Technical field

The present invention lies in the field of digital communications.

Background of the invention

In digital communication systems, data is encoded into signals using a digital modulation technique before being transmitted from a transmitter to a receiver using a communication channel. A digital modulation scheme is typically defined by a signal constellation in a complex plane or in a higher dimensional space, wherein each signal point of the constellation corresponds to a data symbol. Once a receiver demodulates the received signal, the transmitted constellation point may be retrieved using the received signal, based on the signal constellation's geometry.

The type and parameters of the communication channel linking the transmitter to the receiver generally has an impact on the digital modulation and coding scheme that is employed. Real-time adaptation of transmission parameters according to channel conditions is one of the main features of the ever growing high-throughput communication systems. Time and/or user varying channel conditions are inherent characteristics of many communication systems such as satellite, cellular networks and broadcast systems. Adaptive Coding and Modulation, ACM, schemes are used in such systems to provide significant capacity gains by allowing the transmission format to be changed, depending on the application and/or channel quality. By employing an ACM scheme, the transmitter is able to switch between several Modulation and Coding schemes, MODCODs, choosing the largest available modulation and code rate which ensures a target detection error rate, and thus providing the maximum reliable spectral efficiency to each user. ACMs have been adopted in several standards such as Digital Video Broadcasting, DVB, and Consultative

Committee for Space Data Systems, CCSDS, see for example " CCSDS protocols over DVB -S; Summary of definition, implementation and performance, CCSDS 130.12G-1, Nov. 2016".

However, the chosen coding and modulation schemes are usually different from one standard to another.

Typically, in ACM schemes, all MODCODs are predefined and known to both the transmitter and receiver nodes in a communication system. Several factors affect the design of MODCODs for a given system, including the noise model (Additive White Gaussian Noise, AWGN, phase noise,...), the channel model (fading channel, linear channel, non-linear channel, ...), the operating frequency band (Ka band, X band...), the target error rate, and the target spectral efficiency. While the coding scheme is not usually affected by these parameters, poor choice of the modulation set may result in a significant performance loss. In particular, it is known that circular Amplitude and Phase Shift Keying, APSK, constellations perform much better than Quadrature Amplitude Modulation, QAM, constellations over satellite channels with High Power Amplifiers, HP As. This is mainly due to the non- linear characteristics of HP As near the saturation point. Although ACM schemes provide remarkable benefits to a communication system in terms of capacity and transmission flexibility, currently known solutions also increase the complexity of the transmitter and the receiver as well as imposing some overhead on the transmitted data frames. In fact, the larger the number of predefined MODCODs, the higher the additional complexity and the amount of overhead will be. Indeed, for each transmitted frame, one out of the plurality of available MODCODs needs to be uniquely identified and received correctly with high probability at the receiver. In order to achieve this, the unique identifier of each MODCOD must be protected by a highly redundant code word in the preamble of each transmitted frame, thereby increasing the data transmission overhead. Some of the current ACM schemes use over 100 MODCODs, and even higher number of MODCODs may be needed in the next generations due to higher granularity requirements, aiming at providing specific near-optimal MODCODs for a large array of communication channel parameters. Therefore the unique identifier may be large in such cases.

To the best knowledge of the inventors, a high order constellation set that performs well over a wide range of channel models is currently not known in the state of the art. Some families of APSK constellations, namely star-shaped APSK, are shown to achieve the capacity of AWGN channel, see for example H. Meric, "Approaching the Gaussian Channel Capacity With APSK

Constellations", IEEE Commun. Lett., vol. 19, no. 7, pp. 1125-1128, July 2015. However, the convergence rate as a function of constellation size is very slow and often does not provide any gain with respect to DVB-S2X APSK and even QAM constellations in the SNR range of interest. On the other hand, the constellations optimized over linear channels, such as non-uniform QAM, show a rather large gap from the peak-power limit capacity, see for example N. Loghin et al., "Non-uniform constellations for ATSC 3.0, " IEEE Trans. Broadcasting, vol. 62, no. 1, pp. 197-203, Mar. 2016. [6]. To resolve these problems, for example in DVB-S2X, see ETSI 302-307-2, "Digital Video Broadcasting (DVB)Part II: DVBS2-Extensions (DVB-S2X)) ", 2014, it has been proposed some of the MODCODs are designed specifically for the use over the linear channel. As already explained before, this implies increasing the complexity of both transmitters and receivers, as well as increasing the data transmission overhead.

Patent document WO2017/005874 Al discloses a coding and modulation apparatus using non- uniform constellations. The use of, for example, rotated base signal constellations is described therein. However, the receiver is unaware of such geometric transformations. Technical problem to be solved

It is an objective to present a method and device, which overcome at least some of the

disadvantages of the prior art.

Summary of the invention

According to a first aspect of the invention, a method for transmitting and receiving a digital data stream over a communication channel is provided. The method comprises the following steps: a) at a transmitting node, modulating the data stream using modulation means to convert digital data in the data stream into symbols forming a modulated signal for transmission by transmission means, each symbol being one of M possible symbols of a first M-ary signal constellation;

b) at the transmitting node, transmitting the modulated signal over said communication

channel using transmission means;

c) at the receiving node, receiving said modulated signal using receiving means;

d) at the receiving node, detecting and/or demodulating each symbol of said received

modulated signal using detection means.

The method is remarkable in that

said first M-ary signal constellation is such that there exists an M-ary base signal constellation of which the first M-ary signal constellation is a geometric transformation, and in that

at the transmission node, said M-ary base signal constellation and said geometric transformation defining said first M-ary signal constellation are selected by selection means, based on channel state information.

According to a second aspect of the invention, a method for transmitting a digital data stream over a communication channel at a transmitting node is provided. The method comprises the following steps:

aa) modulating the data stream, wherein modulation convert digital data in the data stream into symbols forming a modulated signal for transmission by transmission means, each symbol being one of M possible symbols of a first M-ary signal constellation;

bb) transmitting the modulated signal over said communication channel to a receiving node using transmission means.

