Quadrature Amplitude Modulation Constellations Research Articles

Low‐complexity EDAS and low‐complexity detection scheme for MPSK spatial modulation

Euclidean-distance antenna selection (EDAS) is an effective transmit AS technique for spatial modulation (SM). This study presents a low-complexity (LC) EDAS scheme for the M-ary phase shift keying (MPSK) SM. The LC-EDAS for MPSK SM (LC-MPSK-EDAS) is achieved by exploiting the rotational symmetry of the MPSK constellation and using singular value decomposition (SVD_EDAS) for factorisation of the modified channel matrix. A further reduction in complexity is achieved by eliminating the process of conditioning on elements of the MPSK symbol set. The complexity of the proposed scheme is independent of the order M of MPSK. Also, in this study, an LC near maximum likelihood (ML) detection scheme for MPSK SM systems, signal vector-based detection (SVD), is implemented. Though this scheme provides poor results when using the M-ary quadrature amplitude modulation constellation, it is found that the error performance of this scheme for MPSK constellations has very near ML results. The simulation results show that even at high signal-to-noise values this scheme maintains near ML performance. To support the results, the closed-form expression of the bit error rate for the MPSK constellation is derived.

Symbol Error Probability of Hexagonal QAM

This letter studies the symbol error probability (SEP) of quadrature-amplitude modulation (QAM) signals constructed from the hexagonal lattice, known as hexagonal QAM or triangular QAM. In particular, we propose a simple and accurate approximation for the SEP of hexagonal QAM in additive white Gaussian noise. Simulation results show that the proposed approximation is very accurate for all the best-known QAM constellations constructed from the hexagonal lattice, including triangular QAM, for both high and low signal-to-noise ratio. In addition, the proposed approximation is suitable for the accurate estimation of the SEP of hexagonal QAM in slow-fading channels, such as Rayleigh fading channels.

Channel Estimation and Detection in Hybrid Satellite–Terrestrial Communication Systems

We address the problem of amplify-and-forward (AF) relaying in a hybrid satellite-terrestrial communication system with unknown channel gains. A masked destination earth station (ES) receives the signal forwarded by a relaying ES, i.e., from a terrestrial link. There is no direct transmission from the satellite to the destination ES. The satellite-relay ES (satellite link) and relay ES-destination ES (terrestrial link) links are assumed to follow shadowed Rician fading and Nakagami-m fading, respectively. A scheme for channel estimation and detection of transmitted signal from the satellite to the destination ES is proposed. The terrestrial link is estimated separately, whereas the cooperative hybrid link (satellite-relay-destination) is estimated jointly with symbol detection. The average symbol error rates of the M-ary phase-shift keying and M-ary quadrature amplitude modulation constellations are derived for the considered hybrid communication system. Moreover, we also derive the analytical diversity order of the considered system with estimated channel gains. It is shown by simulation and analysis that the estimation error does not affect the diversity order of the system. Furthermore, the average and asymptotic capacity of the system is also derived by using the moment-generating function approach.

Two-Stage n-PSK Partitioning Carrier Phase Recovery Scheme for Circular mQAM Coherent Optical Systems

A novel two-stage n-PSK partitioning carrier phase recovery (CPR) scheme for circular multilevel quadrature amplitude modulation (C-mQAM) constellations is presented. The first stage of the algorithm provides an initial rough estimation of the received constellation, which is utilized in the second stage for CPR. The performance of the proposed algorithm is studied through extensive simulations at the forward error correction bit error rate targets of 3.8 × 10−3 and 1 × 10−2 and is compared with different CPR algorithms. A significant improvement in the combined linewidth symbol duration product (ΔνTs) tolerance is achieved compared to the single-stage n-PSK partitioning scheme. Superior performance in the ΔνTs tolerance compared to the blind phase search algorithm is also reported. The relative improvements with respect to other CPR schemes are also validated experimentally for a 28-Gbaud C-16QAM back-to-back transmission system. The computational complexity of the proposed CPR scheme is studied, and reduction factors of 24.5 | 30.1 and 59.1 | 63.3 are achieved for C-16QAM and C-64QAM, respectively, compared to single-stage BPS in the form of multipliers | adders.

