Signal Constellation Size Research Articles

Performance Analysis of MIMO Techniques for a Pyramid Receiver in an Indoor MIMO-VLC System

In an indoor multiple-input multiple-output (MIMO) visible light communication (VLC) system, line of sight (LoS) channel links are present between a light-emitting diode (LED) based transmitter and a photodetector (PD) based receiver. The PDs in the receiver are closely packed resulting in a high channel correlation. To overcome channel correlation and improve the performance of the MIMO-VLC system, angle diversity receivers (ADRs) are commonly employed. The channel matrix entries depend on the normal vectors of the PDs, which in turn depend on the elevation angle (EA) of the PDs. Thus, by having normal vectors pointing in different directions, the channel correlation can be considerably reduced. This paper considers a special type of ADR called pyramid receiver (PR) and employs a 4x4 MIMO-VLC system. In this paper, different MIMO algorithms such as repetition coding (RC) and spatial multiplexing (SMP) are considered to exhibit and compare the bit-error-rate (BER) performance of the fixed and variable EA MIMO-VLC systems. The results show that an SMP-employed MIMO-VLC system outperforms the RC-employed MIMO-VLC system. SMP results in an spatial multiplexing gain that varies linearly with the number of LEDs whereas RC does not yield any spatial multiplexing gain. To attain the same spectral efficiency i.e. 4 bit/s/Hz, a larger signal constellation size is required for RC employed MIMO-VLC system to achieve the same BER as of an SMP employed MIMO-VLC system. Similarly, the BER performance of variable EA MIMO-VLC systems is better as compared to fixed EA MIMO-VLC systems.

Optimizing the Shape of Signals with Quadrature Amplitude Modulation According to the Criterion of Given Reduction Rate of Out-of-Band Emissions

Introduction. The growth in the volume of information transmitted through communication channels leads to their significant congestion. Almost all methods conventionally used to increase the data transfer rate in given frequency bands have been exhausted. In this regard, it is of interest to use new approaches aimed at improving the spectral efficiency of radio engineering and telecommunication systems by applying optimal signals that make it possible to use the bandwidth reserves of transmission channels given by Shannon's theory.Aim. Improvement of the spectral efficiency of digital messaging systems by using signals with a compact spectrum and increased volume of the channel alphabet at the same time as minimizing energy losses.Materials and methods. When searching for optimal signals, the mathematical apparatus of communication theory and functional analysis, as well as the methods of calculus of variations, were used. The evaluation of bit error rate performance of the obtained optimal signals transmitted in a channel with additive white Gaussian noise was performed in the MatLab environment. Results. It was established that, in a channel with additive white Gaussian noise, optimal signals with a signal constellation size of 64 in the case of quadrature amplitude-phase modulation provide an energy gain of more than 1 dB relative to signals obtained by narrowband filtering under the conditions of uncontrolled intersymbol interference. Optimal signals were shown to provide for an energy gain of 4.9 dB with respect to signals based on narrow-band filtering at a fixed spectral efficiency of 7 (bit/s)/Hz.Conclusion. The paper proposes a method for improving the spectral efficiency of quadrature signals with amplitudephase modulation, based on the use of optimal pulse shapes obtained as a result of solving an optimization problem. The optimization problem was solved according to the criterion of minimizing out-of-band emissions with the constraint on bit error rate performance in case of amplitude-phase modulation. The energy and spectral efficiency of signals with optimal pulse shapes and signals based on narrow-band filtering were compared.

Efficient Spectrum Utilization via Pulse Shape Design for Fixed Transmission Networks

Microwave backhaul links are characterized by high signal-to-noise ratios permitting spectrally-efficient transmission. The used signal constellation sizes and achievable data rates are typically limited by transceiver impairments, predominantly by phase noise from non-ideal carrier generation. In this paper, we propose a new method to improve the data rate over such microwave links. We make use of the fact that adjacent frequency channels are inactive in many deployment scenarios. We argue that additional data can be transmitted in the skirts of the spectral mask imposed on the transmission signal by regulation. To accomplish this task, we present a shaped wideband single-carrier transmission using non-Nyquist pulse shapes. In particular, we design spectrum-skirt filling (SSF) pulse shaping filters that follow the spectral mask response, and perform detection using an accordingly increased sampling frequency at the receiver. We evaluate the achievable information rates of the SSF-based transmission considering practical dispersive channels and non-ideal transmitter and receiver processing. To compensate for phase noise impairments, we derive carrier phase tracking and estimation techniques, and utilize them in tandem with nonlinear precoding which mitigates the intersymbol interference introduced by the non-Nyquist SSF shaping filter. Quantitative performance evaluations show that the proposed system design achieves higher data rates in a dispersive microwave propagation environment with respect to the conventional transmission with Nyquist pulse shaping.