The method is remarkable in that said first M-ary signal constellation is such that there exists an M- ary base signal constellation of which the first M-ary signal constellation is a geometric transformation, and in that said M-ary base signal constellation and said geometric transformation defining said first M-ary signal constellation are selected by selection means, based on channel state information. Preferably, said first M-ary signal constellation and said geometric transformation may be selected exclusively based on channel state information. Alternatively, it may be preferred that said first M-ary signal constellation and said geometric transformation may be selected based on channel state information and based on other information, preferably comprising an energy constraint.

Preferably, both first and second information identifying respectively said selected M-ary base signal constellation and said selected geometric transformation may be transmitted from the transmitting node to the receiving node as a preamble to said modulated signal.

Preferably, an M-ary base signal constellation may be optimized for a predetermined channel parameter value, for example for a specific value of Signal-to-Noise Ratio, SNR. An M-ary base signal constellation may preferably be optimized for an AWGN communication channel.

Preferably said modulation means may be implemented by a processing unit coupled to a memory element and programmed to transform digital data comprised in said memory element into a modulated signal. Similarly, said detection means selection means may preferably be implemented by a processing unit programmed to achieve the described effect. The corresponding code instructions may preferably be stored in a memory element to which said processing unit has at least read access.

Preferably said transmission and receiving means may comprise a networking interface configured to transmit/receive data over a communication channel.

Said communication channel may be a satellite link, a wireless channel or a wired channel.

The transmitting node may preferably transmit said modulated signal to at least one receiving node over said communication channel. Alternatively, the transmitting node may transmit said modulated signal to a single receiving node, or to a plurality of receiving nodes.

Preferably, information identifying said M-ary base signal constellation and said geometric transformation may be provided at the receiving node.

The identifying information may preferably be transmitted from the transmitting node to the receiving node as a preamble to said modulated signal. At least part of said channel state information, preferably information indicating a time-varying parameter of the channel, may preferably be transmitted as channel state feedback from the receiving node to the transmitting node.

Further preferably, said channel state information may comprise information indicating the type of the communication channel and information indicating a time -varying parameter of the channel, preferably the channel's signal-to-noise ratio, SNR or Bit Error Rate, BER. Preferably, said M-ary base signal constellation may be selected based on said information indicating a time-varying parameter of said channel, preferably SNR, and the geometric transformation may be selected based on the channel's type.

Said M-ary base signal constellation may preferably be a constellation having symbols distributed on a plurality of C concentric squares. Said geometric transformation may further be either of a rotation about the constellation origin, or a bijective mapping of the symbols on a given square to symbols on one of an equal plurality of concentric circles.

In the case of a non-linear communication channel, said geometric transformation may preferably be a bijective mapping of the symbols on a given square of the M-ary base constellation to symbols on one of said concentric circles. In the case of a fading communication channel, said geometric transformation may preferably be a rotation of the M-ary base constellation about the constellation origin. The method may comprise the additional step of

encoding the data stream using coding means at the transmitting node prior to modulating the data stream using a code having a coding rate.

Preferably, the coding rate may be selected by said selection means based at least partly on said channel state information.

Further, the method may preferably comprise the additional step of

decoding said encoded stream at the receiving node following detection and/or demodulation of the encoded data symbols.

Information identifying said code may preferably be provided at the receiving node. Preferably, said code identifying information may be transmitted from the transmitting node to the receiving node as a preamble to said modulated signal. Preferably the preamble is in the form of a data header followed of a data frame, followed by the frame's data payload comprising said modulated data-

According to another aspect of the invention, a data transmission device comprising modulation means, transmission means and selection means is provided. The device is configured for

modulating a data stream by converting digital data in the data stream into symbols forming a modulated signal for transmission by transmission means, each symbol being one of M possible symbols of a first M-ary signal constellation;

transmitting the modulated signal over said communication channel using the transmission means;

The device is remarkable in that the first M-ary signal constellation is such that there exists an M- ary base signal constellation of which the first M-ary signal constellation is a geometric transformation, and in that said selection means are configured to select said M-ary base signal constellation and said geometric transformation defining said first M-ary signal constellation based on channel state information.

According to another aspect of the invention, a data receiving device comprising demodulation means and reception means is provided. The device is configured for receiving a modulated signal using said receiving means, and detecting/demodulating the symbols detected in said modulated signal into said data stream. The device is remarkable in that the signal constellation and coding scheme used for detecting/demodulating the symbols are selected based on information identifying a base M-ary signal constellation and a geometric transformation. The M-ary signal constellation used for detecting/demodulating the symbols is said selected base M-ary signal constellation, which is transformed by said selected geometric transformation.

Preferably, the device may be further configured for carrying out the method steps in accordance with aspects of the invention.

According to yet another aspect of the invention, a computer program comprising computer readable code means is provided, which when run on a computer, causes the computer to carry out at least method steps (a) and (b) or (c) and (d) according to aspects of the invention. According to a further aspect of the invention, a computer program comprising computer readable code means, which when run on a computer, causes the computer to carry out the method according to any aspects of the invention. According to a final aspect of the invention, a computer program product is provided. The computer program product comprises a computer-readable medium on which the computer program according to previous aspects of the invention is stored.

In principle, the presented method can be used in any digital communication system which modulates digital data into constellation points prior to transmission.

