell to improve coverage and throughput. In one deployment scenario under consideration, the small cells will receive signals from the User Equipment (UEs) and relay the signals to the macro base station over a backhaul channel between the small base station and the macro base station. In this deployment scenario, wireless backhaul networks are much more cost- effective than wired backhaul to connect small and macro cells because there is no need to lay cables between the small cells and the macro cells.

The use of FD transmission in 5G networks can potentially double the spectral efficiency of the network. While self-interference is the main drawback of FD transmission, much progress has been made in self-interference suppression by using different cancellation techniques including passive suppression, as well as analog and digital cancellation. Self-interference can be also cancelled out with massive M IMO using s simple zero forcing (ZF)-based precoder.

The concept of massive M IMO, where the base stations are equipped with a large number of antennas, is receiving heightened research interest. Massive M IMO is an extension of M IMO, wherein a large number of antennas are used at the transmitter and receiver to provide greater throughput and improved spectrum efficiency with the goal of increasing system capacity. M IMO transmission schemes are an essential part of many wireless standards including the Institute of Electrical and Electronics Engineers (IEEE) 802.1 1 family of standards Wireless Fidelity (Wi-Fi) , Worldwide Interoperability for Microwave Access (WiMAX) , and Long Term Evolution Advantage (LTE-A) developed by the Third Generation Partnership Project (3GPP) . Massive M IMO systems simplify cellular transmission through channel hardening and by orthogonalizing different users' transmissions. In release 10 of LTE-A, a new small cell called a relay node is introduced for capacity and coverage enhancement at cell boundaries. This relay node supports dual-hop Decode- Forward (DF) relaying where the small cell receives and transmits in different time slots, and the UE signal is received by the small cell only. Moreover, different UEs transmit on different resource blocks.

The uplink transmission in HetNet can be modelled as a Multiple Access Relay Channel (MARC), see Figure 2, where the two UEs comprise the sources, the small cell comprises the relay (the small base station 300 of Figure 1 ) and the macro cell comprises the destination (the macro base station 200 of Figure 2). For a MARC with a single antenna at each node, the spectral efficiency regions have been derived for different coding schemes including DF relaying and Quantize-Forward (QF) relaying. For multiple antenna transmission, the spectral efficiency and reliability performance have been analyzed for half-duplex Amplify-Forward (AF) and DF relaying schemes. However, QF relaying has not been analyzed extensively.

In QF relaying with multiple antennas, it is challenging to design the optimal covariance matrix for the quantization noise vector. To optimize this matrix, some complex iterative numerical methods have been proposed for half-duplex one way and two way relay channels, and for Cloud Radio Access Networks (C-RANs) in which the direct links between sources and the destination do not exist. SUMMARY

The present disclosure relates to an uplink transmission scheme for HetNets that comprise of two or more UEs, one small cell and a macro cell. The small and macro cell base stations have N and M antennas ( »N»iT), respectively, where K is the number of users. Each UE transmits a data signal to both the small cell and macro cell during a first time period. The small-cell deploys ZF detection to detect and separate the data signals from each UE, quantizes the data signals, and generates a an index (e.g. , quantization index or bin index) for each data signal. In a second time period, the small cell transmits the indices to the macro cell. The macro cell employs ZF detection to detect and separate the uplink transmission from the UEs and small cell. The macro cell receives the data signals from the UEs in a first time period and the corresponding indices from the small cell in the second time period. The macro cell decodes the data signals received in the first time period along with the indices received in the second time period.

One aspect of the disclosure comprises methods implemented by a relay node in a heterogeneous network of relaying signals between a user equipment and a base station. In one embodiment, the relay node receives, in a first time period, a combined signal comprising a plurality of individual data signals transmitted by a plurality of user terminals. The relay node quantizes the data signals to generate a quantization index for each data signal and transmits, in a second time period after the first time period, the quantization indices to a base station over a wireless MIMO channel.

Another aspect of the disclosure comprises a relay node (e.g., small base station) in a heterogeneous network configured to perform the method described in the preceding paragraph.

Another aspect of the disclosure comprises a relay node (e.g., small base station) in a heterogeneous network configured to relay signals between a user equipment and a base station (e.g., macro base station). The relay node comprises an antenna array having a plurality of antennas and a processing circuit operatively connected to the antenna array. The processing circuit is configured to receive, in a first time period, a combined signal comprising a plurality of individual data signals transmitted by a plurality of user terminals; quantize the data signals to generate a quantization index for each data signal; and transmit, in a second time period after the first time period, the quantization indices to a base station over a wireless backhaul channel, said wireless backhaul channel comprising a MIMO channel.

Another aspect of the disclosure comprises a method of receiving signals from a plurality of user terminals implemented by a base station (e.g., macro base station) in a heterogeneous network. The base station receives, in a first time period, a combined signal comprising a plurality of individual data signals transmitted by a plurality of user terminals. The base station also receives, in a second time period after the first time period, indices corresponding to the data signals received in the first time period. The indices are received from a relay node over a MIMO channel. The base station decodes the data signals received in the first time period using the indices received in the second time period.

Another aspect of the disclosure comprises a base station (e.g., macro base station) in a heterogeneous network configured to perform the method described in the preceding paragraph.

Another aspect of the disclosure comprises a base station (e.g., macro base station) in a heterogeneous network configured to receive signals from a plurality of user terminals. In one embodiment, the base station comprises an antenna array comprising a plurality of antennas, a processing circuit operatively connected to the antenna array. The processing circuit is configured to receive, in a first time period, a combined signal comprising a plurality of individual data signals transmitted by a plurality of user terminals; detect and separate the data signals received in the first time period with a linear detector; receive in a second time period after the first time period, indices corresponding to the data signals received in the first time period, said indices being received from a relay node over a MIMO channel; detect the indices received in the second time period with a linear detector; and decode the data signals received in the first time period using the indices received in the second time period. BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 illustrates a heterogeneous communication network supporting quantized forward relaying for uplink transmissions.

Figure 2 is a MARC channel model of a heterogeneous communication network supporting quantized forward relaying for uplink transmissions.

Figure 3 is a block diagram illustrating an uplink transmission scheme in a first embodiment.

Figure 4 is a flow chart illustrating the uplink transmission scheme according to a first embodiment.

Figure 5 is a graph comparing the spectral efficiency regions of QF and DF relaying schemes in one example.

Figure 6 is a graph comparing the spectral efficiency regions of QF and DF relaying schemes in another example.

Figure 7 is a graph comparing optimal quantization at the relay node to maximize the total throughput for massive M I MO and a single antenna use cases.

Figure 8 is a graph showing the geometric regions of the relay node location optimal for QF and DF relaying schemes.

Figure 9 is a graph showing throughput performance for a massive M IMNO backhaul channel using Direct Transmission (DT), QF relaying, DF relaying, and dual-hop DF.

Figure 10 is a block diagram illustrating an uplink transmission scheme in a second embodiment.

Figure 1 1 is a block diagram illustrating an uplink transmission scheme in a third embodiment.

Figure 12 is a block diagram illustrating an uplink transmission scheme in a fourth embodiment.

Figure 13 is an uplink transmission method implemented by a relay node in a heterogeneous communication network according to an embodiment.

Figure 14 is an uplink transmission method implemented by a base station in a heterogeneous communication network according to another embodiment.

Figure 15 is a block diagram illustrating the main functional components of a relay node in a heterogeneous communication network according to another embodiment.

Figure 16 is a block diagram illustrating the main functional components of a base station in a heterogeneous communication network according to another embodiment.

Figure 17 is a block diagram illustrating the main functional components of a base station in a heterogeneous communication network according to one embodiment.

Figure 18 is a block diagram illustrating the processing circuit of a base station in a heterogeneous communication network configured to function as a small base station. Figure 19 is a block diagram illustrating the processing circuit of a base station in a heterogeneous communication network configured to function as a macro base station.

DETAILED DESCRIPTION

Turning now to the drawings, Figure 1 illustrates an exemplary heterogeneous communication network (HetNet) 10 according to one exemplary embodiment of the present disclosure. The HetNet 10 in the present disclosure is described in the context of a 5G network that supports massive M IMO and QF relaying. However, those skilled in the art will appreciate that the invention may be applied in other wireless communication networks using M IMO and QF relaying.

