Discrete-input Continuous-output Memoryless Channel Research Articles

Low Complexity Detection of Spatial Modulation Aided OTFS in Doubly-Selective Channels

A spatial modulation-aided orthogonal time frequency space (SM-OTFS) scheme is proposed for high-Doppler scenarios, which relies on a low-complexity distance-based detection algorithm. We first derive the delay-Doppler (DD) domain input-output relationship of our SM-OTFS system by exploiting an SM mapper, followed by characterizing the doubly-selective channels considered. Then we propose a distance-based ordering subspace check detector (DOSCD) exploiting the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information of the transmit symbol vector. Moreover, we derive the discrete-input continuous-output memoryless channel (DCMC) capacity of the system. Finally, our simulation results demonstrate that the proposed SM-OTFS system outperforms the conventional single-input-multiple-output (SIMO)-OTFS system, and that the DOSCD conceived is capable of striking an attractive bit error ratio (BER) vs. complexity trade-off.

Reconfigurable Intelligent Surface Aided Amplitude- and Phase-Modulated Downlink Transmission

New reconfigurable intelligent surface (RIS) based amplitude and phase modulation schemes are proposed as an evolution how the phase-only modulation schemes available in the literature. Explicitly, both the amplitude-phase shift keying (A-PSK) and quadrature amplitudephase shift keying (QA-PSK) are conceived, where the RIS is assumed to be part of a transmitter to deliver information to the multi-antenna aided downlink receiver. In the proposed design, the RIS is partitioned into multiple blocks, and the information bits are conveyed by controlling both the ON-OFF state and the phase shift of the RIS elements in each block. Since the propagation paths spanning from each RIS block to the receiver can be coherently combined as a benefit of appropriately configuring the phase of the RIS elements, the received signal constellations can be designed by controlling both the ON-OFF pattern of the RIS blocks as well as the phase shift of the RIS elements. Both the theoretical analysis and the simulation results show that our proposed RIS-aided modulation schemes outperform the state-of-the-art RIS-based PSK modulation both in terms of its discrete-input-continuous-output memoryless channel (DCMC) capacity and its symbol error probability, especially in the high signal-to-noise-ratio (SNR) region, when considering realistic finite resolution RIS phase shifts.

Deep Learning Aided Physical-Layer Security: The Security Versus Reliability Trade-Off

This paper considers a communication system whose source can learn from channel-related data, thereby making a suitable choice of system parameters for security improvement. The security of the communication system is optimized using deep neural networks (DNNs). More explicitly, the associated security vs reliability trade-off problem is characterized in terms of the symbol error probabilities and the discrete-input continuous-output memoryless channel (DCMC) capacities. A pair of loss functions were defined by relying on the Lagrangian and on the monotonic-function based techniques. These were then used for managing the learning/training process of the DNNs for finding near-optimal solutions to the associated non-convex problem. The Lagrangian technique was shown to approach the performance of the exhaustive search. We concluded by characterizing the security vs reliability trade-off in terms of the intercept probability vs the outage probability.

Abating Jamming in Free Space Optical Systems—A Game-Theoretic Solution

Free space optical (FSO) channel provides a significantly large transmission capacity. However, in the presence of random jamming attacks, the efficacy of FSO communication channel can be affected critically. In this paper, the discrete-input continuous-output memoryless channel (DCMC) capacity of a single-input single-output FSO communication system is investigated under the random jamming effects. The ergodic channel capacity analysis is performed over additive non-Gaussian noise channel (jamming noise channel). The derived closed-form expression of DCMC capacity for the considered FSO system and also, the effects of partial-band jamming and broadband jamming over the FSO channel capacity are verified through simulation results. It is observed that the FSO channel capacity is very sensitive to the degree of jamming and the ergodic channel capacity alters crucially even for small change in jamming probability. The derived results are utilized to study the considered network in the presence of a rational jammer whose ability to jam is limited by its battery capacity. The presence of a rational jammer is addressed by modelling the interaction between the FSO transmitter and the jammer as a non-cooperative game. The closed-form expressions of the equilibrium of the proposed game are derived and verified through simulation. The game-theoretic solution provides a performance improvement of 74% in comparison to uniform power allocation.

