Efficient constellation design is important for improving performance in communication systems. The problem of multidimensional constellation design has been studied extensively in the literature in the context of multidimensional coded modulation and space-time coded MIMO systems. Such constellations are formally called as lattice codes, where a finite set of points from a certain high dimensional lattice is chosen based on some criteria. In this paper, we consider the problem of constellation/signal set design for media-based modulation (MBM), a recent MIMO channel modulation scheme with promising theoretical and practical benefits. Constellation design for MBM is fundamentally different from those for multidimensional coded modulation and conventional MIMO systems mainly because of the inherent sparse structure of the MBM signal vectors. Specifically, we need a structured sparse lattice code with good distance properties. In this work, we show that using an (N,K) non-binary block code in conjunction with the lattice based multilevel squaring construction, it is possible to systematically construct a signal set for MBM with certain guaranteed minimum distance. The MBM signal set obtained using the proposed construction is shown to achieve significantly improved bit error performance compared to conventional MBM signal set. In particular, the proposed signal set is found to achieve higher diversity slopes in the low-to-moderate SNR regime.
A practical $2^m$-ary polar coded modulation (PCM) scheme with optimal constellation labeling is proposed. To efficiently find the optimal labeling rule, the search space is reduced by exploiting the symmetry properties of the channels. Simulation results show that the proposed PCM scheme can outperform the bit-interleaved turbo coded modulation scheme used in the WCDMA (Wideband Code Division Multiple Access) mobile communication systems by up to 1.5dB.
A hierarchical modulation scheme is proposed to upgrade an existing digital broadcast system, such as satellite TV, or satellite radio, by adding more data in its transmission. The hierarchical modulation consists of a basic constellation, which is the same as in the original system, and a secondary constellation, which carries the additional data for the upgraded system. The upgraded system with the hierarchical modulation is backward compatible in the sense that receivers that have been deployed in the original system can continue receiving data in the basic constellation. New receivers can …
Bit-interleaved coded modulation with iterative decoding (BICM-ID) offers very good error performance over additive white Gaussian noise (AWGN) and fading channels if it uses a wisely designed signal mapping. Further, error performance of BICM-ID can significantly be improved by employing multi-dimensional (MD) modulation. However, suitable MD mappings are obtained by computer search techniques except for MD modulations that use smaller constellation e.g., binary phase shift keying (BPSK), quadrature phase shift keying (QPSK) and $8$-ary phase shift keying ($8$-PSK) as basic modulation. The al…
We present a new family of signal constellations, called log constellations, that can be used to design near-capacity coded modulation schemes over additive exponential noise (AEN) channels. Log constellations are designed by geometrically approximating the input distribution that maximizes the AEN channel capacity. The mutual information achievable over AEN channels with both coded modulation (CM) and bit-interleaved coded modulation (BICM) approaches is evaluated for various signal sets. In the case of CM, the proposed log constellations outperform, sometimes by over half a decibel, the best…
The majority of modern communication systems adopts quadrature amplitude modulation (QAM) constellations as transmission schemes. Due to their square structure, however, QAM do not provide satisfying protection to phase noise effects as the number of constellation points grows, increasing at the same time their peak to average power ratio (PAPR). This requires an expensive power amplifier and oscillator at the transmitter to guarantee low distortion, complicating the adoption of dense transmission schemes in practical high-data rate systems. In this paper, we construct a coded modulation schem…
The capacity achieving probability mass function (PMF) of a finite signal constellation with an average power constraint is in most cases non-uniform. A common approach to generate non-uniform input PMFs is Huffman shaping, which consists of first approximating the capacity achieving PMF by a sampled Gaussian density and then to calculate the Huffman code of the sampled Gaussian density. The Huffman code is then used as a prefix-free modulation code. This approach showed good results in practice, can however lead to a significant gap to capacity. In this work, a method is proposed that efficie…
Modulation classification, recognized as the intermediate step between signal detection and demodulation, is widely deployed in several modern wireless communication systems. Although many approaches have been studied in the last decades for identifying the modulation format of an incoming signal, they often reveal the obstacle of learning radio characteristics for most traditional machine learning algorithms. To overcome this drawback, we propose an accurate modulation classification method by exploiting deep learning for being compatible with constellation diagram. Particularly, a convolutio…