The HetNet 10 comprises one or more macro base stations 200 providing radio coverage in respective macro cells 20 of the HetNet 10. One or more small base stations 300 provide coverage in respective small cells 30. Small base stations 300 are low-powered base stations with limited coverage area compared to macro base stations 200. These small base stations 300 may be distributed throughout the coverage area of a macro cell (i.e. , with the macro cell) to improve coverage and throughput. In the exemplary embodiment shown in Figure 1 , one small cell 30 served by small base station 300 is shown within the macro cell 20. The small base station 300 may comprise a pico base station, femto base station, micro base station, or metro base station. While only one macro cell 20 and one macro base station 200 are shown, it will be appreciated that a typical network 10 would comprise many macro cells 20 and macro base stations 200. Within each micro cell 20, there can be many small cells 300.

The HetNet 10 further comprises a plurality of user terminals 40, which are also known as UEs. The UEs 40 may comprise, for example, cellular telephones, smart phones, laptop computers, notebooks, tablets, Machine-Type Communication (MTC) devices. Machine-to- Machine (M2M) communication devices, or other wireless devices capable of communicating over a wireless communication channel with the macro base station 200 or small base stations 300. While two UEs 40, denoted UE1 and UE2 are shown in Figure 1 , it will be appreciated that the macro cell 20 or small cell 30 may comprise any number of UEs 40.

Figure 2 illustrates a model of HetNet 10 that comprises two user terminals 40 communicating with a macro base station 200 in a macro cell 20 with the help of a small base station 300 in a small cell 30. In this transmission scheme, the small base station 300 functions as a relay node. Each UE 40 (e.g. , UE1 and UE2 of Figure 1 ) has a single antenna while the small base station 300 and macro base station 200 have N and M antennas respectively, where M » N » K , and where K is the number of users. The channel model of HetNet 10 is a MARC where the user terminals 40 comprises the sources(s), the small base station 300 comprises the relay (the small base station 300) and the macro base station 200 comprises the destination. Consider transmission over B blocks (B»1), where a block corresponds to a transmission period. The discrete-time channel model at transmission block j ( y e {1, 2, ..., #} ) is given as follows:

y . =h , . +h . + z .,

Eq. 1 where y _r . is the received signal vector of length N at the relay, (e.g., small base station 300) y _{d j} is the received signal sector of length M or the destination (e.g., micro base station 200), x, . is the transmitted signal from node i ; for i e {1, 2, r] ; and z _r ■ and z _d ■ are independent complex Additive White Gaussian Noise (AWGN) vectors of lengths N and M with zero means and covariance matrices and l _M , respectively.

For i e {1, 2} , h _n is the N *1 channel coefficient vector from UE, 40 to the small base station 300 and h _di . is the M x1 channel coefficient vector from UE, 40 to the macro base station 200. H _dr . is the M ^χ N channel coefficient matrix from the small base station 300 to the macro base station 200. Each element of h _n . is complex Gaussian random variable with zero mean and variance . This variance has a path loss modeled as = , where d _n is the distance between UE, and the small base station 300 , and a is the pathloss exponent. The elements of h _{rfi j} and H _{dr j} follow the same definition. All these elements are independent and change independently in each transmission period or block.

In the following discussion it is assumed that the full channel coefficients are known at the small base station 300, i.e., the small base station 300 knows h _{n j} , while the macro base station 200 knows h _di . and H _dr . . Moreover, it is assumed that the small base station 300 knows via feedback from the macro base station 200 the distances from the UEs 40 to macro base station 200 so that it can optimize its quantization for maximum spectral efficiency.

Since the small base station 300 knows h _n . while the macro base station 200 knows h _{dj j} and , they can perform ZF detection to separate the data streams of different UEs 40. Hence, the small base station 300 multiplies its received signal vector y . by the ZF detection matrix Ar, j and the macro base station 200 multiplies y _dj by the ZF detection matrix

A , where: Then, let A _{r j} = [a _r a _{r2 j} ] ,A _dj = [n _dl a _{d2 j} A _{dr j} ] where a _n is an N 1 vector, a _di is an

M x 1 vector and A _dr is an M χ N matrix. After applying ZF detection in Eq. 2 to Eq. 1 , the received signals are given by:

y y

where y _n . is the data stream received at the small base station 300 from UE, for i e {1, 2} , is the data stream received at the macro base station 200 from UE, for i e {1, 2} , and y _dr . is the

N *1 data stream vector received at the macro base station 200 from the small base station 300. Considering the received signals in Eq. 3, one aspect of the disclosure provides a transmission scheme, examples of which are described below.

Generally, embodiments of the present disclosure employ linear detection (e.g., ZF detection) using channel knowledge to separate the data signals received from the UEs 40 in combination with QF relaying and massive MIMO on the backhaul channel between the small base station 300 and the macro base station 200. Four uplink transmission schemes are described based on the channel model shown in Figure 2. While these schemes vary in complexity, they are all carried over B blocks and based on QF relaying at the small base station 300, and sliding window decoding at the macro base station 200.

First Embodiment - Joint decoding of UE signals

A first embodiment of the transmission scheme is based on ZF detection at small base station 300 and macro base station 200s, QF relaying at the small base station 300, and sliding window decoding at the macro base station 200. In this embodiment, each UE 40 aims to send S-1 messages over B-1 transmission periods or blocks. Table 1 shows the transmission scheme according to Embodiment 1 where in block j , the transmission/decoding at each node is given as follows:

At block j , each UE 40 transmits a new message to the small base station 300 and macro base station 200, i.e., UE1 sends its new message (w _{l j} ) by transmitting its codeword 1/1. Similarly, UE2 sends (w _{2 j} ) by transmitting U2. The signals transmitted by UE1 and UE2 respectively are given by: where P\ and P2 are the transmit powers of UE1 and UE2, respectively. The small base station 300 first deploys ZF detection to separate the data streams from each UE 40 and obtain y _{rl j} and y _{r2 j} as in Eq. 3. Then, the base station 300 quantizes these signals to obtain: , y _r 2,j ⁼ y _r 2,j + ^ζ η,) -> Eq. 5 where ^ is the quantized version of j^ and z _{rl j} is the quantization noise with zero mean and Q1 variance ~ (0,(¾) . Similar definitions hold for y _{r2 j} and z _{r2 j} ~ 0,Q ₂ ) . Then, the small base station 300 finds the quantization indices for y _{rl j} and l _{2 j} for y _r2 ■). Next, the small base station 300 generates an N -dimensional codeword for the quantization indices

U _r (/ ,/ _{2 j} ) and transmits it in block j +1 to the macro base station 200. In block j , the small base station 300 constructs its transmit signal as follows:

j = pUNU _r (lu_ ₁ ,l _2J _ ₁ ), Eq. 6 where P _r is the transmit power of the small base station 300. Note that the transmit power is divided equally among antennas.

Similar to the small base station 300, the macro base station 200 first deploys ZF detection to separate the data streams from each UE 40 and the small base station 300. After ZF detection, the macro base station 200 obtains y _{dl j} , y _{d2 j} and y _{dr j} as in Eq. 3. The macro base station 200 then waits another block such that it receives the small base station 300 signal (y _dr that includes information about UE messages sent in block j . Last, the macro base station 200 utilizes y _{dl j} , y _{d2 j} and y _{dr j+1} in parallel to jointly decode both UEs' messages

f ^{or some} quantization indices using Maximum Likelihood (ML) decoding.

Error analyses for macro base station 200 decoding lead to some constraints on the transmission rates of UE1 (R and UE2 that determine spectral efficiency.

Theorem 1 : For two-UE massive MIMO HetNet with QF relaying and joint decoding at the macro base station 200, the achievable rate region consists of all rate pairs (7¾ satisfying:

i¾≤min{/ ₁₅ / ₂ }, i? ₂ ≤min{/ ₃ ,/ ₄ }, R ₁ +R ₂ ≤I ₅ , Eq.7 where:

P^M-N) P M-N^

I _{1 =} C i ₂ =c ⁽ P

^■ ς,

d +a

P ₂ (M-N) P P ₂ (M-N)

I ₃ =C I ₂ =C ^■ ς, Eq.8

V dl J

P^M-N) P ₂ (M-N) f P _r (M-N) /N) (d ^a N

I _S =C -C -g, g = NC -C c

a V Q:

and where C(x) = log(l + x). The conditions given by Eq.8 were obtained from error analyses at the macro base station 200 to insure reliable decoding.