Embodiments of the present invention allow to introduce a set of base Modulation and Coding schemes, MODCODs, which may for example be optimized over the AWGN channel. This set is then modified for the use over other channel models. The set of base MODCODs may for example comprise optimized non-uniform QAM constellations. The MODCODs over nonlinear and fading channels are related to the base set through a predetermined geometric transformation applied on the base constellations. In particular, a radial mapping may be used over the non-linear channel, and the constellation rotation over the fading channel. Radial constellation mappings are for example discussed by F. Kayhan, "QAM to circular isomorphic constellations," in Proc. Advanced Satellite Multimedia Syst. Conf, Palma de Mallorca, Spain, 2016. Rotated constellations for fading channels have been discussed for example by J. Boutros and E. Viterbo, "DVB-T2: Signal space diversity: A power- and bandwidth-efficient diversity technique for the Rayleigh fading channel, " IEEE Trans. Inform. Theory, vol. 44, no. 4, pp. 1453-1467, Jul. 1998. Results show that the overall loss of the proposed transformed MODCOD scheme with respect to DVB-S2X, where MODCODs are separately designed for both linear and nonlinear channels, is around 0.2 dB in the worst case. Beside unifying the MODCODs for different standards, results indicate that fewer MODCODs may be needed compared to the current standards without sacrificing the performance. For example, in the current DVB-S2X standard, some MODCODs are dedicated only to the linear channel and some others to the non- linear channel. These two sets of MODCODs can be merged by introducing an additional block in the communication chain. In the proposed scheme, these MODCODs are related to each other through a deterministic geometric transformation. When a radially mapped or rotated signal constellation is used at the transmitter, only the base MODCOD, as well as an indication of the respective geometric transform, need to be identified for proper decoding at the receiver. This reduces the transmission overhead while at the same time making a high number of MODCODs - all geometrically related to the base MODCODs - available for use with different channel conditions and types. The invention enables a new ACM scheme which can potentially unify the MODCOD design for several existing standards. This is done by introducing a new block, called channel-adapted transformation, CAT, to the communication chain. The functionality of CAT is to adapt an existing MODCOD to the given new channel condition through a deterministic geometric transformation. As a result, in accordance with embodiments of the invention, the MODCODs designed for the linear channel can also be used over non-linear or fading channels by passing them through the CAT block. Another consequence of introducing the CAT block is to reduce the number of existing MODCODs and hence reducing the length of physical layer header.

Brief description of the drawings

Several embodiments of the present invention are illustrated by way of figures, which do not limit the scope of the invention, wherein:

figure 1 illustrates the main steps according to a preferred embodiment of the method according to the invention;

figure 2 is a schematic illustration of a data transmission device according to a preferred embodiment of the invention;

figure 3 is a schematic illustration of a system for implementing a preferred embodiment of the invention;

figure 4(a) shows part of the data frame structure as used in the DVB-S2X standard, figure 4(b) shows part of the data frame structure resulting from a preferred embodiment of the method according to the invention;

figures 5(a)-(c) illustrates an optimized 256-QAM signal constellation and geometric transformations thereof;

figures 6(a)-(b) plot PAMI against SNR/PSNR values for various 16-ary signal constellations and for two different channel types;

figures 7(a)-(b) plot PAMI against SNR/PSNR values for various 64-ary signal constellations and for two different channel types;

figures 8(a)-(b) plots PAMI against SNR/PSNR values for various 256-ary signal constellations and for two different channel types;

figures 9(a)-(b) plot BER against SNR/PSNR values for various 16-ary signal

constellations and for two different channel types;

figures 10(a)-(b) plot BER against SNR/PSNR values for various 64-ary signal constellations and for two different channel types;

figures 1 l(a)-(b) plot BER against SNR/PSNR values for various 256-ary signal constellations and for two different channel types;

figures 12(a)-(c) plot BER against SNR values for various M-ary rotated and non-rotated signal constellations and for a Rayleigh fading channel. Detailed description of the invention

This section describes aspects of the invention in further detail based on preferred embodiments on the figures. Figure 1 shows the main steps according to a preferred embodiment of the method according to the present invention. In a communication network, a transmitting node transmits data to at least one receiving node using a data communication channel. A non-limiting example of such a channel may be a wireless channel, for example a satellite link.

At step (a) of the method, a transmitting node modulates a data stream using modulation means onto a carrier wave to generate a modulated signal. The modulation comprise for example a data processor programmed to convert digital data in the data stream, which is read from a memory element to which said data processor has read access, into symbols for transmission by

transmission means. The transmission means comprise a networking interface operatively connected to the data processor. Each symbol generated by the data processor is one of M possible symbols of a first M-ary signal constellation, where M is the modulation order and is in general a power two, equalling for example 16, 64, 256, etc... At the next step (b) of the method, the resulting modulated signal is put onto said communication channel using the networking interface. The communication channel connects the transmitting node to at least one receiving node, which comprises receiving means such as a networking interface. The networking interface of the receiving node is configured for receiving the modulated signal that was sent by the transmitting node - possibly contaminated by channel noise and/or losses. Detection means, which in accordance with an embodiment of the invention comprise a data processor, are programmed and configured for detecting and/or demodulating the symbols contained in the received modulated signal.

According to a preferred embodiment of the invention, the first M-ary signal constellation is designed such that there exists an M-ary base signal constellation of which the first M-ary signal constellation is a geometric transformation. For example, the first M-ary signal constellation may be obtained by rotating a base signal constellation by a predetermined angle about the

constellation's origin. Or, the base signal constellation may be a non-uniform QAM signal constellation having C concentric squares on which its symbols are distributed. The geometric transformation may bijectively map each symbol of a given square onto a circle associated with that square, the resulting first M-ary signal constellation comprising an equal number of C concentric circles. Other geometric transformations may be chosen without departing from the scope of the invention. The base M-ary signal constellation and the transformation, both of which define the first M-ary signal constellation that is used for generating the modulated signal, are selected based on channel state information. The channel state information comprises information on the channel type (linear, non-linear, fading, ...) and/or information on the channel's state, described by at least one parameter such as SNR or BER. All or part of the channel state information is obtained at the transmitting node as feedback information using a feedback channel connecting the receiving node to the transmitting node.