The capacity of the AWGN broadcast channel is achieved by superposition coding, but superposition of individual coded modulations expands the modulation alphabet and distorts its configuration. Coded modulation over a broadcast channel subject to a specific channel-input modulation constraint remains an important open problem. Some progress has been made in the related area of unequal-error protection modulations which can be considered single-user broadcast transmission, but it does not approach all points on the boundary of the capacity region. This paper studies broadcast coded modulation u…
In this paper, we derive a maximum likelihood (ML) decoder of the differential data in a decode-and-forward (DF) based cooperative communication system utilizing uncoded transmissions. This decoder is applicable to complex-valued unitary and non-unitary constellations suitable for differential modulation. The ML decoder helps in improving the diversity of the DF based differential cooperative system using an erroneous relaying node. We also derive a piecewise linear (PL) decoder of the differential data transmitted in the DF based cooperative system. The proposed PL decoder significantly reduc…
Media-based modulation (MBM) is a recently proposed modulation scheme which uses radio frequency (RF) mirrors at the transmit antenna(s) in order to create different channel fade realizations based on their ON/OFF status. These complex fade realizations constitute the modulation alphabet. MBM has the advantage of increased spectral efficiency and performance. In this paper, we investigate the performance of some physical layer techniques when applied to MBM. Particularly, we study the performance of $i)$ MBM with generalized spatial modulation (GSM), $ii)$ MBM with mirror activation pattern (M…
A practical communication channel often suffers from constraints on input other than the average power, such as the peak power constraint. In order to compare achievable rates with different constellations as well as the channel capacity under such constraints, it is crucial to take these constraints into consideration properly. In this paper, we propose a direct approach to compare the achievable rates of practical input constellations and the capacity under such constraints. As an example, we study the discrete-time complex-valued additive white Gaussian noise (AWGN) channel and compare the …
We study the problem of constructing coded modulation schemes over multidimensional signal sets in Nakagami-$m$ block-fading channels. In particular, we consider the optimal diversity reliability exponent of the error probability when the multidimensional constellation is obtained as the rotation of classical complex-plane signal constellations. We show that multidimensional rotations of full dimension achieve the optimal diversity reliability exponent, also achieved by Gaussian constellations. Multidimensional rotations of full dimension induce a large decoding complexity, and in some cases i…
In this paper, we have considered the optimization of the $M$-ary quadrature amplitude modulation (MQAM) constellation size to minimize the bit energy consumption under average bit error rate (BER) constraints. In the computation of the energy expenditure, the circuit, transmission, and retransmission energies are taken into account. A combined log-normal shadowing and Rayleigh fading model is employed to model the wireless channel. The link reliabilities and retransmission probabilities are determined through the outage probabilities under log-normal shadowing effects. Both single-hop and mul…
Spectrally efficient multi-antenna wireless communication systems are a key challenge as service demands continue to increase. At the same time, powering up radio access networks is facing environmental and regulation limitations. In order to achieve more power efficiency, we design a directional modulation precoder by considering an $M$-QAM constellation, particularly with $M=4,8,16,32$. First, extended detection regions are defined for desired constellations using analytical geometry. Then, constellation points are placed in the optimal positions of these regions while the minimum Euclidean …
Dual mode orthogonal frequency division multiplexing with index modulation (DM-OFDM-IM) is recently proposed, which modulates all subcarriers to eliminate the limits of spectrum efficiency in OFDM with index modulation (OFDM-IM). In DM-OFDM-IM, the subcarriers within each subblock are divided into two groups, which are modulated by two distinguishable constellation alphabets drawn from the distinct two constellations. In this paper, a new constellation design for DM-OFDM-IM is proposed based on the pairwise error probability (PEP) analysis. In previous works, the design of the constellation pa…
To achieve reliable and efficient transmissions in free-space optical (FSO) communication, this paper designs a new protograph low-density parity-check (PLDPC) coded generalized spatial multipulse position modulation (GSMPPM) system over weak turbulence channels. Specifically, we investigate the PLDPC code, generalized space shift keying (GSSK) modulation, and MPPM constellation. First, we propose a type of novel GSMPPM constellations that intelligently integrates the GSSK into MPPM, referred to as asymmetric dual-mode (ADM) constellations, so as to improve the performance of the PLDPC-coded G…
Recent breakthroughs in machine learning especially artificial intelligence shift the paradigm of wireless communication towards intelligence radios. One of their core operations is automatic modulation recognition (AMR). Existing research focuses on coherent modulation schemes such as QAM, PSK and FSK. The AMR of (non-coherent) space-time modulation remains an uncharted area despite its wide deployment in modern multiple-input-multiple-output (MIMO) systems. The scheme using a so called Grassmann constellation enables rate-enhancement using multi-antennas and blind detection. In this work, we…