New four‐dimensional signal constellations construction

In this study, the authors present new four-dimensional signal constellations constructed based on combinations of binary frequency shift keying and M -ary phase-shift keying. Such a system contains two sub-constellations and phase shift keying modulation is carried out based on two different frequencies. They obtained an analytical expression for calculating of squared Euclidean distance for different signal constellations. The new method of system construction and optimisation is presented with the help of this formula. Having used this method for various signal constellations and modulation indexes, they constructed optimised systems. In tables, they present the parameters for signal constellation sizes 4, 5, …,16 and modulation indexes 0.1, 0.2, …,1. Such signal constellations can be used in MIMO systems and, in particular, in generalised multi-stream spatial modulation systems.

Turbo Message Passing-Based Receiver Design for Time-Varying OFDM Systems

In this paper, we study time-varying orthogonal frequency division multiplexing (OFDM) systems, and propose a joint channel-and-signal estimation receiver based on turbo message passing (TMP) to efficiently suppress inter-carrier interference (ICI). We establish a factor graph representation of the problem and divide the whole factor graph into two parts, one for channel estimation and the other for signal detection. For the first part, we use Gaussian message passing (GMP) for channel estimation; for the second part, a discrete state space (DSS) model is employed to describe the transition of signal states, and a forward-backward algorithm is adopted for message passing over the transition trellis in signal detection. The resulting algorithm is referred to as DSS-GMP. The complexity of DSS-GMP quickly becomes the bottleneck as the increase of the signal constellation size and the ICI width. To address this issue, we further develop a continuous-state-space (CSS) model based turbo message passing algorithm, where the messages of modulated signals are approximated as continuous Gaussian messages. Numerical results demonstrate that the TMP based scheme significantly outperforms the state-of-the-art schemes.

Opportunistic Group Antenna Selection in Spatial Modulation Systems

This paper proposes an opportunistic spatial modulation (OSM) scheme where the transmit antennas are divided into $K\geq 1 $ equal groups, and the best antenna from each group is selected to form a $K$ transmit antenna subset for implementing spatial modulation (SM). Thus, the activation of one antenna from the subset to transmit one of the $M$ -ary modulation symbols achieves a data rate of $\log _{2} (K) +\log _{2} (M)$ bits per channel use. Notably, special cases of OSM include conventional SM and pure single transmit antenna selection. To characterize and comparatively evaluate OSM, we first consider phase-shift keying modulation and derive a closed-form, improved union-bound of symbol error probability (SEP) with a single-antenna receiver. Explicit expressions for the SEP in the high signal-to-noise ratio regime are also presented. Extensions to quadrature amplitude modulation analysis and simulations of multiple-antenna reception case are also provided. Simulation results corroborate the analytical results and reveal the interesting interplay between the signal and spatial constellation diagrams. For a given number of transmit antennas and targeted data rate, asymptotically, the SEP can be minimized by using only one antenna group and the largest size of signal constellation, as this configuration achieves the full-diversity order.

A simple low-complexity algorithm for generalized spatial modulation

Generalized spatial modulation (GSM) is an extension of spatial modulation which is significant for the next generation communication systems. Optimal detection process for the GSM is the maximum-likelihood (ML) detection which jointly detects the antenna combinations and transmitted symbols. However, the receiver is much more complicated than SM due to inter-antenna interference and/or increased number of combinations. Therefore, the computational complexity of the ML detection grows with the number of transmit antennas and the signal constellation size. In this letter, we introduce a novel and simple detection algorithm which uses sub-optimal method based on the least squares solution to detect likely antenna combinations. Once the antenna indices are detected, ML detection is utilized to identify the transmitted symbols. For obtaining near-ML performance while keeping lower complexity than ML detection, sphere decoding is applied. Our proposed algorithm reduces the search complexity while achieving a near optimum solution. Computer simulation results show that the proposed algorithm performs close to the optimal (ML) detection resulting in a significant reduction of computational complexity.