Priority-Aware Secure Precoding Based on Multi-Objective Symbol Error Ratio Optimization

The secrecy capacity based on the assumption of having continuous distributions for the input signals constitutes one of the fundamental metrics for the existing physical layer security (PHYS) solutions. However, the input signals of real-world communication systems obey discrete distributions. Furthermore, apart from the capacity, another ultimate performance metric of a communication system is its symbol error ratio (SER). In this article, we pursue a radically new approach to PHYS by considering rigorous direct SER optimization exploiting the discrete nature of practical modulated signals. Specifically, we propose a secure precoding technique based on a multi-objective SER criterion, which aims for minimizing the confidential messages' SER at their legitimate user, while maximizing the SER of the confidential messages leaked to the illegitimate user. The key to this challenging multi-objective optimization problem is to introduce a priority factor that controls the priority of directly minimizing the SER of the legitimate user against directly maximizing the SER of the leaked confidential messages. Furthermore, we define a new metric termed as the security-level, which is related to the conditional symbol error probability of the confidential messages leaked to the illegitimate user. Additionally, we also introduce the secure discrete-input continuous-output memoryless channel (DCMC) capacity referred to as secure-DCMC-capacity, which serves as a classical security metric of the confidential messages, given a specific discrete modulation scheme. The impacts of both the channel's Rician factor and the correlation factor of antennas on the security-level and the secure-DCMC-capacity are investigated. Our simulation results demonstrate that the proposed priority-aware secure precoding based on the direct SER metric is capable of securing transmissions, even in the challenging scenario, where the eavesdropper has three receive antennas, while the legitimate user only has a single one.

On the Discrete-Input Continuous-Output Memoryless Channel Capacity of Layered ACO-OFDM

Layered Asymmetrically Clipped Optical Orthogonal Frequency Division Multiplexing (LACO-OFDM) has been proposed for optical communications and has attracted much attention, thanks to its flexibility in terms of power vs. spectral efficiency. In this article, we propose algorithms for optimizing the Discrete-input Continuous-output Memoryless Channel (DCMC) capacity of LACO-OFDM. Then, an algorithm is proposed for maximizing the capacity for twin-layer LACO-OFDM by optimizing the power sharing between the layers. This is followed by the conception of a more general algorithm applicable to LACO-OFDM having an arbitrary number of layers. Numerical results are provided for quantifying the capacity improvement attained by the proposed algorithm. Moreover, an adaptive scheme is proposed for adjusting the number of layers to be used for maximizing the capacity at different SNRs.

Polarization Modulation Design for Reduced RF Chain Wireless

In this treatise, we introduce a novel polarization modulation (PM) scheme, where we capitalize on the reconfigurable polarization antenna design for exploring the polarization domain degrees of freedom, thus boosting the system throughput. More specifically, we invoke the inherent properties of a dual polarized (DP) antenna for transmitting additional information carried by the axial ratio (AR) and tilt angle of elliptic polarization, in addition to the information streams transmitted over its vertical (V) and horizontal (H) components. Furthermore, we propose a special algorithm for generating an improved PM constellation tailored especially for wireless PM modulation. We also provide an analytical framework to compute the average bit error rate (ABER) of the PM system. Furthermore, we characterize both the discrete-input continuous-output memoryless channel (DCMC) capacity and the continuous-input continuous-output memoryless channel (CCMC) capacity as well as the upper and lower bounds of the CCMC capacity. The results show the superiority of our proposed PM system over conventional modulation schemes in terms of both higher throughput and lower BER. In particular, our simulation results indicate that the gain achieved by the proposed $Q$ -dimensional PM scheme spans between 10dB and 20dB compared to the conventional modulation. It is also demonstrated that the PM system attains between 54% and 87.5% improvements in terms of ergodic capacity. Furthermore, we show that this technique can be applied to MIMO systems in a synergistic manner in order to achieve the target data rate target for 5G wireless systems with much less system resources (in terms of bandwidth and the number of antennas) compared to existing MIMO techniques.