Low-Complexity Demapping Algorithm for Two-Dimensional Non-Uniform Constellations

Non-uniform constellations (NUCs) have been recently introduced in digital broadcasting systems to close the remaining gap to the unconstrained Shannon theoretical limit. Compared to uniform quadrature amplitude modulation (QAM) constellations, NUCs provide a signal-to-noise ratio (SNR) gain (i.e., a reduction in the required SNR), especially for high-order constellations. One-dimensional NUCs (1D-NUC) have a squared shape with non-uniform distance between the constellation symbols. Since the I and Q components remain as two independent signals, a 1D-demapper as for uniform QAM constellations is feasible. Two-dimensional NUCs (2D-NUC) provide a better performance than 1D-NUCs, since they are designed by relaxing the square shape constraint, with arbitrary shape along the complex plane. However, the main drawback of 2D-NUCs is the higher complexity at the receiver, since a 2D-demapper is needed. In this paper, we propose a demapping algorithm that reduces from 69% to 93% the number of required distances when using 2D-NUCs. The algorithm discards or replicates those constellation symbols that provide scarce information, with a performance degradation lower to 0.1 dB compared to the optimal maximum likelihood demapper.

Locally Diverse Constellations From the Special Orthogonal Group

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 cutoff rate at low signal-to-noise ratio (SNR) and bit error rate at high SNR in dimension $n = 4$ . However, a quadrature amplitude modulation (QAM) constellation rotated by such a matrix lacks full diversity, in contrast with the conventional wisdom that good signal sets exhibit full diversity. A new notion of diversity, referred to as local diversity, is introduced to attempt to account for this behavior. Roughly, a locally fully diverse constellation is fully diverse only in small neighborhoods. A local variant of the minimum product distance is also introduced and is shown experimentally to be a superior predictor of constellation performance than the minimum product distance in dimension $n = 4$ .

Discrete Multi-Tone Transmission With Optimized QAM Constellations for Short-Reach Optical Communications

We investigate performance of optimized M-ary quadrature amplitude modulation (M-QAM) constellations in short-reach single-polarization (SP) and dual-polarization (DP) discrete multitone (DMT) with direct detection. The constellations are obtained by using an iterative gradient-search algorithm. For the nonsquare constellations, we find bit-to-symbol mappings with a blind search method. Our experiments show that the data rate can be improved in both SP and DP DMT systems by using optimized constellations instead of square M-QAM. Net data transmission rates of 165 and 152 Gb/s are respectively achieved for back-to-back and 2.2 km in a direct-detection DP DMT system assuming forward error correction threshold of $3.8\times 10^{-3}$ .

Green MU-MIMO/SIMO Switching for Heterogeneous Delay-Aware Services With Constellation Optimization

In this paper, we propose adaptive techniques for multiuser multiple-input and multiple-output (MU-MIMO) cellular communication systems, to solve the problem of energy efficient communications with heterogeneous delay-aware traffic. In order to minimize the total transmission power of the MU-MIMO, we investigate the relationship between the transmission power and the M-ary quadrature amplitude modulation (MQAM) constellation size and get the energy efficient modulation for each transmission stream based on the minimum mean square error (MMSE) receiver. Since the total power consumption is different for MU-MIMO and multiuser single input and multiple output (MU-SIMO), by exploiting the intrinsic relationship among the total power consumption model, and heterogeneous delay-aware services, we propose an adaptive transmission strategy, which is a switching between MU-MIMO and MU-SIMO. Simulations show that in order to maximize the energy efficiency and consider different Quality of Service (QoS) of delay for the users simultaneously, the users should adaptively choose the constellation size for each stream as well as the transmission mode.

Layered Multiplexed-Coded Relaying in Wireless Multicast Using QAM Transmissions

We propose layered multiplexed-coded decode-and-forward (LMDF) relaying for a wireless multicast network. Splitting the message into two layers, the source encodes them separately and maps them to a quadrature amplitude modulation (QAM) constellation to achieve superposition, thus allowing partial message recovery at the relay and the destinations. The key component of LMDF is multiplexed coding at the relay that enables each destination to divert all channel resources toward decoding the layers that remain unrecoverable from the source’s transmission. We derive information theoretic achievable rates for LMDF and consider network outage as a performance measure. For a setup with 15 users uniformly spread around the relay, simulations indicate that LMDF outperforms conventional unlayered DF by 1.7 dB and superposition coding-based DF by 1.1 dB, while the respective gains in outage rate at individual users are up to 48.6% and 31.4%.