Deep learning-based joint source-channel coding (JSCC) has shown excellent performance in image and feature transmission. However, the output values of the JSCC encoder are continuous, which makes the constellation of modulation complex and dense. It is hard and expensive to design radio frequency chains for transmitting such full-resolution constellation points. In this paper, two methods of mapping the full-resolution constellation to finite constellation are proposed for real system implementation. The constellation mapping results of the proposed methods correspond to regular constellation…
In this paper, we consider the problem of constellation design for a visible light communication (VLC) system using red/green/blue light-emitting diodes (RGB LED), and propose a method termed DC-informative joint color-frequency modulation (DCI-JCFM). This method jointly utilizes available diversity resources including different optical wavelengths, multiple baseband subcarriers, and adaptive DC-bias. Constellation is designed in a high dimensional space, where the compact sphere packing advantage over lower dimensional counterparts is utilized. Taking into account multiple practical illuminat…
In classic trellis-coded modulation (TCM) signal constellations of twice the cardinality are applied when compared to an uncoded transmission enabling transmission of one bit of redundancy per PAM-symbol, i.e., rates of $\frac{K}{K+1}$ when $2^{K+1}$ denotes the cardinality of the signal constellation. In order to support different rates, multi-dimensional (i.e., $\mathcal{D}$-dimensional) constellations had been proposed by means of combining subsequent one- or two-dimensional modulation steps, resulting in TCM-schemes with $\frac{1}{\mathcal{D}}$ bit redundancy per real dimension. In contras…
Massive MIMO, a candidate for 5G technology, promises significant gains in wireless data rates and link reliability by using large numbers of antennas (more than 64) at the base transceiver station (BTS). Extra antennas help by focusing the transmission and reception of signal energy into ever-smaller regions of space. This brings huge improvements in throughput. However, it requires a large number of Radio Frequency (RF) chains (usually equal to number of transmit antennas), which is a major drawback. One approach to overcome these issues is to use Spatial Modulation (SM). In SM, an index of …
The idea of Media-based Modulation (MBM) is to embed information in the variations of the transmission media (channel states). Using an RF closure with $w$ RF walls, MBM creates a set of $2^w$ select-able states for the end-to-end channel. Each state represents an index of an MBM constellation point. In each state, the wave (tone) emanating from the transmit antenna experiences many pseudo-random back-and-forth reflections within the RF closure. The RF signal, upon finally leaving the RF closure, further propagates in the rich scattering environment to reach the receiver. This results in an in…
We optimize modulation formats for the additive white Gaussian noise channel with nonnegative input, also known as the intensity-modulated direct-detection channel, with and without confining them to a lattice structure. Our optimization criteria are the average electrical, average optical, and peak power. The nonnegative constraint on the input to the channel is translated into a conical constraint in signal space, and modulation formats are designed by sphere packing inside this cone. Some dense packings are found, which yield more power-efficient modulation formats than previously known. Fo…
With no CSI at the users, transmission over the two-user Gaussian Multiple Access Channel with fading and finite constellation at the input, is not efficient because error rates will be high when the channel conditions are poor. However, perfect CSI at the users is an unrealistic assumption in the wireless scenario, as it would involve massive feedback overheads. In this paper we propose a scheme which uses only quantized knowledge of CSI at the transmitters with the overhead being nominal. The users rotate their constellation without varying their transmit power to adapt to the existing chann…
Residual self-interference (SI) cancellation in the digital baseband is an important problem in full-duplex (FD) communication systems. In this paper, we propose a new technique for estimating the SI and communication channels in a FD communication system, which is inspired from superimposed signalling. In our proposed technique, we add a constant real number to each constellation point of a conventional modulation constellation to yield asymmetric shifted modulation constellations with respect to the origin. We show mathematically that such constellations can be used for bandwidth efficient c…
Modulation schemes for two-way bidirectional relay network employing two phases: Multiple access (MA) phase and Broadcast (BC) phase and using physical layer network coding are currently studied intensively. Recently, adaptive modulation schemes using Latin Squares to obtain network coding maps with the denoise and forward protocol have been reported with good end-to-end performance. These schemes work based on avoiding the detrimental effects of distance shortening in the effective receive constellation at the end of the MA phase at the relay. The channel fade states that create such distance…
High spectral efficiency and low power consumption are the most challenging requirements of 5G networks since the number of devices are increased drastically. Media-based modulation (MBM) is a promising scheme in order to achieve these requirements. In this paper, the spectral efficiency of MBM scheme in single- and multi-user networks is studied. To find the spectral efficiency, information theoretical methods are used and tight lower- and upper-bounds are derived for the achievable rate. The performance of the system is studied for both correlated and uncorrelated constellation diagrams. It …