Compressed Sensing-Aided Multi-Dimensional Index Modulation

In this paper, we conceive a compressed sensing (CS)-aided multi-dimensional index modulation (IM) scheme, where the benefits of space–time shift keying, orthogonal frequency-division multiplexing relying on the frequency domain IM, and spatial modulation are explored. Explicitly, extra information bits are transmitted through the active indices of both the transmit antennas and subcarriers, while striking a flexible design tradeoff between the throughput and the diversity order. Furthermore, CS is invoked in both the transmitter and the receiver of our multi-dimensional system for the sake of improving the system’s design flexibility, while reducing the detector’s complexity. We first present the maximum likelihood (ML) detector of the proposed CS-aided multi-dimensional IM system for characterizing the best-case bound of the proposed system’s performance. Specifically, an upper bound is derived for the average bit error probability, and it is observed that the derived theoretical upper bound becomes very tight with the ML detector simulation curves as the signal-to-noise ratio increases. Then, we propose a reduced complexity detector imposing only a modest bit-error-ratio degradation, where we analyze the computational complexities of both the ML detector and the reduced complexity detector. Furthermore, a soft-input soft-output decoder is proposed for attaining a near-capacity performance, which is analyzed with the aid of extrinsic information transfer (EXIT) charts. The maximum achievable rate of the proposed CS-aided multi-dimensional IM system relying both on the ML detection and on our reduced-complexity-based detector is also evaluated using EXIT charts. In addition, the discrete-input continuous-output memoryless channel capacity of the proposed CS-aided multi-dimensional IM scheme is formulated.

Low complexity LED grouping based precoding‐aided spatial modulation for highly correlated large‐scale MIMO‐VLC channels

In this study, the authors propose a new precoding-aided spatial modulation (SM) to improve the transmission performance over significantly high correlated indoor multi-input multi-output visible light communication (MIMO-VLC) channels. Especially, their precoder design relies on the fixed-sized light-emitting diode (LED) grouping and transmit beamforming, which plays an important role in enhancing the system performance. First, they propose an approximate discrete-input continuous-output memoryless channel capacity based precoder design, which offers better performance at the cost of high-computational complexity. As far as large-scale MIMO-VLC schemes are considered, the proposed precoder design presents to be impractical. Therefore, they develop a spatial correlation measure-based fast LED grouping algorithm to construct the precoder for large-scale MIMO-VLC systems. Their simulation results show that the proposed precoding-aided SM scheme can outperform the precoding-aided spatial multiplexing over significantly high correlated large-scale MIMO-VLC channels when the proposed fast LED grouping is performed, whereas the latter scheme can perform better than their proposed scheme for less correlated channels.