Carrier Phase Recovery Algorithms for Coherent Optical Circular mQAM Systems

The phase noise tolerance of circular multilevel quadrature amplitude modulation (C-mQAM) constellations employing different carrier phase recovery (CPR) algorithms is studied. A differential decoding scheme and a bit mapping for this type of constellations are proposed. A novel CPR scheme for C-mQAM constellations is also presented. The particular distribution of the constellation points in a C-mQAM signal is exploited to reduce the required Nth power for the removal of the modulation component by a factor of two. Hence, the computational complexity of the proposed algorithm is drastically reduced. The combined linewidth symbol duration product $(\Delta \nu T_{s})$ tolerance of different CPR algorithms for C-mQAM constellations is studied and compared with the proposed CPR scheme. The results are analyzed at 3.8e-3 and 1e-2 bit error rate forward error correction limits. The proposed CPR scheme achieves similar $\Delta \nu T_{s}$ tolerance compared to single stage BPS algorithm while its computational complexity is reduced by group factors of 27.2 | 32.3, and 30.5 | 32.6 (in the form of multipliers | adders ) for C-16QAM and C-64QAM, respectively.

Multilevel space–time trellis coded cooperation with channel state information at transmitter

SummaryIn this paper, the authors propose a system where a number of cooperating mobile nodes transmit information to a common destination node. Each cooperating node has a set of decoders to detect the information of other nodes and a set of encoders to further encode the decoded information as well as its own information using multilevel space–time trellis coding (MLSTTC) scheme. The coded information is mapped using multi‐resolution modulation partitioning to M‐ary quadrature amplitude modulation constellation. The mapped symbols are weighted based on the available channel state information at transmitting nodes. The weighting of transmitting symbols provides beamforming resulting in receive signal‐to‐noise ratio gain. The weighted symbols are sent to destination node through two transmit antennas. If the information of other nodes has been correctly decoded at the cooperating node, then the destination node receives the information of each node as many times as there are number of transmitting nodes, thus achieving full diversity order. A multistage Viterbi decoder is used at the destination node to extract information of each mobile node. The results indicate that the performance of proposed cooperative MLSTTC system is superior to non‐cooperative MLSTTC system. Copyright © 2016 John Wiley & Sons, Ltd.

Constellation Collaborated Non-linear Orthogonal Space-Time Block Codes with Fast Maximum Likelihood Detection

In this paper, constellation collaborated nonlinear orthogonal space–time block codes (OSTBCs) for wireless communication systems are considered. Using the recently developed unique factorization of signals, several uniquely factorable constellation pairs (UFCPs) generated from cross quadrature amplitude modulation (QAM) constellations are chosen for transmission through all the transmitter antennas, with one random symbol acting as a coordinator to control all the symbols embedded in each coding matrix. The coding gains of collaborated orthogonal codes are calculated, and some optimal constellation pairs with maximum coding gains are presented, including orthogonal codes with different antennas and UFCPs with different groups. Despite the fact that the proposed code is nonlinear, a fast maximum likelihood (ML) decoding algorithm is developed, and its complexity is analyzed in detail. By comparing the decoding complexity of conventional Alamouti code, the ML algorithm, and the fast ML decoding algorithm of collaborative Alamouti code, it can be observed that the complexity of fast ML algorithm is still linear in terms of the square root of the cardinality of the cross QAM constellations with no performance loss. Computer simulations are performed to verify the performance of collaborative OSTBCs and the fast ML Algorithm under different conditions, and the results demonstrate that the average error rate of the collaborative nonlinear orthogonal codes outperforms that of the conventional OSTBCs.