Millimeter-Wave MIMO Prototype: Measurements and Experimental Results

Millimeter-wave MIMO systems are one of the candidate schemes for 5G wireless standardization efforts. In this context, the main contributions of this article are three-fold. First, we describe parallel sets of measurements at identical transmit-receive location pairs with 2.9, 29 and 61 GHz carrier frequencies in indoor office, shopping mall, and outdoor settings. These measurements provide insights on propagation, blockage and material penetration losses, and the key elements necessary in system design to make mm-Wave systems viable in practice. Second, one of these elements is hybrid beamforming necessary for better link margins by reaping the array gain with large antenna dimensions. From the class of fully-flexible hybrid beamformers, we describe a robust class of directional beamformers toward meeting the high data-rate requirements of mm-Wave systems. Third, leveraging these design insights, we then describe an experimental prototype system at 28 GHz that realizes high data rates on both the downlink and uplink and robustly maintains these rates in outdoor and indoor mobility scenarios. In addition to maintaining large signal constellation sizes in spite of radio frequency challenges, this prototype leverages the directional nature of the mm-Wave channel to perform seamless beam switching and handover across mm-Wave base stations, thereby overcoming the path losses in non-line-of-sight links and blockages encountered at mm-Wave frequencies.

Capacity achieving nonbinary LDPC coded non-uniform shaping modulation for adaptive optical communications.

A mutual information inspired nonbinary coded modulation design with non-uniform shaping is proposed. Instead of traditional power of two signal constellation sizes, we design 5-QAM, 7-QAM and 9-QAM constellations, which can be used in adaptive optical networks. The non-uniform shaping and LDPC code rate are jointly considered in the design, which results in a better performance scheme for the same SNR values. The matched nonbinary (NB) LDPC code is used for this scheme, which further improves the coding gain and the overall performance. We analyze both coding performance and system SNR performance. We show that the proposed NB LDPC-coded 9-QAM has more than 2dB gain in symbol SNR compared to traditional LDPC-coded star-8-QAM. On the other hand, the proposed NB LDPC-coded 5-QAM and 7-QAM have even better performance than LDPC-coded QPSK.

Performance Analysis of Multiantenna MC DS CDMA System Over Correlated η–µ Multipath Fading Channels

In wireless communication channels, the performance of the wireless communication systems deteriorate due to the severe influence of interference, multipath fading, path loss, shadowing, and noise, respectively. In this paper, we investigate the performance of the system transmitting over correlated ź---µ frequency selective fading channels in terms of average error rates. Based on moment generating function approach, closed form expressions for average error probabilities for the system are derived and represented in terms of Appell's hypergeometric functions and Lauricella's multivariate hypergeometric functions. In addition, probability density function based approach is employed to determine the formulae for average error probabilities of the system operating over correlated ź---µ multipath fading channels. The numerical results reveal that, the effects of correlation, decaying power factor and signal constellation size can be reduced using frequency, spatial antennas and path diversities, respectively. Furthermore, we confirm the correctness of the analytical approaches through Monte Carlo simulation technique.

Error rate performance analysis of multiantenna MC DS-CDMA system over η–μ frequency selective fading channels with arbitrary parameters

Wireless communication channels have harmful impact on the performance of the wireless communication systems due to the severe influences of multipath fading, path loss, shadowing, intentional and unintentional interference, and noise, respectively. In this paper, we investigate the performance of the orthogonal multicarrier direct sequence code division multiple access (MC DS-CDMA) system coupled with multiple input multiple output (MIMO) system operating over independent nonidentically distributed (i.ni.d) η–μ multipath fading channels in terms of average error probability. Based on moment generating function (MGF) and probability density function (PDF) approaches, closed form expressions for average error probability of binary phase shift keying (BPSK), multilevel phase shift keying (MPSK), and square M-ary quadrature amplitude modulation (MQAM) schemes are derived and expressed in terms of Appell's hypergeometric functions and Lauricella's multivariate hypergeometric functions. The numerical results show that the effects of arbitrary fading parameters, decaying power factor (d), and signal constellation size on the system performance can be reduced using spatial and temporal path diversities. We validate the correctness of the analytical approaches using Monte Carlo simulation techniques.