The proposed transmission scheme can be clarified further with the help of Figures 3 and 4. Figure 3 shows the block diagram for the encoding and decoding process at each node in a transmission block j . At UE1 and UE 2, an encoder 45 encodes the information w _lj and w _2j to generate the coded signals x,(w, .) and x ₂ (w _2j ) respectively. UE1 and UE2 transmit these coded signals to both the macro base station 200 and the small base station 300. The channel from UE1 and UE2 to the small base station 300 are denoted respectively h _rl . and h _r2j . The channel from UE1 and UE2 to the macro base station 200 are denoted respectively h _dXj and h _d2j . The coded signals combine in transit from the UEs 40 to the small base station

300. The combined signal received at the small base station 300 is input to a ZF detector. The received data signals at the small base station 300 after ZF detection are denoted respectively y _rXj and y _r2j . A quantizer at the small base station 300 quantizes the data signals y _rXj and y _r2j to generate the and y _r2 (l _2j )- At block j , the encoder outputs a single codeword x _r i ^,1 ₂ containing quantization indices corresponding to data signals y _rXj _ _x and y _r2j _ _x received at block The codeword x _r (l _Xj - _{x 2j} -i) is transmitted at block j from the small base station 300 to the macro base station 200. The MIMO channel from the small base station 300 to the macro base station 200 is denoted H , . A ZF detector at the macro base station 200 detects the data signals y _dlj and y _d2j for the UEs 40, and the signal y _drj from the small base station 300. The data signals y _dlj and y _d2j , after a one block delay, are decoded along with the signal y _drj from the small base station 300. At time j , the decoder at the macro base station 200 jointly decodes both the UE1 and UE2 messages (w _lj _ ₁ and w _2j _ ₁ ) using the data signals y _dXj _ _x and y _d2j _ _x received at block j-\ along with y _drj containing the quantization indices for the data signals y _rlJ _ _x and y _r2j _ and outputs estimates W _j and w _2j _ _x of the information w _lj _ ₁ and w _2j _ ₁ transmitted by UE1 and UE 2 at block

Figure 4 illustrates the flowchart of the proposed transmission scheme. It is assumed in this example that each UE 40 needs to transmit 5-1 messages and that the transmission is carried out over B transmission blocks or periods. For each transmission block up to block 5-1, each ofUE1 and UE2 transmits a coded signal x,(w, _; ) , where i is an index denoting the

UE 40. In the last transmission block (j = B), the UEs 40 do not transmit, or alternatively, transmit known information. When the first transmission block ( j = 1 ) is transmitted, the small base station 300 does not have any specific quantization indices to send. Hence, it transmits a known signal to the macro base station 200, e.g., / ₁₀ =l ₂₀ =1 . For each subsequent transmission block (j >1), the small base station 300 generates and transmits a codeword x _r (li _j -i _2j -i) containing the quantization indices for the data signals y _rXj _ _x and y _r2j _ _x received in the previous transmission block. The macro base station 200 performs sliding window decoding over two transmission blocks, i.e., the current transmission j and the previous transmission block j-\ to estimate the information w _lj _ _l and w _2j _ ₁ transmitted by UE1 and UE2at block j-l.

For a practical implementation, it is important to specify the optimal quantization at small cell base station 300 for each UE data stream. As the quantization levels increase, the quantizer becomes finer with smaller noises (Q ₁ ,Q ₂ ) at its outputs in Eq.5. Therefore, we derive here the optimal quantization parameters (Q ^* ,Q ₂ ) that maximize the rate region in Eq.7.

The maximum individual and sum rates are obtained by noting that Ι _λ (1 ₃ ) is a decreasing function with Q1 (Q2) while / ₂ (/ ₄ ) is an increasing function and l ₅ is increasing with both Q1 and Q2. Hence, the optimal Q1 and Q2 are those that equalize ^(^and / ₂ (/ ₄ )to maximize i? ₁ (i¾)and Ι _λ +/ ₃ and / _j to maximize R _x + ¾ , which are given as follows:

The maximum individual rate for UE1 (R is achieved by setting the quantization parameters Q ^* and ^* as follows:

The maximum throughput (sum rate) for UE1 and UE2 (R ₁ +R ₂ ) is achieved by setting Q ^* and Q ^* as follows:

{\ + P ₂ {M-N)ld _d ^a ₂ ) ^ -l where C( ) + C(l ₂ ) = c(P _r (M -N)/Nd _d ^a _r ) . With this definition of λ1 and A2, Q'andQ in Eq.

10 are obtained from the intersection of l _x +/ ₃ and / ₅ and deriving / _j With respect to M. Note that the optimal quantization is inversely proportional to the Nth order of the small-to-macro base station 200 signal-to-noise ratio (SNR).

Figures 5 and 6 compare the spectral efficiency regions of the proposed QF scheme with DF scheme, the direct transmission without the small base station 300 and the cut-set bound. In these figures, both UEs transmit at the same power P ₁ = P ₂ while P _r = 5P ₁ . The small- cell has 50 antennas and the macro base station 200 has 500. The inter-node distances in meters are: d _dl =105; d _d2 =110; and d _dr =100 ; while c^and d _r2 are given in each figure. For these distances, the path loss fading is determined by a path loss exponent a = 2.7 . As expected, results show that QF relaying outperforms DF relaying as UEs 40 get further from the small base station 300.

For the same channel settings as in Figure 5, Figure 7 shows the optimal quantization parameters for throughput maximization and compares it with the single antenna case. Results show how massive Ml MO significantly reduces the quantization noise variance and allows very fine quantization.

The first embodiment described above assumes a two UEs scenario. The first embodiment of the transmission scheme can be generalized to K-UEs 40 where K may be greater than two, which is more practical than the two-UE case. Similar to the two-UE case, in block j ( j e {l, 2, ..., B} ), the received signals y . and j _{rf j} , in Eq. 1 , the ZF detection matrices in Eq. 2, and ZF detection outputs in Eq. 3 are respectively given as follows:

- ^h rk,j ^X k,j + Zrj > y _dJ =∑ ,j ^X kJ + ^drJ ^X r,j + ¾, > Eq. 1 1 k=\ k=\ j = (Gi _j G _rJ y G^. , A _d = (G _jGd y G ,

< _rj = [Ku _2j - K _K ], G _d = [h _dl h _dl ... h _dK H _dr ] , Eq. 12

^■ k,j ^{' a} rk,jZ _r ,j > y<ik,j ^{~ X} k ^{+ a} AjZd,. k e {l, 2, ..., K}

where all parameters in Eqs. 1 1 -13 have similar definitions as those in Eqs. 1 -3, respectively.

The transmission scheme remains the same as each UE 40 transmits a new message in each block, the small base station 300 deploys ZF detection, quantizes each UE data stream, and sends a common codeword for all quantization indices in the next block. The macro base station 200 decodes all messages jointly over two consecutive blocks (sliding window decoding).

For K-UE massive MIMO HetNet with QF relaying and joint decoding at the macro base station 200, the rate region (spectral efficiency region) consists of all K-tuples rate vectors (R R∑, RK) satisfying the following:

where,

For all subsets Λ c [l : K] where R _A =∑R, , P _k , d _dk , d _rk , and Q _k are UE _k 's transmit power, distance to macro base station 200, distance to small base station 300 and the quantization noise variance of its data stream at the small base station 300, respectively.

A similar approach is taken to maximum total throughput (sum rate) for the two UE scenario.