Hierarchical Multi-Functional Layered Spatial Modulation

In pursuit of optimal index modulation -aided multiple-input multiple-output (MIMO) systems, where information is implicitly conveyed by relying on the on/off mechanism of the system’s components in addition to the classical amplitude, phase, or frequency components, we present in a tutorial style our novel multi-functional (MF) architecture of layered multi-set (LMS) modulation. This generalized framework subsumes various MIMO techniques exhibiting different multiplexing and diversity functionalities. Our LMS design relies on three constituents, namely the space-time (ST) unit, the layered unit and the spatial switching unit. More specifically, the ST unit relies on the generalized space-time shift keying (GSTSK) scheme, where $P$ – rather than one – out of $Q$ ST dispersion matrices are selected for dispersing an equivalent number of phase-shift keying/quadrature amplitude modulation symbols across the antennas and time-slots. In the layered unit, multiple GSTSK codewords are stacked within the layers of codewords spread over time and space. The spatial switching unit activates $N_{c}^{t}$ out of $N_{t}$ transmit antennas. Owing to its hierarchical MF architecture, our LMS system strikes a flexible design trade-off between the achievable throughput as well as the attainable diversity gain and it can potentially subsume various conventional MIMO schemes, such as Bell Lab’s Layered Space-Time, space-time block codes, layered steered space-time codes, spatial modulation (SM), space-shift keying, linear dispersion codes, generalized SM, STSK, GSTSK, quadrature SM and multi-set STSK. Additionally, we derive the LMS system’s discrete-input continuous-output memoryless channel capacity, which encompasses the capacity limit of all the LMS subsidiaries. We also propose a two-stage serially concatenated soft-decision (SD) based LMS detector by relying on an inner and an outer decoder that iteratively exchange their extrinsic information in order to achieve a near-capacity performance. Last but not least, we utilize the extrinsic information transfer charts for analyzing the convergence behavior of our SD-aided coded LMS scheme.

Compressed Sensing-Aided Index Modulation Improves Space-Time Shift Keying Assisted Millimeter-Wave Communications

In this treatise, we present the concept of compressed-sensing (CS)-aided space-time shift keying index modulation (STSK-IM), where a virtual domain orthogonal frequency division multiplexing (OFDM) symbol is divided into $N_{a}$ -sized blocks, which carry $K$ STSK codewords over a specific combination of virtual-domain sub-carriers and then converted to the frequency domain with the aid of a CS matrix. We design the system for operation in the milli-meter wave (mmWave) frequency band. Furthermore, we amalgamate our soft-decision-aided scheme both with the concept of coordinate-interleaving as well as a discrete Fourier transform-aided codebook design conceived for analogue beamforming, which is vitally important for mmWave systems. In the proposed system, the number of implicit bits conveyed by the activated sub-carrier frequency index (FI) is determined by the number of the available $K$ to $N_{a}$ sub-carrier permutations. Hence, we propose two FI allocation techniques, namely the distinct FI and the shared FI-based schemes, which strike a tradeoff between the attainable sparsity level and the achievable capacity limit. We then introduce a reduced-complexity detection technique in order to mitigate the detection complexity order of the optimum detector from $\mathcal {O}(N_{c}\cdot (Q\cdot \mathcal {L})^{K})$ to $\mathcal {O}(\hat {N}_{c}\cdot (Q\cdot \mathcal {L})^{K})$ , where $\hat {N}_{c}\le N_{c}$ . We also formulate the discrete-input continuous-output memoryless channel capacity and invoke EXtrinsic Information Transfer charts for characterizing the achievable performance limit of the reduced-complexity aided detector. Finally, we analyze the bit error rate performance of both the uncoded and of our coded CS-aided STSK-IM systems associated with both the optimum and the reduced-complexity detectors.

Channel Capacity of High Altitude Platform Systems: A case study

This paper presents a model for Multiple-Input Multiple-Output (MIMO) Land High Altitude Platform channels and analytical evaluation of Discrete-input Continuousoutput Memoryless Channel capacity for High Altitude Platform (HAP)–MIMO systems, where practical transmission environments are considered. Furthermore, for HAP– Single-Input Single-Output (SISO) systems, we propose an adaptive transmission mechanism relying on the transmit power characterized by value at the transmitter side. Achievable channel capacity bounds are established for both idealized and realistic adaptive coding schemes with well-adopted modulation types, namely Phase Shift Keying and Quadrature Amplitude Modulation. DOI: 10.32913/rd-ict.vol3.no14.540

Discrete‐input continuous‐output memoryless channel capacity of cooperative hierarchical modulation

Hierarchical modulation (HM) is a layered modulation scheme, which is widely employed by the telecommunication industry. The higher flexibility and lower complexity of the HM scheme has its dramatic benefits for wireless communications, hence the achievable performance of cooperation-aided coded HM has drawn substantial research interests. In this study, a triple-layer HM-aided four-node cooperative communication system is proposed, and its discrete-input continuous-output memoryless channel capacity is derived, which is used for finding the optimal position of the relay nodes as well as to design appropriate HM constellations. The authors’ simulation results show that if a rate-1/2 ‘perfect’ channel code is assumed, the four-node network becomes capable of conveying a coded HM-64QAM signal in three time slots at an average signal-to-noise ratio of ?0.71 dB.