Bounds on Fast Decodability of Space-Time Block Codes, Skew-Hermitian Matrices, and Azumaya Algebras

We study fast lattice decodability of space-time block codes for n transmit and receive antennas, written very generally as a linear combination Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i=1</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2l</sup> s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> , where the si are real information symbols and the A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> are n×n ℝ-linearly independent complex-valued matrices. We show that the mutual orthogonality condition A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> * + A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> * = 0 for distinct basis matrices is not only sufficient but also necessary for fast decodability. We build on this to show that for full-rate (l = n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) transmission, the decoding complexity can be no better than |S|(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> +1), where |S| is the size of the effective real signal constellation. We also show that for full-rate transmission, g-group decodability, as defined by Jithamithra and Rajan, is impossible for any g ≥ 2. We then use the theory of Azumaya algebras to derive bounds on the maximum number of groups into which the basis matrices can be partitioned so that the matrices in different groups are mutually orthogonal-a key measure of fast decodability. We show that in general, this maximum number is of the order of only the 2-adic value of n. In the case where the matrices A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> arise from a division algebra, which is most desirable for diversity, we show that the maximum number of groups is only 4. As a result, the decoding complexity for this case is no better than |S|⌈l/2⌉ for any rate l.

MGF Based Approximate SER Calculation of SM MIMO Systems Over Generalized η − μ and κ − μ Fading Channels

Spatial modulation (SM) is a multiple input multiple output (MIMO) wireless communication system that gives better spectral efficiency without costing extra bandwith for the same signal constellation size. In an SM MIMO system with $$N_t$$Nt transmitting antennas, spectral efficiency increases by $$log_2(N_t)$$log2(Nt). The superior performance of SM systems over other MIMO systems like Alamouti Space-Time Block Codes and Vertical Bell Laboratories Layered Space-Time is already reported in the literature. In this paper, we analyzed the symbol error rate (SER) performance of an SM system in generalized $$\eta-\mu $$?-μ and $$\kappa - \mu $$?-μ fading channels for several modulation schemes. A closed form expression for approximate SER is derived using moment generating function (MGF) approach and the results are validated using Monte Carlo simulations. The approximate SER expression obtained in this communication is applicable for any fading channels whose MGF is known. The SER analysis over generalized fading channels can be easily deduced to various classical fading channels like Rayleigh, Rician, Nakagami-m and Nakagami-q fading channels by choosing appropriate values of $$\kappa $$?, $$\mu $$μ and $$\eta $$?.

An Efficient Space Time Block Code for LTE-A System

In this study, a new space time block code (STBC) is proposed for long term evolution-advanced (LTE-A) system that is equipped with three time slots and two antennas. The introduced STBC has the following characteristics: i) it achieves rate one and full diversity, ii) its maximum likelihood (ML) decoding requires a joint detection of three real symbols, iii) the minimum determinant value (MDV) does not vanish by increasing signal constellation size, and iv) bit error rate (BER) results show that the proposed STBC outperforms previously presented schemes for LTE-A at high SNRs.

Partition-Based Hybrid Decoding (PHD): A Class of ML Decoding Schemes for MIMO Signals Based on Tree Partitioning and Combined Depth- and Breadth-First Search

In this paper, we propose a hybrid maximum likelihood (ML) decoding scheme for multiple-input multiple-output(MIMO) systems. After partitioning the searching tree into several stages, the proposed scheme adopts thecombination of depth- and breadth-first search methods in an organized way. Taking the number of stages, the size ofsignal constellation, and the number of antennas as the parameter of the scheme, we provide extensive simulationresults for various MIMO communication conditions. Numerical results indicate that, when the depth- and breadth-firstsearch methods are employed appropriately, the proposed scheme exhibits substantially lower computationalcomplexity than conventional ML decoders while maintaining the ML bit error performance.

OFDM AF Relaying Under I/Q Imbalance: Performance Analysis and Baseband Compensation

We analyze the outage performance of half-duplex amplify-and-forward relaying in an OFDM system with MRC detection in the presence of I/Q imbalance and compare it with that of the direct transmission mode. Both analytical and numerical results demonstrate that the direct mode can outperform the amplify-and-forward mode even under moderate levels of uncompensated I/Q imbalance. The cross-over I/Q imbalance levels are determined analytically to be inversely proportional to the cube of the signal constellation size. In addition, we present a low-complexity receiver-based digital baseband I/Q imbalance compensation scheme for the amplify-and-forward mode and analyze its EVM performance. Furthermore, we derive accurate analytical approximations for the EVM performance as a function of relay location and I/Q imbalance level with and without compensation.