The throughput ∑R _k of the Kth UE transmission can be obtained from Eq. 14 as follows: max mini/ , , / "

Q _t ,k£{l,2,...,K } '

where I _k and ς are given in Eq. 8. Similar to the two-UE optimization, I _sl is decreasing with every Q _k while I _s2 is increasing with every Q _k . Therefore, the optimal quantization is obtained from the intersection of I _sl and I _s2 . Table 2 below illustrates a procedure for maximizing throughput of Massive MIMO HetNet with QF relaying at small base station 300:

Table 2 Throughput Maximization For Joint Decoding at MBS

Input: M, N, P _r , P _k , d* , cf _dk , cf _dr , ke{1 ,2, ... , };

Output: Optimal quantization noise varinces at small base station 300 Q _k ^* ;

Definitions:

d ^¾ * ^k d _k ^k - Ndi ,

Step 1 Obti ain A _k as follows

Step 2 Obtain ^* as follows

i e S

Step 3 For any subset S c [l : K] , if λ ^* < 1 where set ^* = 1 and reobtain ^* and

Q _j for e ^ ^c as in steps 1 and 2 where ^ is the complement of S

End

Figures 8 and 9, assume a HetNet that comprises 1) a macro base station 200 of radius R=500 with 500 antennas; 2) a small base station 300 of radius Rs=50 and 50 antennas; and 3) four UEs 40 distributed uniformly inside the small base station 300. Figure 8 illustrates the geometric regions for deploying DF or QF relaying at the small base station 300 in order to maximize throughput of the 4 UEs 40. The QF scheme is preferred when the small base station 300 is close to the macro base station 200 (center) while DF is preferred in the opposite scenario. These results are expected since at a far distance from the macro base station 200, the UE-to-small base station 300 links becomes much stronger than those links to the macro base station 200. Hence, the small base station 300 prefers decoding instead of quantizing the UE messages. Figure 9 shows that the actual throughput of the four UEs 40 for each small base station 300 location on the x-axis from the macro base station 200 center to the edge. The figure shows significant improvement (>50%) of the proposed full-duplex QF and DF schemes over the direct transmission (no small base station 300) and dual-hop LTE-A schemes.

In throughput (sum rate) maximization, all users have the same priority. However, some applications have unequal user priority as different users have different quality-of-service requirements. Hence, to simultaneously satisfy these requirements, it is quite useful to maximize the weighted sum rate.

For the rate region in Lemmal , maximizing the weighted sum rate can be expressed as follows:

s.t. R _k ≤mm {l _k ,J _k ) , R _A ≤J _A ,

For all subsets A c [l : ^] where R _A = R, and μ _/ζ is the weighting factor for the transmission rate of UEk (0≤μ]{≤\ and _Mk = i).

Similar to the two-user sum rate optimization, each I _k is decreasing with Q _k while each J _A is increasing with all Q ^* for k e {\, 2...,K} . Therefore, by equalizing the sum of all I _k with

J _A , the optimal quantization parameters are derived. Table 3 shows a procedure for maximizing the weighted sum rate of massive MIMO HetNet with QF relaying at small base station 300.

Table 3- Throughput Maximization For Separate Decoding At MBS

Input: M, N, P _r , P _k , cf _rk , c/ _dk , cf _dr , and ^and ke{1 ,2,..., },

Output: Optimal quantization noise varinces at small base station 300 Q _k ; and their transmission rates (R _qk ).

Definitions:

P _r (M-N)

δ.

Nd

Step 1 Obtain δ ^* as a solution of = 0 where

Step 2 Obtain ^* as S _k = (a _k S ^* +b _k ) .

Step 3 Obtain ^* as follows

.

(\+p _k (M-N)ld _d ^a _k )(s;-\)

Step 4 For any subset S c [l : K] , if δ ^* < 1 where z e S ,

set ^* = 1 and reobtain δ ^* and Q ^* for y e S ^* as in steps 1 , 2 and 3.

Step 5 Obtain the transmission rate (R _qk ) for the quantization index (I _k )

End

The procedure shown in Table 3 includes individual rate maximization and equal sum rate maximization as special cases. Individual rate: the individual rate of UE, is maximized by setting = 1 and the remaining μ _Ιί = 0 for all k≠ i .

Equal sum rate maximization (throughput) in Algorithm 2: the throughput maximization is obtained by setting μ _/ζ = 1 / K for all k e {\, 2...,K} .

Second embodiment - Separate decoding of UE signals

In the first embodiment, the macro base station 200 needs to simultaneously decode the messages from all UEs 40, which requires very efficient (complex) decoder at the macro base station 200. This joint decoding can be simplified by separate decoding for each UE message. However, in a joint decoding scheme, the small base station 300 sends a common codeword for all quantization indices to the macro base station 200. Therefore, to simplify the macro base station 200 decoding in the second embodiment, the small base station 300 generates a separate codeword for each quantization index and transmits the codewords over different time slots to the macro base station 200. Consequently, after ZF detection, the macro base station 200 can decode each UE message and its corresponding quantization index separately using the signals received from that UE in block ( j ) and small base station 300 in block ( j + 1) during the time slot in which the quantization index of that UE is sent.

The second transmission scheme is similar to the first embodiment, except that the small base station 300 generates separate codewords U _rl and U _r2 for each quantization index and transmits them to the macro base station 200 in separate time slots, and the macro base station 200 separately decodes each UE message.

At block j , each UE 40 in the second embodiment transmits a new message to the small base station 300 and macro base station 200, i.e. UE1 sends its new message ( W _j . ) by transmitting its codeword 1/1. Similarly, UE2 sends ( w ₂ . ) by transmitting U2. The signals transmitted by UE1 and UE2 respectively are given by Eq. 4.

The small base station 300 first deploys ZF detection to separate the data streams from each UE 40 and obtain y _{rl j} and y _{r2 j} as in Eq. 3. Then, the base station 300 quantizes these signals to obtain y _rl and y _r2 given by Eq. 5. Then, the small base station 300 finds the quantization indices (Ι _] for j^ and l _{2 j} for y _{r2 j} ). The small base station 300 generates a separate codeword for each quantization index ( U _{rl j} ) and U _r2 (l _{2 j} ) ) and transmits them in block + l over two time slots of durations ¾ and β ₂ , respectively. Similarly, in block j , the small base station 300 constructs its transmit si nals as follows:

= ^{l n} P ^{nase 1} . ^{and E} q- ^{1 8}

Xr2j ), In phase 2, Eq. 19 where β _ι + β ₂ = 1 , and p _rl + p _r2 = P _r . Note that the small base station 300 also deploys power control as it transmits with powers (p _rl / ¾) in phase 1 and (p _r2 1 β ₂ ) in phase 2.

Similar to the small base station 300, the macro base station 200 first deploys ZF detection to separate the data streams from each UE 40 and the small base station 300. After ZF detection, the macro base station 200 obtains y _dlj ,y _dlj and y _drj as in Eq.3. The macro base station 200 then waits another block such that it receives the small base station 300 signals y _drlj and y _dr2j that include information about UE messages sent in block j . The macro base station 200 performs sliding window decoding as previously described but separately decodes each UE message. More specifically, after ZF detection, the received signal from the small base station 300 in Eq.3 becomes two signals received over two phases as follows:

The macro base station 200 utilizes y _dlj and j _rfrlJ+1 to decode (w, .) and y _d2 and y _{dr2 j+1} to decode (w _{2 ;} ).

To insure reliable decoding, the transmission rates of UE1 (i¾) and UE2 (R ₂ ) need to satisfy the following constraints:

¾ <min{/ ₁ ,J ₂ }, ¾ <min{/ ₃ ,J ₄ }, Eq.21 where I and I ₃ are given in Eq.8 while

where C(x) = log(l + x)

Figure 10 is a block diagram of the encoding and decoding process at each node in a transmission block j according to the second embodiment. At UE1 and UE 2, an encoder encodes the information w _{l j} and w _{2 j} to generate the coded signals x ₁ (w _{l j} ) and x ₂ (w _{2 j} ) respectively. UE1 and UE2 transmit these coded signals to both the macro base station 200 and the small base station 300. The channel from UE1 and UE2 to the small base station 300 are denoted respectively h _rl . and The channel from UE1 and UE2 to the macro base station 200 are denoted respectively and The coded signals combine in transit from the UEs 40 to the small base station 300. The combined signal received at the small base station 300 is input to a ZF detector. The received data signals at the small base station 300 after ZF detection are denoted respectively y _{rl j} and y _{r2 j} . A quantizer at the small base station 300 quantizes the data signals y _{rl j} and y _{r2 j} to obtain y _r i {h _j ) ^and y _r i { _j ) - ^At block j , the encoder generates separate codewords x^i^ _j ^) and ^ ( ₂ -i ) _> ^eacn containing a quantization index for a respective one of the data signals y _{rl j} _ _x and y _{r2 j} _ _x received at block