Irregular Trellis for the Near-Capacity Unary Error Correction Coding of Symbol Values From an Infinite Set

Irregular joint source and channel coding (JSCC) scheme is proposed, which we refer to as the irregular unary error correction (IrUEC) code. This code operates on the basis of a single irregular trellis, instead of employing a set of separate regular trellises, as in previous irregular trellis-based codes. Our irregular trellis is designed with consideration of the UEC free distance, which we characterize for the first time in this paper. We conceive the serial concatenation of the proposed IrUEC code with an irregular unity rate code (IrURC) code and propose a new EXtrinsic Information Transfer (EXIT) chart matching algorithm for parametrizing these codes. This facilitates the creation of a narrow EXIT tunnel at a low $E_\text{b}/N_0$ value and provides near-capacity operation. Owing to this, our scheme is found to offer a low symbol error ratio (SER), which is within 0.4 dB of the discrete-input continuous-output memoryless channel (DCMC) capacity bound in a particular practical scenario, where gray-mapped quaternary phase shift keying (QPSK) modulation is employed for transmission over an uncorrelated narrowband Rayleigh-fading channel with an effective throughput of $0.508 \,\text{bit}\,{\text{s}}^{-1}\,{\text{Hz}}^{-1}$ . Furthermore, the proposed IrUEC–IrURC scheme offers a SER performance gain of 0.8 dB, compared to the best of several regular and irregular separate source and channel coding (SSCC) benchmarkers, which is achieved without any increase in transmission energy, bandwidth, transmit duration, or decoding complexity.

Near-Capacity Wireless System Design Principles

In this tutorial, the design procedure of near-capacity channel code design invoking non-binary EXtrinsic Information Transfer (EXIT) charts is illustrated by using design examples of Irregular Concatenated Coding Arrangements (ICCAs) relying on Irregular Convolutional Codes (IrCCs). More specifically, in order to benchmark the near-capacity design examples, both the capacity and the Outage Probability (OP) of the Continuous-input Continuous-output Memoryless Channel (CCMC), of the Discrete-input Continuous-output Memoryless Channel (DCMC) as well as of the Differential Discrete-input Continuous-output Memoryless Channel (D-DCMC) are characterised. Furthermore, the EXIT-chart aided near-capacity design principles are illustrated by detailing the design process of three characteristic prototype schemes, which represent the family of coherent and non-coherent detection based systems as well as Multi-Input Multi-Output (MIMO) systems, respectively. Moreover, the beneficial application of the EXIT-chart based design principle is also demonstrated in the context of cooperative systems using a specific distributed MIMO prototype scheme.

Error Probability and Capacity Analysis of Generalised Pre-Coding Aided Spatial Modulation

The recently proposed multiple input multiple output (MIMO) transmission scheme termed as generalized pre-coding aided spatial modulation (GPSM) is analyzed, where the key idea is that a particular subset of receive antennas is activated and the specific activation pattern itself conveys useful implicit information. We provide the upper bound of both the symbol error ratio (SER) and bit error ratio (BER) expression of the GPSM scheme of a low-complexity decoupled detector. Furthermore, the corresponding discrete-input continuous-output memoryless channel (DCMC) capacity as well as the achievable rate is quantified. Our analytical SER and BER upper bound expressions are confirmed to be tight by our numerical results. We also show that our GPSM scheme constitutes a flexible MIMO arrangement and there is always a beneficial configuration for our GPSM scheme that offers the same bandwidth efficiency as that of its conventional MIMO counterpart at a lower signal to noise ratio (SNR) per bit.