This paper investigates the bit-interleaved coded generalized spatial modulation (BICGSM) with iterative decoding (BICGSM-ID) for multiple-input multiple-output (MIMO) visible light communications (VLC). In the BICGSM-ID scheme, the information bits conveyed by the signal-domain (SiD) symbols and the spatial-domain (SpD) light emitting diode (LED)-index patterns are coded by a protograph low-density parity-check (P-LDPC) code. Specifically, we propose a signal-domain symbol expanding and re-allocating (SSER) method for constructing a type of novel generalized spatial modulation (GSM) constella…
In this paper, we present three new signal designs for Enhanced Spatial Modulation (ESM), which was recently introduced by the present authors. The basic idea of ESM is to convey information bits not only by the index(es) of the active transmit antenna(s) as in conventional Spatial Modulation (SM), but also by the types of the signal constellations used. The original ESM schemes were designed with reference to single-stream SM and involved one or more secondary modulations in addition to the primary modulation. Compared to single-stream SM, they provided either higher throughput or improved si…
A game-theoretic framework is used to study the effect of constellation size on the energy efficiency of wireless networks for M-QAM modulation. A non-cooperative game is proposed in which each user seeks to choose its transmit power (and possibly transmit symbol rate) as well as the constellation size in order to maximize its own utility while satisfying its delay quality-of-service (QoS) constraint. The utility function used here measures the number of reliable bits transmitted per joule of energy consumed, and is particularly suitable for energy-constrained networks. The best-response strat…
An uplink system with a single antenna transmitter and a single receiver with a large number of antennas is considered. We propose an energy-detection-based single-shot noncoherent communication scheme which does not use the instantaneous channel state information (CSI), but rather only the knowledge of the channel statistics. The suggested system uses a transmitter that modulates information on the power of the symbols, and a receiver which measures only the average energy across the antennas. We propose constellation designs which are asymptotically optimal with respect to symbol error rate …
In learning-based semantic communications, neural networks have replaced different building blocks in traditional communication systems. However, the digital modulation still remains a challenge for neural networks. The intrinsic mechanism of neural network based digital modulation is mapping continuous output of the neural network encoder into discrete constellation symbols, which is a non-differentiable function that cannot be trained with existing gradient descend algorithms. To overcome this challenge, in this paper we develop a joint coding-modulation scheme for digital semantic communica…
Bit-interleaved coded modulation (BICM) using (bi-)orthogonal signals is especially well suited for the application in impulse-radio ultra-wideband transmission systems, which typically operate in the power-limited regime and require a very low-complexity transmitter and receiver design. In this paper we analyze the capacity of BICM using (bi-)orthogonal signals with coherent and noncoherent detection and put particular focus on the power-limited or wideband regime. We give analytical expressions for the ratio energy per bit vs. noise power spectral density in the limit of infinite bandwidth a…
In this paper we use a variation of simulated annealing algorithm for optimizing two-dimensional constellations with 32 signals. The main objective is to maximize the symmetric pragmatic capacity under the peak-power constraint. The method allows the joint optimization of constellation and binary labeling. We also investigate the performance of the optimized constellation over nonlinear satellite channel under additive white Gaussian noise. We consider the performance over systems with and without pre-distorters. In both cases the optimized constellations perform considerably better than the c…
A game-theoretic framework is used to study the effect of constellation size on the energy efficiency of wireless networks for M-QAM modulation. A non-cooperative game is proposed in which each user seeks to choose its transmit power (and possibly transmit symbol rate) as well as the constellation size in order to maximize its own utility while satisfying its delay quality-of-service (QoS) constraint. The utility function used here measures the number of reliable bits transmitted per joule of energy consumed, and is particularly suitable for energy-constrained networks. The best-response strat…
Constellation shaping is an energy-efficient strategy involving the transmission of lower-energy signals more frequently than higher-energy signals. Previous work has shown that shaping is particularly effective when used with coded amplitude phase-shift keying (APSK), a modulation that has been popularized recently due to its inclusion in the DVB-S2 standard. While shaped APSK can provide significant gains when used with standard off-the-shelf LDPC codes, such as the codes in the DVB-S2 standard, additional non-negligible gains can be achieved by optimizing the LDPC code with respect to the s…