The codewords are transmitted at block j from the small base station 300 to the macro base station 200 in different phases, i.e., time slots of transmission period j . The MIMO channel from the small base station 300 to the macro base station 200 is denoted H _{dr j} . A ZF detector at the macro base station 200 detects the signals y _{dl j} and y _{d2 j} from the UEs 40, and the signals y _{drl j} and y _{dr2 j} from the small base station 300, which are received in different phases. The UE signals y _{drl j} and y _{dr2 j} , after a one block delay, are input to a decoder along with the signals y _{drl j} _ _x and y _{d2 j} _ ₁ from the small base station 300. At time j , the decoder at the macro base station 200 separately decodes each UE message using the data signals y _{dl j} _ ₁ and y _{d2 j} _ received during block j - \ from the UEs 40, and the signals y _{drl j} and y _{dr2 j} received from the small base station 300 during block j . More particularly, the message w _{l j} _ ₁ from UE1 is separately decoded using y^ -^ for some quantization index Hence, the decoder estimates ν _{λ ]} _ _λ of the information w _{l j} _ ₁ transmitted respectively by UE1 during block Similarly, decoding holds for the message w _{2 j} _ ₁ from UE2.

The transmission scheme according to the second embodiment employing separate decoding at the macro base station 200 can be generalized to any number of UEs 40. As in the joint decoding scheme (Embodiment 1), it is straightforward to generalize the separate decoding scheme into K UE transmissions. The small base station 300 generates a separate codeword for each quantization index and transmits the K codewords of all indices to the macro base station 200 over K phases (time slots) of durations β ₁ , β ₂ ..., and β _κ . For K-UE massive MIMO HetNet with QF relaying and separate decoding at the macro base station 200, the rate region (spectral efficiency region) consists of all K-tuples rate vectors (R _x , .&, ,...¾ ) satisfying the following:

¾ < min {l _k , T _k } , Eq. 23 where I _k is given in Eq. 8 while

for all sets of power allocations ( p _rk ) and phase durations ( _k ).

To maximize the weighted sum rate subject to the constraints in Eq. 22, we need to find each optimal quantization noise variances Q ^* , phase duration β ^* and power allocation p _r ^* _k .

First, similar to the transmission scheme of the first embodiment (joint decoding), Q ^* is obtained from the intersection of I _k and T _k . Second, since separate decoding (if possible) can do at most the same as joint decoding, the optimal phase durations and power allocations are those that equalize the weighted sum rate of scheme 2 to that of Embodiment 1 . Therefore, these optimal parameters are obtained as in the procedure shown in Table 5:

With the optimal parameters in Table 5, the transmission scheme with separate decoding and time division achieves the same performance as the joint decoding in the first embodiment.

Third Embodiment - Sequential Decoding with Wyner-Ziv Binning

The transmission scheme (separate decoding) of Embodiment 2 simplifies the first transmission scheme (of the first embodiment) by allowing separate decoding for each UE message and its quantization index. However, each message and the quantization index are decoded simultaneously by the macro base station 200. Another aspect of the disclosure comprises a third transmission using Wyner-Ziv binning at the small base station 300 to allow sequential decoding for each quantization index and UE's message. Wyner-Ziv binning involves coding, compression and quantization of the signal.

In the third transmission scheme, the operation of the UEs 40 is the same as previously described. At block j , each UE 40 in the third embodiment transmits a new message to the small base station 300 and macro base station 200, i.e., UE1 sends its new message ( W _j . ) by transmitting its codeword 1/1. Similarly, UE2 sends (w _{2 j} ) by transmitting U2. The signals transmitted by UE1 and UE2 respectively are given by Eq. 4.

The small base station 300 first deploys ZF detection to separate the data streams from each UE 40 and obtain y _rl and y _r2 as in Eq. 3. Then, the small base station 300 quantizes these signals to obtain and y _r2 (/ _{2 j} ) given by Eq. 5. Then, the small base station 300 finds the quantization indices (Ι _] for j^ and l _{2 j} for y _{r2 j} ). After generating the quantization indices, the small base station 300 performs Wyner-Ziv binning to map the quantization indices / _j . and l _{2 j} to corresponding bin indices b _x and b ₂ . For each data signal, the small base station

300 partitions the quantization indices into a plurality of equal size bins and maps the quantization index for the data signal to a corresponding bin. The small base station 300 then generates a common codeword U _r for both bin indices and b ₂ and transmits the codeword

U _r to the macro base station 200 in block j + \ . Similarly, in block j , the small base station

300 constructs its transmit signals as previously described except that the codeword U _r conveys the bin indices and b ₂ instead of the quantization indices.

The macro base station 200 performs sliding window decoding to sequentially decode the bin indices, quantization indices and then UEs' messages. More specifically, after ZF detection, the macro base station 200 decodes in the following sequence. The macro base station 200 first deploys ZF detection to separate the data streams from each UE 40 and the small base station 300. After ZF detection, the macro base station 200 obtains y _dl , y _{d2 j} and d _{r j} as in Eq. 3. The macro base station 200 then waits another block such that it receives the small base station 300 signal y _{dr j+1} that includes information about UE messages sent in block j . Decoding is performed as follows:

• The macro base station 200 simultaneously (jointly) decodes all binning indices by

utilizing the received signal from the small base station 300 in block j + \ .

• The macro base station 200 separately decodes the quantization index for each UE (e.g., UE1) data stream using y _{rl j} and y _{dl j} given that the quantization index falls in the bin index decoded in block j + \ .

• The macro base station 200 decodes each UE (e.g., UE1) message using y _{dl j} .

Figure 1 1 is a block diagram describing the encoding and decoding process at each node in a transmission block j for the third embodiment. At UE1 and UE 2, an encoder encodes the information w ₁ . and w _{2 j} to generate the coded signals x ₁ (w ₁ .) and x ₂ (w _{2 j} ) respectively. UE1 and UE2 transmits these coded signals to both the macro base station 200 and the small base station 300. The channel from UE1 and UE2 to the small base station 300 are denoted respectively h _rl . and h _{r2 j} . The channel from UE1 and UE2 to the macro base station 200 are denoted respectively h _{dl j} and h _d2 . . The coded signals combine in transit from the UEs 40 to the small base station 300. The combined signal received at the small base station 300 is input to a ZF detector. The received data signals at the small base station 300 after ZF detection are denoted respectively y _rl and y _{r2 j} . A quantizer at the small base station

300 quantizes the data signals y _{rl j} and y _{r2 j} to obtain and y _r (l _{2 }} ) . In this embodiment, the small base station 300 performs Wyner-Ziv binning to map each quantization index to a corresponding bin index b _tj More particularly, quantization index y^^ _j ) is mapped to bin index b _Xj and quantization index y _r2 (/ _2j ) is mapped to bin indexZ> _2j . At block j , the encoder outputs a single codeword x _r (b _Xj _ _x ,b _2j _ _x ) containing the bin indices corresponding to data signals y _rlj _ _x and y _r2j _ _x received at block j-l. The codeword x _r (b _Xj ^,b _2j _ _x ) ^is transmitted at block j form the small base station 300 to the macro base station 200. The MIMO channel from the small base station 300 to the macro base station 200 is denoted H , .

A ZF detector at the macro base station 200 detects the signals y _dl and y _d2 from the UEs 40, and the signal y _drj from the small base station 300. The received data signals y _dXj and y _d2j , after a one block delay, are sequentially decoded. The macro base station 200 decodes received signal y _drj from the small cell to obtain the bin indices b _Xj _ _x and b _2j _ _x . The bin indices b _Xj _ _x and b _2j _ _x are input to respective decoders. At time j , the decoder at the macro base station 200 utilizes the codeword y _{rX X} {l _Xj ^ and the signal y _dXj _ _x to separately decode (obtain estimates) the quantization index l _Xj _ _x that falls within the bin index b _Xj _ _x . Similarly, the codeword y (l ^{and tne} signal y _d2j _ _x are used to decode l _2j _ _x that falls within the bin index b _2j _ _x , respectively. Given l _2j _ _x and y {h _j - _\ ) · ^tne decoder then utilizes the data signal y _dlj _ _x received at block j-l to decode (obtain an estimate of) w _Xj _ _x of the information w _Xj _ _x transmitted by UE1 in block j-l. Similar decoding holds for UE2 message w _2j _ _x . Note that for each user message, the macro cell sequentially decodes its corresponding bin index, quantization index and then the message of that UE.