Instead of explicitly identifying the first M-ary signal constellation, the base M-ary signal constellation and the selected geometric transformation are identified at the receiving node. Using this information, the receiving node is capable of detecting/demodulating the received modulated signal, and to extract the original data stream for further use by a data processor. The receiving node may able to detect the used signal constellation based on a power spectral analysis of the received modulated signal. However, in preferred embodiments, the information identifying the base M-ary signal constellation and the selected geometric transformation is transmitted to the receiving node in a header or preamble to the actual modulated data stream. The preamble only needs to identify a base M-ary signal constellation, and a geometric transformation. While the number of possible MODCOD combinations and resulting first M-ary signal constellation is large, the data overhead is significantly reduced as to the case in which a resulting combination would be identified explicitly among all possible combinations. The receiving node only needs to store the base M-ary signal constellation. As this constellation is identified in the preamble, the receiving node selects it. It then applies the geometric transform, which is also identified in the preamble, to the selected base M-ary signal constellation. The resulting constructed M-ary signal constellation allows for proper detection/demodulation of the received symbols.

In a preferred embodiment, the transmitting node has access to a set of base M-ary signal constellations, each base M-ary signal constellation being optimized for a specific SNR value or value range and for an AWGN linear channel. At least part of the channel state information, for example an observed SNR value, is transmitted to the transmitting node as feedback from the receiving node. Using this observed SNR value, the transmitting node selects a corresponding M- ary signal constellation from the base set. Generally, the transmitting node has knowledge of the channel type of the communication on which it transmits data, so that it selects a corresponding geometric transform and thereby identifies the M-ary signal constellation that is used for modulating the data stream. Alternatively, the channel type may also be obtained via feedback from the receiving node. Figure 2 schematically illustrates an example of a device for implementing the steps (a) and (b) outlined here above. The data transmission device 10 comprises a memory element 1 1 , which may be a volatile memory for storing the data that is to be transmitted, a consistent memory element 13 in which the base and/or transformed M-ary signal constellations are stored, and modulation means 12 for modulating the data onto a carrier wave in accordance with the first M-ary signal constellation. While the consistent memory element 13 is shown to be physically collocated with the device 10, it may as well be remote to the device. In such a case, the device 10 has remote access to the networked memory resource 13 using a communication channel. The resulting modulated signal is transmitted using transmission means 14 over a communication channel 30. In order to determine which is the first M-ary signal constellation to be used by the modulation means 12, the device 10 further comprises selection means 16. Based on channel state information, shown in Figure 2 in a non-limiting way as being obtained through channel feedback 5, the selection means determine the base M-ary signal constellation and the geometric transform that match the channel type and channel parameters best, thereby defining the first M-ary signal constellation to be used by the modulation means. In order to perform the selection, the selection means have preferably access to a look-up table stored in a memory element, which associates channel types and parameters to base constellations and geometric transforms.

A corresponding receiver, which is not illustrated, received a noisy version of the modulated signal and demodulates/detects the symbols that have been transmitted. Using the information identifying the base MODCOD and the geometric transform that were used by the modulation means at the transmitter, the receiver is able to identify the M-ary signal constellation used to generate the modulated signal - which is the information it needs to retrieve the transmitted data from the received symbols.

In what follows, a particularly preferred embodiment in accordance with the invention is described. 1 Overview

The remainder of the description is organized as follows. A system model is outlined in Section 2. This is followed by defining the channel-adapted transformation block. In Section 3, a mutual information analysis for various constellations of interest is provided. Simulation results are reported in Section 4 and the Bit Error Rate, BER, of the proposed ACM scheme is compared to those of DVB-S2X and DVB-T2. 2 System Model

In a simple communication chain, the input sequence of data bits u are first encoded to a longer sequence c in order to increase the robustness of detection against non-deterministic effects of the physical medium (e.g., wireless channel). In the present framework, the inventors use the low- density parity check codes, LDPC, of the DVB-S2X standard, however, any other coding scheme may be used in general, without departing from the scope of the present invention. The encoded data sequence is then mapped into symbols x with a specific constellation set χ. The number of bits per symbol (also known as modulation order) affects the transmission bit rate. More bits per symbol ensures higher throughput, but deteriorates the accuracy of detection at the receiver if the SNR is kept fixed.

The same process is usually performed in reverse order at the receiver, i.e., first detecting the transmitted symbol x and then decoding the coded sequence to obtain the estimated data sequence u . Due to the stochastic nature of the channel, the knowledge of short-term or long-term status of the channel is useful to increase the reliability of the communication. Having the channel estimation, for example, the transmitter can adapt the instantaneous transmission rate and modulation order according to the current channel condition. There are several ways to adjust the transmission rate in order to have a reliable communication over a physical channel. Changing the modulation order and the coding rate are two most common mechanisms which are used in an Adaptive Coding and Modulation, ACM, system.

A conventional ACM scheme, is able to switch between a number of MODCODs as a function of the instantaneous channel state and the target spectral efficiency. The MODCOD is selected based on the channel estimation at the receiver which is available to the transmitter using a finite rate feedback channel. Depending on the application and the wireless environment, a sufficiently wide range of received SNRs is divided into several intervals, each of which is assigned a MODCOD with respect to the spectral efficiency requirements. Therefore, any given spectral efficiency is supported by changing either the number of bits per modulated symbol or the coding rate.

However, in general, the same MODCODs cannot be used for different channel models (e.g. linear/non-linear), and therefore, separate MODCOD sets are needed for each channel model which leads to increasing the total number of MODCODs. In accordance with the present invention, an ACM scheme that can be adapted to different channel models is proposed. This is done by first defining a set of base MODCODs and then modifying this set as a function of channel model using a deterministic geometric transformation. In other words, the MODCOD set for any given channel model is related to the base MODCOD set through an additional system block, which is referred to as channel-adapted transformation, CAT. The CAT block is basically a multicriteria deterministic function. The proposed scheme is illustrated in

Figure 3, where the MODCOD set and the CAT functionality are selected based on the information provided by the receiver through a feedback channel. This model can be readily applied to any ACM communication system by proper designing of base MODCODs and the CAT block.