In this paper, we propose a geometric shaping (GS) strategy to design 8, 16, 32 and 64-ary modulation formats for the optical fibre channel impaired by both additive white Gaussian (AWGN) and phase noise. The constellations were optimised to maximise generalised mutual information (GMI) using a mismatched channel model. The presented formats demonstrate an enhanced signal-to-noise ratio (SNR) tolerance in high phase noise regimes when compared with their quadrature amplitude modulation (QAM) or AWGN-optimised counterparts. By putting the optimisation results in the context of the 400ZR impleme…
By using joint modulation and customized constellation set, we show that Quasi-Orthogonal Space-Time Block Code (QO-STBC) can be used to form a new differential space-time modulation (DSTM) scheme to provide full transmit diversity with non-coherent detection. Our new scheme can provide higher code rate than existing DSTM schemes based on Orthogonal STBC. It also has a lower decoding complexity than the other DSTM schemes, such as those based on Group Codes, because it only requires a joint detection of two complex symbols. We derive the design criteria for the customized constellation set and…
Hierarchical modulation (HM) is able to provide different levels of protection for data streams and achieve a rate region that cannot be realized by traditional orthogonal schemes, such as time division (TD). Nevertheless, criterions and algorithms for general HM design are not available in existing literatures. In this paper, we jointly optimize the constellation positions and binary labels for HM to be used in additive white gaussian noise (AWGN) channel. Based on bit-interleaved coded modulation (BICM) with successive interference cancellation (SIC) capacity, our main purpose is to maximize…
In this paper, a downlink macro-diversity precodingaided spatial modulation (MD-PSM) scheme is proposed, in which two base stations (BSs) communicate simultaneously with a single mobile station (MS). As such, the proposed scheme achieved twice the spectral efficiency of the conventional PSM scheme. To render the demodulation possible, the two signal constellation sets used at the two BSs should be disjoint. Also, since the two BSs use the same spatial dimension, i.e., indices of receive antennas, the Minkowski sum of the two constellation sets should include unrepeated symbols. This is achieve…
We develop two new designs of unitary differential space-time modulation (DSTM) with low decoding complexity. Their decoder can be separated into a few parallel decoders, each of which has a decoding search space of less than sqrt(N) if the DSTM codebook contains N codewords. Both designs are based on the concept of joint modulation, which means that several information symbols are jointly modulated, unlike the conventional symbol-by-symbol modulation. The first design is based on Orthogonal Space-Time Block Code (O-STBC) with joint constellation constructed from spherical codes. The second de…
Sparsely spread code division multiple access (SCDMA) is a non-orthogonal superposition coding scheme that permits a base station simultaneously communicates with multiple users over a common channel. The detection performance of an SCDMA system is mainly determined by its signature matrix, which should be sparse to guarantee large Euclidean distance for the equivalent signal constellation after spreading and superposition. Good signature matrices that perform well under both belief prorogation and the maximum likelihood detections are designed. The proposed design applies to several similar w…
Trellis-coded modulation (TCM) is a power and bandwidth efficient digital transmission scheme which offers very low structural delay of the data stream. Classical TCM uses a signal constellation of twice the cardinality compared to an uncoded transmission with one bit of redundancy per PAM symbol, i.e., application of codes with rates $\frac{n-1}{n}$ when $2^{n}$ denotes the cardinality of the signal constellation. Recently published work allows rate adjustment for TCM by means of puncturing the convolutional code (CC) on which a TCM scheme is based on. In this paper it is shown how punctured …
In this letter, we propose an autoencoder (AE) for designing Grassmannian constellations in noncoherent (NC) multiple-input multiple-output (MIMO) systems. To guarantee the properties of Grassmannian constellations, the proposed AE constructs the transmitted symbols following an unitary space-time modulation. It penalizes the difference between input and output symbols in terms of cross entropy during the training, which is regarded as a generic optimization method. The constellations learned by the proposed AE have substantial symbol error rate (SER) performance gains compared to the non-Gras…
Generalized product codes (GPCs) are extensions of product codes (PCs) where coded bits are protected by two component codes but not necessarily arranged in a rectangular array. It has recently been shown that there exists a large class of deterministic GPCs (including, e.g., irregular PCs, half-product codes, staircase codes, and certain braided codes) for which the asymptotic performance under iterative bounded-distance decoding over the binary erasure channel (BEC) can be rigorously characterized in terms of a density evolution analysis. In this paper, the analysis is extended to the case w…
To optimize rotated, multidimensional constellations over a single-input, single-output Rayleigh fading channel, a family of rotation matrices is constructed for all dimensions which are a power of 2. This family is a one-parameter subgroup of the group of rotation matrices, and is located using a gradient descent scheme on this Lie group. The parameter defining the family is chosen to optimize the cutoff rate of the constellation. The optimal rotation parameter is computed explicitly for low signal-to-noise ratios. These rotations outperform full-diversity algebraic rotations in terms of cuto…