Optimization of irregular mapping for error floor removed bit-interleaved coded modulation with iterative decoding and 8PSK

Bit-interleaved coded modulation with iterative decoding (BICM-ID) is investigated for bandwidth efficient transmissions, where the error performance can be improved by employing a suitable symbol mapping. In this paper, we introduce a low-complexity irregular mapping optimization for BICM-ID with irregular doping and 8-ary phase-shift keying (8PSK) modulation over both additive white Gaussian noise (AWGN) and Rayleigh fading channels, for the purpose of achieving near-capacity performances. The Euclidean distance spectrum and the extrinsic information transfer (EXIT) chart analysis are aided for the proposed optimization to provide design guidelines of mappings. The bit error rate (BER) results demonstrate that the BICM-ID system with the proposed optimal irregular mapping and doping outperforms the other typical symbol mappings, and yields a gain of about 0.1 and 0.5 dB for AWGN and Rayleigh fading channels, respectively. Moreover, it is only about 0.5 and 0.73 dB away from the discrete-input continuous-output memoryless channel (DCMC) capacity limits of AWGN and Rayleigh fading channels, respectively, at the BER of 10−4 and for the spectral efficiency of 2 bits/channel use.

Irregular Convolution and Unity-Rate Coded Network-Coding for Cooperative Multi-User Communications

Near-Capacity Multi-user Network-coding (NCMN) based systems operating in multiple modes and relying on an amalgamated Irregular Convolutional Code, a Unity-Rate Code and M-ary Phase-Shift Keying are proposed. We consider a multiuser network in which the users cooperatively transmit their independent information to a common base station (BS). Extrinsic Information Transfer (EXIT) charts were used for designing the proposed NCMN scheme for the sake of approaching the Discrete-input Continuous-output Memoryless Channel's (DCMC) capacity. The NCMN systems are capable of simultaneously exploiting the advantages of all the new modes we designed for our system and those of the conventional mode. The design principles presented in this contribution can be extended to a vast range of NCMN based systems using arbitrary channel coding schemes.

Successive AF/DF Relaying in the Cooperative DS-CDMA Uplink: Capacity Analysis and Its System Architecture

A successive-relaying-aided network (SRAN) is designed for a multiuser spread-spectrum scenario conceived for noncoherent (NC) detection to convert the typical 50% half-duplex relaying induced throughput loss to a potential user-load reduction of the code-division multiple-access (CDMA) system, where the NC allows us to avoid the extra power consumption imposed by channel estimation. We commence by evaluating the NC discrete-input-continuous-output memoryless channel (DCMC) capacity of both the amplify-and-forward-based (AF) and decode-and-forward-based (DF) SRANs in the direct-sequence CDMA (DS-CDMA) uplink (UL). While NC detection has the added benefit of eliminating both the pilot overhead and the power-hungry channel estimation, it tends to form an error floor at high Doppler frequencies. We mitigate this problem using multiple-symbol detection, which increases the detection complexity upon extending the detection window. Finally, a relay-aided soft-input-soft-output multiple-symbol differential sphere detection (SISO-MSDSD) CDMA regime is proposed, which significantly reduces the system's complexity without sacrificing its performance.

On the Joint Optimization of Dispersion Matrices and Constellations for Near-Capacity Irregular Precoded Space-Time Shift Keying

Joint dispersion-matrix and constellation optimization algorithm is proposed, which is invoked for the recent space-time shift keying (STSK) scheme. More specifically, the theoretical gradients of the discrete-input continuous-output memoryless channel's (DCMC) capacity with respect to both a dispersion-matrix set and to the modem constellations are derived, which allows a substantial reduction in the computational complexity required for maximizing the system's capacity. Furthermore, we also conceive a near-capacity irregular-precoded STSK (IR-PSTSK) architecture, which is designed with the aid of extrinsic information transfer (EXIT) charts, while invoking STSK subcodes, which are optimized by using the proposed algorithm.