One of the advantages of adding the CAT block in the ACM scheme is the reduced number of required bits to distinguish all the predefined MODCODs. In Figure 4, the basic frame structure of the current DVB satellite standard is compared to the frame structure of the proposed scheme. In DVB-S2X, some bits in the PLS header are defined to determine the MODCOD. By employing the CAT block in accordance with the present embodiment, the number of allocated bits can be decreased as a result of having less number of MODCODs, while covering the same range of SNR with the same granularity. This reduction is achieved by having a base MODCOD set designed only for the linear channel and then extended to the non- linear channel through the CAT block. Instead, the transmitter only has to declare the channel model (i.e., the functionality of the CAT block) once at the beginning of the transmission of the superframe. This can be considered as an initialization step and is depicted by the CAT header in Figure 4. The length of the CAT header depends on the number of functions defined in the CAT block. For example, for a two-mode unified ACM system (e.g., operating over linear and non-linear channel models), only one bit per superframe is needed for this one-time header.

It is important to note that the use of CAT block is just a systematic way to distinguish between the MODCODs designed for different channel models or conditions. In principle, if the channel model is fixed during the frame (or superframe) time, one may define a header similar to the CAT header to indicate the channel model without specifically going to the CAT block. In such case, all the MODCODs are defined off-line but only a portion of them is used at any given frame (or superframe).

If a given MODCOD is used for each frame; then the receiver has to be informed of the used MODCOD to correctly detect and read the frames. This is done by adding extra bits to the frame headers specifying the MODCOD associated with each frame. Obviously, specifying a MODCOD that is selected from a large set of MODCODs requires more extra bits. Therefore, there is a tradeoff between the granularity and the additional overhead which has to be dealt with in designing an ACM scheme.

In what follows, it is described how to find the base MODCOD set for the linear channel, the set being adaptable to other channel models through the CAT block. It is important to notice that one may define different base MODCODs for another channel model, which will result in a different CAT block, without however departing from the framework of the present invention. 2.1 Base MODCOD set

The first step in designing the unified ACM framework in accordance with the invention, is to find a base MODCOD set. Only the modulation scheme to be used in each MODCOD is defined in this preferred embodiment, and therefore the coding scheme is not changed. In alternative

embodiments, the coding scheme may also be varied as a function of the channel state information available at the transmitter.

The MODCODs in DVB-S2X and DVB-T2 standards cannot be interchangeably used without a substantial loss in one or the other system. The DVB-S2X standard mainly adopts APSK constellations in the MODCODs targeted for non-linear channels. In general, APSK constellations are not optimal over linear channels. Therefore, some MODCODs in DVB-S2X are specifically designed for use over linear channels. On the other hand, DVB-T2 uses QAM constellations in its MODCODs, but it is well known that the QAM signaling leads to noticeable performance loss over non-linear channels. The opposing performance of these MODCODs over different channel models leads the inventors to design channel-adapted MODCODs with competitive performance over both linear and non- linear channels.

Non-uniform QAM constellations have been studied by several authors due to their potential shaping gain and higher mutual information with respect to the conventional uniform QAM over the AWGN channel - see for example B. Mouhouche, D. Ansorregui, and A. Mourad, "High order non-uniform constellations for broadcasting UHDTV, " in Proc. IEEE Wirel. Commun. and Netw. Conf, Istanbul, Turkey, 2014, and references cited therein. These constellations also allow for a low complexity detection, as they can be obtained by the Cartesian product of two non-uniform pulse amplitude modulation, PAM, constellations. This family of QAM constellations is considered to be employed in ATSC 3.0 broadcasting standard as outlined in "ATSC Standard, Physical Layer Protocol, Doc. A/322:2017", Jun. 2017 . The underlying idea is to use equiprobable symbols with unequal spacing, which results in approximately Gaussian input distribution at high SNR. It should be noted that finite non-uniform QAM constellations are not the best known constellations over AWGN channel when the input-output mutual information is considered. An example of a method for optimizing non-uniform QAM constellations by maximizing the mutual information over the AWGN channel is presented by J. Zoellner and N. Loghin, "Optimization of high-order nonuniform QAM constellations, " in Proc. IEEE Int. Symp. Broadband Multimedia Syst. and

Broadcasting, London, 2013. Taking into account the quadrant symmetry of QAM, this optimization can be simplified to only finding the optimal positive amplitudes of a PAM constellation (i.e., ID optimization). For a square M-QAM constellation, this leads to have a set of PAM symbols to be optimized. The Cartesian product of this set with itself gives the constellation points on the first quadrant, and the remaining points can be easily constructed by the quadrant symmetry. In an ACM system, the non-uniform QAM constellations to be used in different MODCODs need to be optimized separately for each SNR range.

In the present embodiment of the invention non-uniform QAM constellations, obtained by optimization over the linear AWGN channel, are used as the set of base MODCODs. These constellations are referred to as non-uniform (NU) QAM for simplicity. A simulated annealing algorithm is used to perform ID optimization at any given SN, as discussed in F. Kayhan and G. Montors, "Constellation design for memoryless phase noise channels, " IEEE Trans. Wirel.

Commun., vol. 13, no. 5, pp. 2874-2883, May 2014. A typical plot of NU 256-QAM constellation is shown in Figure 5(a).

2.2 Channel-adapted MODCOD transformation

Having chosen the set of base MODCODs, the next step is to define the functions in the CAT block in order to obtain the MODCODs for other channel models. For non-linear satellite channels, a class of circular constellations has been introduced in F. Kayhan, "QAM to circular isomorphic constellations," in Proc. Advanced Satellite Multimedia Syst. Confi, Palma de Mallorca, Spain, 2016. The proposed constellation exhibit achievable mutual information being very close to the peak-power limited channel capacity. This type of constellations, named QCI, is in fact the transformation of QAM points under the radial isomorphism, which converts the concentric squares into concentric rings. Let (u,v) £ , denote a QAM constellation point, then the radial mapping is defined as

A ( _U , t = ^ ^' -«), for («. *)≠ (0, 0) ^{( 1 )} where _/ (0,0) = (0,0). It is important to notice that the binary Gray labeling of QAM constellation is preserved under f and therefore the resulting QCI constellation has also a Gray labeling. Using this isomorphism, for each M-QAM constellation, a unique M-QCI constellation can be constructed.