Error analyses for the decoding rules at the macro base station 200 lead to some rate constraints that determine the spectral efficiency region. For massive MIMO HetNet, the achievable rate region of QF relaying with Wyner-Ziv binning and sequential decoding consists of all K-tuples rate vectors (R R ₂ , RK) satisfying

P _r (M-N)

R _k ≤I _k , s.t. ∑L _k ≤Nlog 1 + Eq.25

d ^a

for all ke{1,2,...,K} where I _k is given in Eq.8 while

The rate constraints (I _k ) ensure the reliable decoding of UEs' messages while the subjective constraint insures reliable decoding of the binning and quantization indices. It is straightforward to obtain the optimal quantization noise variances ( Q _K ^* ) by noting

K

that when the subjective constraint hold with equality, it is equivalent to∑I _k = J _A , A≡[\ : K],

k=l

which are given in Embodiment 1. Hence, the optimal Q ^* and R _≠ ^* are derived according to the procedure shown in table 3, while the optimal bin index transmission rate R ^* _K is equal to Z ^* at Q; .

Fourth Embodiment - Sequential Decoding with Wyner-Ziv Binning, Time Division and Power Control

This aspect of the disclosure combines the sequential coding scheme of embodiment 2 with Wyner-Ziv binning, time division and power control. Embodiment 3 allows sequential decoding for the quantization indices and UE messages. However, all binning indices are decoded simultaneously. To allow sequential decoding for the binning indices as well, time division may be deployed for the transmission from the small base station 300 to macro base station 200.

In the transmission scheme according to the fourth embodiment, the operation of the UEs 40 is the same as previously described. At block j , each UE 40 in the second embodiment transmits a new message to the small base station 300 and macro base station 200, i.e., UE1 sends its new message ( w _{1 ;} ) by transmitting its codeword 1/1. Similarly, UE2 sends (w _{2 j} ) by transmitting U2. The signals transmitted by UE1 and UE2 respectively are given by Eq. 4.

The small base station 300 first deploys ZF detection to separate the data streams from each UE 40 and obtain y _rl . and y _{r2 j} as in Eq. 3. Then, the small base station 300 quantizes these signals to obtain and y _r2 (/ _{2 j} ) given by Eq. 5. Then, the small base station 300 finds the quantization indices (Ι _] for ^ and l ₂ for y _{r2 j} ). After generating the quantization indices, the small base station 300 performs Wyner-Ziv binning to map the quantization indices l _{X j} and l _{2 j} to corresponding bin indices b _x and Z> ₂ . For each data signal, the small base station 300 partitions the quantization indices into a plurality of equal size bins and maps the quantization index for the data signal to a corresponding bin. In contrast to the third

embodiment, the small base station 300 generates separate codewords and

(# ₂ .^) for the binning indices and transmits them in block y + l over K time slots of durations β ₁ ,β ₂ , β ₃ ... and β _κ as in Embodiment 2.

The macro base station 200 performs sliding window decoding similar to Embodiment 3, except that in block j + the macro base station 200 utilizes the small base station 300 received signal in each time slot (phase) to separately decode the binning index sent in that slot instead of jointly decoding all binning indices as in Embodiment 3. Then, the decoding of quantization indices and messages from that UEs 40 is identical to Embodiment 3.

Figure 12 is a block diagram describing the encoding and decoding process at each node in a transmission block j for the fourth embodiment. At UE1 and UE 2, an encoder 45 encodes the information w ₁ . and w _{2 j} to generate the coded signals x ₁ (w ₁ .) and x ₂ (w _{2 j} ) respectively. UE1 and UE2 transmit these coded signals to both the macro base station 200 and the small base station 300. The channel from UE1 and UE2 to the small base station 300 are denoted respectively h _rl . and h _r2 . . The channel from UE1 and UE2 to the macro base station 200 are denoted respectively h _{dl J} and h _d2 . . The coded signals combine in transit from the UEs 40 to the small base station 300. The combined signal received at the small base station 300 is input to a ZF detector. The received data signals at the small base station 300 after ZF detection are denoted respectively y _{rX j} and y _r2 . A quantizer at the small base station 300 quantizes the data signals y _{rX j} and y _{r2 j} to obtain ^ _i ( ) ^and _y )■ ^{l n tnis} embodiment, the small base station 300 performs Wyner-Ziv binning to map each quantization index to a corresponding bin index b _{t j} More particularly, quantization index y^ ^ _j ) is mapped to bin index b _{X j} and quantization index y _rl l _{2 j} ) is mapped to bin index b _{2 j} . At block j , the encoder generates separate codewords , ^eacn containing a bin index for a respective one of the data signals y _{rX j} _ _x and y _{r2 j} _ _x received at block j - \ . The codewords are transmitted at block j from the small base station 300 to the macro base station 200 in different phases, i.e., time slots of transmission period j . The MIMO channel from the small base station 300 to the macro base station 200 is denoted H _dr . . A ZF detector at the macro base station 200 detects the signals y _dx . and y _d2 . from the

UEs 40, and the signal y _{dr j} from the small base station 300. The received data signals y _{dX j} and y _{d2 j} , after a one block delay, are input to respective decoders. The macro base station 200 separately decodes the received codewords y _{dX j} and y _{d2 j} to obtain the bin indices b _{X j} _ _x and b _{2 j} _ _x . The bin indices b _{X j} _ _x and b _{2 j} _ _x are input to respective decoders. At time j , the decoder at the macro base station 200 separately decodes the bin indices b _{X j} _ _x and b _{2 j} _ _x to obtain estimates of the corresponding quantization indices l _{X j} _ _x and l ₂ _ _x . The decoder then sequentially decodes the data signals y _{rX j} _ _x and y _{r2 j} _ _x received at block j - \ along with their respective quantization indices ί _{γ γ} and ί _{2 γ} to obtain estimates and w ₂ of the information w _{l j} _ _l and w _{2 j} _ ₁ transmitted by UE1 and UE 2 at block j -l .

Error analyses for the decoding rules at the macro base station 200 lead to some rate constraints that determine the spectral efficiency region. For massive MIMO HetNet, the achievable rate region of QF relaying with Wyner-Ziv binning time division, power control and sequential decoding consists of all K-tuples rate vectors (R R ₂ , ...,RK) satisfying for following:

P _rk (M - N)

≤I _k , s.t. L, <N , \og 1 - Eq. 27 for all ke{1 ,2, ... ,K} where I _k , is given in Eq. 8, and L _k , β _Ιί and p _rk are the same as

Embodiment 3. As noted above, the rate constraint (I _k ) ensures the reliable decoding of UE _k 's message while the subjective constraints insure reliable decoding of the binning and quantization indices.

For Embodiment 4, the optimal quantization noise variances ( (¾ ), phase durations and power allocations are identical to the transmission scheme of Embodiment 2 since when the subjective constraints hold with equality, they are equivalent to having I _k = T _k in Eq. 23 for the transmission scheme of Embodiment 3. Moreover, the optimal transmission rates for quantization indices ( R^ ) and binning indices ( R _B ^* _K ) are identical to scheme 3 since they are dependent on

The performance of a transmission scheme can be measured by its spectral efficiency, decoding delay and computational complexity. The spectral efficiencies for the four transmission schemes described above are the same. The decoding delay is the same for all schemes as they all perform sliding window decoding over two blocks. However, the complexity is different between the four transmission schemes.

The complexity of each scheme is determined by the set of codewords required in each scheme and the computational complexity at the decoder. As the encoding at UEs is the same for all schemes, we only focus on the codebook size and the decoding complexity at the macro base station 200.

The number of codewords generated for UE messages are the same in all four schemes. However, the codewords for the quantization and binning indices are different as shown in Table 6, where scheme 4 requires the lowest number of codewords. · Embodiment 1 generates 2 ⁴⁼¹ codewords ( x ■) to represent all sets of quantization indices. κ

Embodiment 2 generates ^2 ^nR≠ codewords (x _rlj ,x _r2j ,... , and x _rKj ) to represent all k=l

quantization indices individually.