A Novel Space Time Block Code Scheme for Three Time Slots and Two Transmit Antennas

Mobile station (MS) in the Long Term Evolution Advanced (LTE-A) equips with two transmit antennas and the data are transmitted during three time slots. This has brought up an interesting space time block code (STBC) design for LTE-A. In this paper, a novel STBC scheme is proposed for three time slots and two antennas. The proposed STBC scheme has these properties: i) the scheme can achieve full rate and full diversity, ii) its maximum likelihood (ML) decoding requires a joint detection of three real symbols, iii) the minimum determinant values (MDVs) do not vanish by increasing signal constellation sizes, iv) compatible with the single antenna transmission mode. Simulation results show that the proposed scheme has the same bit error rate (BER) performance with the best known scheme at high signal to noise ratio (SNR).

Performance Comparison of MIMO Techniques for Optical Wireless Communications in Indoor Environments

In this paper, we compare the performance of multiple-input-multiple-output (MIMO) techniques applied to indoor optical wireless communications (OWC) assuming line-ofsight (LOS) channel conditions. Specifically, several 4 × 4 setups with different transmitter spacings and different positions of the receiver array are considered. The following MIMO algorithms are considered: Repetition Coding (RC), Spatial Multiplexing (SMP) and Spatial Modulation (SM). Particularly, we develop a framework to analytically approximate the bit error ratios (BERs) of these schemes and verify the theoretical bounds by simulations. The results show that due to diversity gains, RC is robust to various transmitter-receiver alignments. However, as RC does not provide spatial multiplexing gains, it requires large signal constellation sizes to enable high spectral efficiencies. In contrast, SMP enables high data rates by exploiting multiplexing gains. In order to provide these gains, SMP needs sufficiently low channel correlation. SM is a combined MIMO and digital modulation technique. We show that SM is more robust to high channel correlation compared to SMP, while enabling larger spectral efficiency compared to RC. Moreover, we investigate the effect of induced power imbalance between the multiple transmitters. It is found that power imbalance can substantially improve the performance of both SMP and SM as it reduces channel correlation. In this context, we also show that blocking some of the links is an acceptable method to reduce channel correlation. Even though the blocking diminishes the received energy, it outweighs this degradation by providing improved channel conditions for SMP and SM. For example, blocking 4 of the 16 links of the 4 × 4 setup improves the BER performance of SMP by more than 20 dB, while the effective signal to noise ratio (SNR) is reduced by about 2 dB due to the blocking. Therefore, MIMO techniques can provide gains even under LOS conditions which provide only little channel differences.

Capacity maximisation in eigen-multiple-input multiple-output using adaptive modulation and Reed–Solomon coding

Eigen-multiple-input multiple-output (MIMO) with water-filling gives the maximum information-theoretic capacity, but realising this maximisation is not straightforward because practical factors are omitted. Adaptive modulation and error coding are combined for finding the maximum practicable capacity (throughput of correctly detected bits) in eigen-MIMO. Quadrature amplitude modulation (QAM) is the logical choice of modulation and here Reed–Solomon (RS) coding is used. RS coding has the advantages of algorithmic simplicity, low-memory requirements, and decoder complexity, and its unique closed-form error probability makes it possible to obtain an optimal power allocation, signal constellation size(s), and code rate(s) on the eigenchannels, for the maximum practicable capacity. The proposed adaptive scheme is applied to two architectures for the encoders/decoders (CODECs): outer coding, where a single CODEC is deployed for the overall serial data; and inner coding, where there is a CODEC for each eigenchannel. The optimal power allocation is different to the water-filling used for the information-theoretic capacity. Also, simple and accurate approximations are found for the bit-error rate (BER) of a single Rayleigh channel and of a 2×2 system. Finally, a selection procedure between different system configurations is presented for obtaining the highest practicable capacity subject to either average or instantaneous output BER.

Nonbinary LDPC-Coded Modulation for Rate-Adaptive Optical Fiber Communication Without Bandwidth Expansion

A rate-adaptive nonbinary low-density parity-check-coded modulation scheme is proposed to enable fiber-optic transmission at variable bit rates by adjusting the spectral efficiency (SE) of transmission while keeping the occupied bandwidth fixed. To achieve a given SE within a fixed bandwidth, both the underlying signal constellation size and the forward error correction code rate are adjusted. Using the scarce resource of bandwidth more effectively, the proposed scheme is expected to find applications in both current fixed-grid networks and in future networks that might adopt flexible grid approach.