The radial mapping in Eq. (1) can also be applied to NU QAM signal set. The result will be a QCI constellation with concentric rings of non-uniform radii (see Figure 5(b)). Even though the resulting QCI constellations are not optimal over the non-linear channel, as will be outlined in Section 3, they perform very close to the state of the art. These signal constellations as NU QCI in the remainder of the present description.

In addition to non-linear channels, multipath fading channels are also of interest. An effective solution to increase the robustness of the receiver in severe fading scenarios is shown to apply a certain rotation to the constellation points, as outlined for example in J. Boutros and E. Viterbo, "DVB-T2: Signal space diversity: A power- and bandwidth-efficient diversity technique for the Rayleigh fading channel, " IEEE Trans. Inform. Theory, vol. 44, no. 4, pp. 1453- 1467, Jul. 1998 This technique introduces signal space diversity that can achieve substantial coding gain over fading channels without spending additional power or bandwidth; the only drawback is higher detection complexity. The simplest form of rotation is given by the function:

where the rotation angle ϋ needs to be optimized depending on the modulation type and order. The constellation rotation in Eq. (2) is followed by an interleaver through a cyclic delay of quadrature components (Q-delay). Therefore, the in-phase and quadrature components of a transmitted symbol are sent via different carriers and time slots, and thus are affected by independent fadings. As a result, either the quadrature or the in-phase component can be used to recover the information. The constellation rotation and cyclic Q-delay (RQD) technique has been adopted in the DVB-T2 standard. The transformation of NU 256QAM constellation under a rotation angle of atan(\/\ 6) degrees is illustrated in Figure 5(c). As an example for a possible design, we consider the CAT block containing the transformations in Eq. 1 and Eq. 2, i.e.,

{ (it. v)→ (u. v) for linear channel (3) (u. v) -+ /i (tt, v) for non-linear channel

(u. v) —► fa (u, v) for fading channel

Such a CAT block enables the base MODCOD set to be adapted to use over non-linear and fading channels by a simple geometric transformation of symbols. This will not only reduce the number of MODCODs needed but also allow for lower transmitter and receiver complexities and decrease the amount of MODCOD signaling overhead. The definition in Eq. (3) can be regarded as one possible realization of the unified ACM scheme; in general, one may define extra criteria to extend the compatibility of CAT with a diverse range of wireless applications.

2.3 Changing the coding parameters through CAT

Although the above example only considers the adaptability of the modulation type to different channel models, it is also feasible to modify the whole MODCOD (i.e., both the modulation and the coding scheme) through the CAT block. One possible way is to change the coding rate through the puncturing a rate-compatible code. The puncturing table can be merged into the CAT block through properly assigning the code rates to the set of base MODCODs. Using rate-compatible channel codes is an effective solution to keep the amount of MODCOD signaling overhead almost unchanged, and thus is closely aligned with the primary goal of the unified ACM design. Another coding parameter which can be modified through the CAT block is the length of code. As an example, in DVB satellite standard two families of LDPC codes with different lengths are used, namely short and long codes. By assuming that all the codes used in a single frame are either short or long, one can further decrease the PLH length and increase the CAT header to contain also the information regarding the code length. This functionality can be added to the CAT block by simply introducing a flag parameter which can take two values each associated with a code length. A very simplified case is demonstrated in the following CAT block where the parameter CL is a flag for the code length and by default it is set to zero for the long codes in DVB-S2X:

(u. v) -¥ /i(tt, v) for non-linear channel (4)

CAT ;

CL -4 1 for indicating short codes in the following frame 3 Mutual Information Analysis

An appropriate measure for constellation performance is its input-output mutual information. In particular, the inventors are interested in pragmatic communication systems, where symbol demapping is completely decoupled from channel decoding with an interleaver placed in between. The resulting system is called bit- interleaved coded modulation, BICM, see for example G. Caire, G Taricco, and E. Biglieri, "Bit-interleaved coded modulation, " IEEE Trans. Inform. Theory, vol.

44, no. 3, pp. 927-946, May 1998. The relevant measure is BICM capacity, also known as pragmatic average mutual information PAMI, which is defined as follows:

where χ and x are respectively the constellation set and its constituting points, μ is the symbol labeling with μ'(χ) representing the z ^' -th bit of the label assigned to x, and y denotes the received signal at the output of the channel.

Assuming a memoryless ideal non-linearity model (hard limiter) for the HP A, and ignoring the effect of filters, leads one to set the unit maximum power constraint for the constellations when employed over such channels. As a result, the PAMI is calculated as a function of PSNR.

In the following, the mutual information of a number of possible MODCODs in the proposed unified ACM in accordance with embodiments of the invention are compared with some of the MODCODs used in DVB-S2X and DVB-T2 standards, where PAMI is plotted versus SNR (linear channel) and PSNR (non-linear channel). The PAMIs over the non-linear channel are compared with the capacity of peak-power constrained channels derived by Shamai et al. in "The capacity of average and peak-power-limited quadrature Gaussian channels," IEEE Trans. Inform. Theory, vol. 41, no. 4, pp. 1060- 1071, Jul. 1995. The considered base MODCODs comprise NU QAM constellations of M = 16, M = 64 and M = 256 points optimized for target SNRs of 10 dB, 15 dB and 20 dB, respectively. For each constellation size, only the DVB-S2X MODCOD designed for the same range of SNR (or PSNR) with highest PAMI over the linear (or nonlinear) channel is considered. We adopt the notation introduced in the DVB standard for the DVB-S2X MODCODs. For instance, 64-APSK 132/180 refers to the MODCOD designed for the non- linear channel with LDPC code identifier 132/180, and 64-APSK 128/180-L is the MODCOD designed for the linear channel with LDPC code identifier 128/180.