Embodiment 3, generates 2 ⁴⁼¹ codewords (x _r ) to represent all sets of binning

indices.

K

· Embodiment 4 generates ^2" ^¾ codewords (x _rlj ,x _r2j ,... , and x _rKj ) to represent all k=l

binning indices individually.

As all schemes achieve the same spectral efficiency, scheme 1 is not preferred since joint decoding is more complex and requires more calculations than separate or sequential decoding. Considering ML decoding, each scheme estimates the transmitted messages by calculating different number of likelihoods. Table 7 shows these numbers where scheme 4 requires the fewest computations. In Embodiment 1 , the macro base station 200 jointly (simultaneously) decodes all UE messages and all quantization indices (but not necessary correctly) by calculating n∑R _t +R _≠

2 ⁴⁼¹ likelihoods.

In Embodiment 2, the macro base station 200 simultaneously decodes each UE

message and its corresponding quantization index (not necessary correctly) but separately from other pairs. Hence, the number of likelihoods calculated are: k=l

In Embodiment 3, the macro base station 200 successively decodes the binning indices, each quantization index and each UE message as in the following sequence:

• First: the macro base station 200 simultaneously (jointly) decodes all binning indices (correctly) by calculating 2 ⁴⁼¹ likelihoods.

• Second: given that each quantization index falls in the decoded binning index, the macro base station 200 separately decodes the quantization indices by calculating ^ 2" ^i¾~%) likelihoods.

• Third: after decoding the quantization indices, the macro base station 200

K

separately decodes all UE messages by calculating ^ 2" ^¾ likelihoods.

k=l

• Table 7 shows the sum of the three steps.

In Embodiment 4, The macro base station 200 successively decodes each binning

index, each quantization index and each UE message as in the following sequence:

• First: the macro base station 200 separately decodes all binning indices

K

(correctly) by calculating ^ 2" ^¾4 likelihoods.

k=l

• Second and third steps are similar to Scheme 3.

• Table 7 shows the sum of the three steps.

Table 7: Number of likelihoods required to estimate the transmitted messages

Definitions: 1) n : codeword length, 2) R _k : transmission rate of LIE* message, 3) R _qk : transmission rate of the quantization index l _k , 4) R _bk : transmission rate of the binning index b _k ,

5) 0 < R _M ≤R ,

Scheme Number of likelihoods

K

Embodiment 1

2 ^{k=l K} l \

Embodiment 2 k=l

K

Embodiment 3

2 + ^ 2 ^{n qk bk} > +∑ 2 ^nRk

k=l k=l

K K K

Embodiment 4

^ 2 ^W¾ + ^ 2 ^niRqk~Rh ^ + ^ 2 ^nRk

k=l k=l k=l

The results from Tables 6 and 7 show that the transmission scheme of Embodiment 4 achieves the same spectral efficiency of the other schemes and 2) has lowest complexity by requiring the smallest codebook size and lowest calculations at the macro base station 200. Furthermore, although scheme 4 (compared to scheme 1) requires Wyner-Ziv binning and transmission over multiple time slots from the small base station 300, the optimal binning rate, phase durations and power allocation are simply obtained as functions of the optimal quantization derived in scheme 1 .

Figure 13 illustrates an exemplary method 400 of relaying signals implemented by a small base station 300 functioning as a relay node in a heterogeneous communication network. The small base station 300 receives, in a first time period, a combined signal comprising a plurality of individual data signals transmitted by a plurality of UEs 40 (block 410). The data signals may be received, for example, over a physical uplink shared channel (PUSCH). In some embodiments, the combined signal is received by an antenna array having multiple antennas configured for massive MIMO. In one embodiment, the linear detector comprises a zero forcing detector. Once the data signals are separated, the small base station 300 quantizes the data signals to generate a quantization index for each data signal (block 420). The small base station 300 then transmits the quantization indices to a macro base station over a wireless MIMO channel in a second time period after the first time period (block 430). In some embodiments, transmitting the quantization indices comprises transmitting bin indices or other information from which the quantization indices can be derived. In one embodiment, the wireless MIMO channel comprises a massive MIMO wireless channel where the number of antennas is greater than the number of data signals received from the UEs 40.

In some embodiments, the macro base station 200 detects and separates the data signal in the combined signal with a linear detector. In one embodiment, the linear detector comprises a zero forcing detector. In some embodiments of the method, quantizing the data signals to generate the quantization index for each data signal comprises optimizing quantization parameters to maximize throughput for a selected one of the data signals. In other embodiments, quantizing the data signals to generate the quantization index for each data signal comprises optimizing quantization parameters to maximum the sum rate or It involves coding, compression and quantization of the the signalsum rate for a group of the data signals.

In some embodiments of the method 400, the small base station 300 transmits, over the wireless backhaul channel, the quantization indices for all data signals in a common codeword. In this embodiment, the the macro base station 200 jointly decodes all UE's messages for some quantization indices. In other embodiments, the small base station 300 transmits the quantization indices for different data signals in separate codewords. In one embodiment, the separate codewords are transmitted in separate time slots in the second time period. In this embodiment, the macro base station 200 separately decodes the message received from each UE 40 for some quantization index that corresponds the signal received at the small base station 300 from that UE 40.

In some embodiments of the disclosure, the small base station 300 maps the quantization indices for the data signals to corresponding bin indices and transmits the bin indices to the macro base station 200. For each data signal, the small base station 300 partitions the quantization indices into a plurality of equal size bins and maps the quantization index for the data signal to one of the bins. The small base station 300 then transmits the bin indices for the corresponding bins to the macro base station 200. In one embodiment, the bin indices are transmitted over the wireless backhaul channel in a single codeword. In other embodiments, the bin indices are transmitted over the wireless backhaul channel in separate codewords. In one embodiment, the separate codewords are transmitted in different time slots over the second time period. Figure 14 illustrates an exemplary method 450 of receiving signals from a plurality of UEs 40. The method 450 is implemented by a macro base station 200 in a heterogeneous network 10. The macro base station 200 receives, in a first time period, a combined signal comprising a plurality of individual data signals transmitted by a plurality of UEs 40 (block 460). The data signals may be received, for example, over a wireless uplink channel, such as the PUSCH. The macro base station 200 also receives, in a second time period after the first time period, quantization indices corresponding to the data signals received in the first time period from a relay node (block 470). The quantization indices are received from a relay node (e.g., small base station 300) over a wireless MIMO channel. In one embodiment, the wireless MIMO channel comprises a massive MIMO channel where the number of antennas is greater than the number of data signals received from UEs 40. After receiving the quantization indices, the base station 200 decodes the UE messages using the data signals received in the first time period along with the indices received in the second time period (block 480).

In some embodiments, the macro base station 200 detects and separates the data signals received in the first time period with a linear detector. In one embodiment, the linear detector comprises a zero forcing detector. In some embodiments of the method 450, the quantization indices are received over the wireless MIMO channel in a common codeword. In this case, the macro base station 200 jointly decodes the data signals for all UEs 40 using the quantization indices received from the relay node. In other embodiments, the indices are received over the wireless MIMO channel from the relay node in separate codewords. The separate codewords may be transmitted in separate time slots in the second time period. In this case, the macro base station 200 separately decodes each user message using its data signal along with its respective index.

In some embodiments, the macro base station 200 detects and separates the separate codewords with a linear detector. In one embodiment, the linear detector comprises a zero forcing detector.

In some embodiments, the quantization indices are mapped by the relay node to corresponding bin indices and the bin indices are transmitted to the macro base station 200. In some embodiments, the macro base station 200 receives a common codeword containing bin indices for all data signals. In this case, the macro base station 200 jointly decodes the bin indices received in the second time period to obtain a set of quantization indices. Each quantization index corresponds to a respective data signal. The macro base station separately decodes each data signal along with its respective index.

In some embodiments, the macro base station 200 detects and separates the common codeword with a linear detector. In one embodiment, the linear detector comprises a zero forcing detector.