3.1 16-ary Constellations

Figure 6 compares the PAMI of various constellations with 16 points. For the linear channel in Figure 6(a), there is a slight difference (always below 0.05 bits/symbol in the depicted range of SNR) between the PAMI of 16-APSK 20/30-L constellation and that of NU 16-QAM. As will be shown below in Section 4, this results in NU 16-QAM being very close to 16-APSK 20/30-L MODCOD in performance. From the same figure, it can also be seen that NU 16-QAM has higher PAMI than 16-QAM which is clearly the result of optimization over the linear AWGN channel. However, this difference is not significant because there is only one tunable parameter in the optimization, i.e., the ratio between the two corresponding positive PAM amplitudes. As for the non- linear channel, the achievable mutual information of 16-APSK 13/18 is slightly higher than the NU 16-QCI constellation, as depicted in Figure 6(b). Notice that NU 16-QCI constellation performs very close to 16-QCI.

In order to have a comprehensive understanding of the plots in Figure 6, the results are summarized in Table I. In this table, the comparison of the sum capacity gap and the overall loss with respect to the capacity limits for four different MODCOD pairs is presented. For each pair of MODCODs (the first two columns), the sum capacity gap is obtained by adding the PAMI loss of the linear MODCOD with respect to the Shannon limit and the PAMI loss of the non-linear MODCOD with respect to the Shamai limit for a given SNR value. Similarly, the Overall loss is computed by adding the SNR loss of linear and non- linear MODCODs with respect to the corresponding capacity limits for a fixed value of PAMI. As it can be seen in Table I, the best result is obtained by selecting two different MODCODs

(DVBS2X MODCODs), each targeting the corresponding channel. However, this gain for DVB- S2X MODCODs is achieved by using two MODCODs, as opposed to only one MODCOD in the CAT scheme. The sum capacity gap and overall loss of NU 16-QAM and NU 16-QCI pair are smaller than those obtained by using a single MODCOD over both the channels. MODCODs Sum capacity gap Overall loss Notes

(bits/symbol) (dB)

Linear Non-linear

16-APSK 20/30-1, 16-APSK 20/30-L 0.45 1.85 1 MODCOD

16-APS 13/18 16-APSK 13/18 0,39 1 ,22 1 M.ODCOD

16-APSK 20/30-L 16-APSK 13/18 0,24 0,88 2 MODCODs

NU 16-QAM NU 16-QCI 0,29 1,08 CAT scheme

Table I: Numerical comparison of sum capacity gap and overall loss for the MODCODs with 16- ary constellations. The capacity gaps are obtained for fixed SNR=8.43 dB (linear channel) and PSNR=1 1.52 dB (non- linear channel), and the losses with respect to the capacity limits are calculated for fixed PAMI=2.818 bits/symbol (linear channel) and PAMI=3.219 bits/symbol (nonlinear channel).

MODCODs Sum capacity gap Overall lost ; Notes

(bits/symbol) (dB)

Linear Non- linear

64-APSK 128/180-L 64-APSK 128/180-L 0,58 2.06 1 MODCOD

64-APSK 132/180 64-APSK 132/180 0,53 1.67 1 MODCOD

64-APSK 128/180-L 64-APSK 132/180 0.38 1.25 2 MODCODs

N U 64-QAM NU 6 -QCI 0,10 1.34 CAT scheme

Table II: Numerical comparison of sum capacity gap and overall loss for the MODCODs with 64- ary constellations. The capacity gaps are obtained for fixed SNR=13.98 dB (linear channel) and PSNPv= 17.97 dB (non- linear channel), and the losses with respect to the capacity limits are calculated for fixed PAMI=4.498 bits/symbol (linear channel) and PAMI=4.822 bits/symbol (nonlinear channel). 3.2 64-ary Constellations

For 64-ary constellations, the comparison of PAMI is drawn in Figure 7. It can be seen from Figure 7(a) that the PAMI curve of 64-APSK 128/180-L is just over that ofNU 64-QAM, with a maximum distance of less than 0.05 bits/symbol in the desired range of SNR. Furthermore, similar to NU 16-QAM, NU 64-QAM also outperforms 64-QAM but with higher PAMI differences. Over the non-linear channel (Figure 7(b)), using NU 64-QCI achieves almost the same PAMI compared to the best DVB-S2X constellation (64-APSK 132/180 MODCOD).

The results are summarized in Table II. The difference between the capacity gap of CAT-related MODCODs and the two DVB-S2X MODCODs (each to be used over the targeted channel) is about 0.03 bits/symbol.

3.3 256-ary Constellations

The PAMI comparison for various 256-ary constellations is shown in Figure 8. As it can be observed in Figure 8(a), over the linear channel, the constellation of 256-APSK 22/30-L

MODCOD achieves about 0.1 bits/symbol higher PAMI than NU 256-QAM. Over the non-linear channel, 256-APSK 135/180 and NU 256QCI both achieve the same PAMI in the desired SNR range, as shown in Figure 8(b). As a consequence, in comparison with the DVB-S2X MODCODs, employing the CAT-related MODCODs of the unified ACM does not lead to significant performance loss in terms of achievable spectral efficiency. The numerical comparison of the four MODCOD pairs is shown in Table III. The overall conclusion is similar to the previous cases; the loss due to using the CAT scheme is about 0.27 dB when compared to the 2-MODCOD DVB-S2X scenario.

4 Simulation Results

In this section, the Bit Error Rate, BER, simulation results are shown for all the constellations analyzed in the previous section. The results are obtained over various channel models according to DVB-S2X and DVB-T2 scenarios. For DVB-S2X, the simulations are performed over both linear and non-linear channels. Comparisons under the DVB-T2 scenario are drawn assuming an i.i.d Rayleigh fading channel.