In other embodiments, the macro base station 200 receives, from the relay node, a plurality of separate codewords, each containing a bin index for one of the data signals. The separate codewords may be received in different time slots in the second time period. In this case, the macro base station 200 separately decodes the bin indices received in the second time period. Then, given each bin index, the macro base station 200 obtains the quantization index that belongs to the bin index and corresponds to a respective data signal. Last, given each quantization index, the macro base station 200 decodes each user message using its data signal. Therefore, the macro base station separately decodes each user message by sequentially decoding its corresponding bin index, quantization index and then the user message.

In some embodiments, the macro base station 200 detects and separates the codewords with a linear detector. In one embodiment, the linear detector comprises a zero forcing detector.

Figure 15 illustrates a small base station 300 in accordance with one or more embodiments. The small base station 300 comprises an antenna array 310 having multiple antennas 315, a receiving module 320 for receiving the data signals from the UEs 40, a quantization module 330 for quantizing or binning the received data signals as herein described, and a transmitting module 340 for transmitting the quantized or binned signals to the macro base station 200. The various modules 320, 330, and 340 can be implemented by hardware and/or by software code that is executed by a processor or processing circuit. The antenna array 310 is configured for massive MIMO transmission and reception. The receiving module 310 comprises the hardware and/or software for receiving the data signals from the UEs 40 over a wireless uplink channel, such as the Physical Shared Uplink Channel (PUSCH). In one embodiment, the data signals are received and separated by a linear detector, such as a ZF detector. The quantization module 330 quantizes the data signals as herein described to generate the indices corresponding to the data signals from UE's 40. The indices may comprise a quantization index or bin index for each data signal. The transmitting module 340 transmits the indices to the macro base station 200 over the wireless backhaul channel. In some embodiments, the transmitting module 340 transmits the indices for two or more (or all) of the data signals in a single codeword during a second time period. In other embodiments, the transmitting module 350 transmits the indices for different data signals in separate codewords. In this case, the separate codewords may be transmitted in different time slots in the second time period.

Figure 16 illustrates a macro base station 200 in accordance with one or more embodiments. As shown in Figure 16, the macro base station 200 comprises an antenna array 210 having multiple antennas 215, a first receiving module 220 for receiving the data signals from the UEs 40, a second receiving module 230 for receiving the data signals from the small base station 300, and a decoding module 240 for decoding the data signals from the UEs 40 using the indices from the small base station received in a second time period after the first time period. The various modules 220, 230 and 240 can be implemented by hardware and/or by software code that is executed by a processor or processing circuit. The antenna array 210 is configured for massive MIMO transmission and reception. The receiving module 210 comprises the hardware and/or software for receiving the data signals from the UEs 40 over a wireless uplink channel, such as the PUSCH, between the UEs 40 and the macro base station 200. In one embodiment, the data signals are received and separated with a linear detector such as a zero forcing detector. The second receiving module 240 includes the hardware and/or software for receiving the quantization indices from the small base station 300 over the wireless MIMO channel between the small base station 300 and the macro base station 200. Receiving modules 220 and 230 may share hardware and software components. In one embodiment, the quantization indices are received by a linear detector such as a ZF detector. The decoding module 240 comprises the hardware and/or software for decoding the data signals from the UEs 40 along with the indices from the small base station 300 as herein described.

Figure 17 illustrates a base station 500 according to one embodiment that may be configured to function as a macro base station 200 or small base station 300 as herein described. The base station 500 comprises an antenna array 510 having multiple antenna elements or subarrays 515, an interface circuit 520, processing circuit 530, and memory 590.

The antenna array 510 is configured for massive MIMO transmission and reception. The interface circuit 520 is coupled to the antenna array 510 and comprises the radio frequency (RF) circuitry needed for transmitting and receiving signals over a wireless communication channel.

The processing circuit 530 processes the signals transmitted to or received by the macro base station 500. Such processing includes coding and modulation of transmitted data signals, and the demodulation and decoding of received data signals. The processing circuit 530 may comprise one or more microprocessors, hardware, firmware, or a combination thereof. The base station 500 is configured to use massive MIMO for data transmission and/or reception over a wireless backhaul channel, and zero forcing detection to detect signals from the UEs 40.

Memory 590 comprises both volatile and non-volatile memory for storing computer program code and data needed by the processing circuit 530 for operation. Memory 590 may comprise any tangible, non-transitory computer-readable storage medium for storing data including electronic, magnetic, optical, electromagnetic, or semiconductor data storage.

Memory 590 stores a computer program 595 comprising executable instructions that configure the processing circuit 530 to implement methods 400 or 450 according to Figures 13 or 14 as described herein. In general, computer program instructions and configuration information are stored in a non-volatile memory, such as a read only memory (ROM), erasable programmable read only memory (EPROM) or flash memory. Temporary data generated during operation may be stored in a volatile memory, such as a random access memory (RAM). In some

embodiments, computer program 595 for configuring the processing circuit 530 as herein described may be stored in a removable memory, such as a portable compact disc, portable digital video disc, or other removable media. The computer program 595 may also be embodied in a carrier such as an electronic signal, optical signal, radio signal, or computer readable storage medium.

Figure 18 shows a processing circuit 530 for a base station 500 configured to function as a small base station 300. The processing circuit 530 includes a receiving unit 535 for receiving the data signals form the UEs 40, a quantization unit 540 for quantizing or binning the received data signals as herein described, and a transmitting unit 545 for transmitting the quantized or binned signals to the macro base station 200. In one embodiment, the receiving unit 535, quantizing unit 540 and transmitting unit 545 are implemented by a single microprocessor. In other embodiments, the receiving unit 535, quantizing unit 540 and transmitting unit 545 are implemented using different microprocessors.

The receiving unit 535 is configured to receive the data signals from the UEs 40 over a wireless uplink channel, such as the Physical Shared Uplink Channel (PUSCH). In one embodiment, the data signals are received by a linear detector such as a ZF detector. The quantization unit 540 quantizes the data signals as herein described to generate quantization indices. The transmitting unit 545 transmits the indices to the macro base station 200 over the wireless backhaul channel. In some embodiments, the transmitting unit 545 transmits the indices for two or more (or all) of the data signals in a single codeword. In other embodiments, the transmitting unit 545 transmits the indices for different data signals in separate codewords.

Figure 19 shows a processing circuit 530 for a base station 500 configured to function as a macro base station 200. The processing circuit 530 includes a first receiving unit 550 for receiving the data signals form the UEs 40, a second receiving unit 555 for receiving quantization indices over a wireless backhaul channel from a small base station 300, and a decoding unit 560 for decoding the data signals a received from the UEs 40 using the quantization indices received from the small base station 300. In one embodiment, the receiving unit 550, receiving unit 555 and decoding unit 560 are implemented by a single microprocessor. In other embodiments, the first receiving unit 550, second receiving unit 555, and decoding unit 580 are implemented using different microprocessors.

The receiving unit 550 is configured to receive the data signals from the UEs 40 over a wireless uplink channel, such as the PUSCH, between the UEs 40 and the macro base station 200. In one embodiment, the quantization indices are received using a linear detection such as a zero forcing detector. The second receiving unit 555 includes the hardware and/or software for receiving the quantization indices from the small base station 300 over the wireless MIMO channel between the small base station 300 and the macro base station 200. The quantization indices may be received using a linear detector such as a zero forcing detector for detecting and separating the data signals as described above. The decoding unit 560 is configured to decode the data signals from the UEs 40 along with the quantization indices from the small base station 300 as herein described. The present disclosure provides a new uplink transmission schemes for Massive MIMO HetNet with QF relaying. The transmission schemes herein described enable efficient utilization of 5G technologies including massive MIMO, HetNet, full-duplex transmission, and linear processing at receivers (ZF detection). The design of the transmission schemes are simplified. First, at the small base station 300, the optimization parameters 1) scale with the number of UEs instead of small base station 300 antennas' number, 2) are independent of small scale fading, and 3) can be derived in closed forms, which reduces the computational cost and processing delay associated with iterative numerical methods in regular MIMO and 4) very small for at least one user detected signal, which allows very fine quantization at the relay node. Second, at the macro base station 200, Embodiment 4 shows that simple successive decoding for UEs messages is sufficient to achieve the same performance of joint decoding in

Embodiment 1 .