MODCODs Sum capacity gap Overall loss Notes

(bits/symbol) (dB)

Linear Non-linear

256- APSK 22/30-L 256-APSK 22/30-L 0.54 1,77 1 MODCOD

256- APSK 135/180 256-APSK 135/180 0.51 1.61 1 MODCOD

256- A SK 22/30-L 256-A PSK 135/180 0,40 1 .31 2 MODCODs

N U 256-QAM NU 256-QCI 0.49 1.58 CAT scheme

Table III: Numerical comparison of sum capacity gap and overall loss for the MODCODs with 256-ary constellations. The capacity gaps are obtained for fixed SNR=18.84 dB (linear channel) and PSNR=24.02 dB (non- linear channel), and the losses with respect to the capacity limits are calculated for fixed PAMI=6.128 bits/symbol (linear channel) and PAMI=6.524 bits/symbol (non- linear channel).

In all simulations, a simple communication chain is assumed, where the information bits are encoded via an LDPC encoder, modulated and then passed through the channel. A pragmatic receiver is also assumed, wherein the demodulator computes log-likelihood ratio, LLR, value for each bit and then passes it on to the LDPC decoder, and no iteration occurs between them. In order to have a fair comparison, the same LDPC code of rate 3/4 from DVB-S2X standard is selected. This coding rate is selected to be as close to the LDPC code identifiers of all the DVB-S2X MODCODs of interest as possible. For the other MODCODs than DVB-S2X, the code identifier ¾ is dropped; for instance, NU 16-QAM MODCOD (or NU 16-QAM for short) refers to the combination of NU 16-QAM and the selected LDPC code with rate 3/4. 4.1 Comparison over DVB-S2X channel models

Similar to the previous section, the simulation results are categorized based on the modulation order. As will be seen, the BER results confirm the theoretical studies of PAMI in all cases. 4.1.1 MODCODs with 16-ary Constellations

Figure 9 compares the BER performance of various MODCODs that use 16-ary constellations. As it can be seen in Figure 9(a), the performance of NU 16-QAM over the linear channel is quite close to 16-APSK 20/30-L and superior to 16-QAM. Over the non-linear channel (Figure 9(b)), NU 16- QCI shows a slight loss (less than 0.1 dB) with respect to 16-APSK 13/18 MODCOD. One can further observe that the difference between NU 16-QCI and 16-QCI is insignificant.

4.1.2 MODCODs with 64-ary Constellations

For MODCODs with 64-ary constellations, the BER curves are plotted in Figures 10(a) and 10(b) for linear and non-linear channels, respectively. As before, the BER simulations confirm closely the PAMI results. A loss of 0.1 dB is resulted from using NU 64-QAM compared to 64-APSK

128/180-L MODCOD. But over the non- linear channel, using the NU 64-QCI MODCOD provides a small gain compared to 64-APSK 132/180.

4.1.3 MODCODs with 256-ary Constellations

The BER performance of various MODCODs with 256-ary constellations is depicted in Figure 1 1. As it can be seen from Figure 1 1(a), NU 256-QAM MODCOD shows a performance loss of about 0.25 dB compared to 256-APSK 22/30-L, but a gain of 0.5 dB against the uniform 256-QAM. As for the non- linear channel, Figure 1 1(b) shows that NU 256-QCI performs around 0.1 dB better than the best DVB-S2X non-linear MODCOD in this SNR range (256-APSK 138/180). It follows from the BER results that the CAT-related MODCODs provide competitive performance with respect to the separate linear and non- linear MODCODs of DVB-S2X, which is in line with the PAMI results obtained in the previous section.

Rotated. Non-rotated.

Table IV: Performance gain of the proposed ACM scheme with respect to the two broadcasting standards over the Rayleigh fading channel. All the gains are computed at BER = 10 ^"2 .

4.2 Comparison over DVB-T2 channel model

In simulations over the i.i.d. Rayleigh channel the data transmission has been considered both with and without RQD. The BER results are depicted in Figure 12. The same rotation angle as in the DVB-T2 standard is adopted for each modulation order. As mentioned earlier in Section 2, the RQD technique provides higher probability of successful detection for deeply faded symbols. Without RQD, the BER performance is substantially degraded, falling into the error floor region at rather high BER. Comparing with the BER results over the AWGN channel, using RQD reduces the fade margin from 8 dB (for the non-rotated constellations) to 3 dB (at 10 ^"2 ) over the assumed Rayleigh channel.

Furthermore, the BER results show that NU QAM performs better than QAM over fading channels for all the constellation sizes of interest. The BER of the best linear DVB-S2X MODCOD for each constellation size has also been simulated. All the considered DVB-S2X linear MODCODs show a loss with respect to both QAM and NU QAM, even if RQD is employed. As one other possible scenario for APSK constellations, the cyclic Q-delay without constellation rotation has been aplied. The BER results in that case were slightly worse than those obtained with RQD, and thus are not presented here. A numerical performance comparison is presented in Table IV, where the approximate gains of the NU QAM constellations with respect to DVB-T2 and DVB-S2X constellations over the Rayleigh channel are shown. Both the rotated and non-rotated constellations with 16, 64 and 256 points are considered. NU QAM has always better or equal BER performance with respect to the QAM constellation. Moreover, NU QAM shows performance gains up to 1 dB compared to the DVB- S2X MODCOD in all cases. It should be noted that the gains in Table IV are obtained using the optimal rotation angles for uniform QAM constellations. However, if one optimizes the rotation angle for each NU QAM constellation, even higher gains might be achievable.

It should be noted that features described for a specific embodiment described herein may be combined with the features of other embodiments unless the contrary is explicitly mentioned.

Based on the description and figures that has been provided, a person with ordinary skilled in the art will be enabled to construct a computer program for implementing the described methods without undue burden. Research leading to this invention is supported by the Luxembourg National Research Fund under CORE Junior project: C16/IS/1 1332341 Enhanced Signal Space opTImization for satellite ComMunication Systems (ESSTIMS).

It should be understood that the detailed description of specific preferred embodiments is given by way of illustration only, since various changes and modifications within the scope of the invention will be apparent to the person skilled in the art. The scope of protection is defined by the following set of claims.