Blind adaptive carrier phase recovery for QAM systems

This paper provides a study of adaptive phase recovery in quadrature amplitude modulation (QAM) based communication systems. Here, we modify the traditional fourth-power phase recovery algorithm (FP-PRA) to propose three improved algorithms, and analyze their performances in the presence of additive white Gaussian noise, phase noise, frequency-offset, and inter-symbol interference. We demonstrate that it is possible to obtain the optimal values of step-sizes (or loop-gains) in closed-form in the presence of phase noise and/or frequency-offset. In particular, we discuss two methods to improve FP-PRA. The first method involves utilizing the idea of partitioning the QAM constellation into QPSK-like and not-QPSK-like annular regions. The phase synchronizer is allowed to update only when a derotated QAM symbol lies in QPSK-like region; otherwise, the update process is stopped. The second method exploits an evolving idea of QAM-to-QPSK transformation, and uses transformed symbols to estimate phase mismatch. We provide a new interpretation of this transformation method and relate it to the quadrant-wise centroid of the rotated constellation. Furthermore, we discuss the feasibility of this method for both square and cross-QAM, and, identify and verify numerically the existence of false-locks in the case of cross-QAM. To the best of our knowledge, the ideas of constellation partitioning and constellation transformation have not appeared earlier in the context of adaptive phase recovery. We discuss adaptive blind estimation of optimal step-sizes in the presence of phase noise and frequency-offset. Finally, we discuss the modification of the proposed stochastic gradient methods to transform them into batch processing algorithms so as to make them more suitable for higher data rate systems. Numerical experiments indicate that the proposed algorithms can outperform the traditional FP-PRA algorithm for a number of practical QAM sizes under different mismatch conditions, and that our analytical findings are in close agreement with the simulation results.

A 3-D Polarization Quadrature Amplitude Modulation method and constellation mapping

As a new three-dimensional (3-D) modulation, Polarization Quadrature Amplitude Modulation (PQAM) can be regarded as the combination of Pulse amplitude modulation (PAM) and Quadrature Amplitude Modulation (QAM) Modulation. It can better improve the digital communication efficiency and reduce the Symbol error rate (SER) of the system than one-dimensional or two-dimensional modulation scheme. How to design a feasible constellation is the most concerned problem of PQAM currently. This paper first studies the relationship between the SER theoretical value of PQAM and the distribution of M and N, proposes a new M, N allocation scheme. Secondly, a new and straightforward design method of constructing higher-level 3-D signal constellations, which can be matched with the PQAM, and the constellation can divided into three different structures according to the ary for PQAM. Finally, the simulation results show that: in PQAM system, the modulation scheme and the constellation mapping scheme are proposed in this paper which can effectively reduce the system SER and improve the anti-noise performance of the system.

On the Sum of Correlated Squared <inline-formula> <tex-math notation="TeX">$\kappa-\mu$</tex-math></inline-formula> Shadowed Random Variables and Its Application to Performance Analysis of MRC

In this paper, we study the statistical characterization of the sum of the squared $\kappa-\mu$ shadowed random variables with correlated shadowing components. The probability density function of this sum is obtained in the form of a power series. The derived pdf is utilized for obtaining the performance results of the maximal ratio combining (MRC) scheme over correlated $\kappa-\mu$ shadowed fading channels. First, we derive the moment-generating function (mgf) of the received signal-to-noise ratio of the MRC receiver. By using the derived mgf expression, the analytical diversity order is obtained; it is deduced on the basis of this analysis that the diversity of the MRC receiver over correlated $\kappa-\mu$ shadowed channels depends upon the number of diversity branches and $\mu$ parameter. Further, the analytical average bit error rate of the MRC scheme is also derived, which is applicable for $M$ -ary phase shift keying and $M$ -ary quadrature amplitude modulation constellations. The Shannon capacity of the correlated $\kappa-\mu$ shadowed channels is also derived in the form of the Meijer-G function.

Energy-Efficient Communications in MIMO Systems Based on Adaptive Packets and Congestion Control With Delay Constraints

In this paper, we propose adaptive techniques for multiple input and multiple output (MIMO) systems, to solve the problem of energy efficient communications with delay constraint, where the energy efficiency is defined as the number of bits per second correctly received per power consumed. We first investigate the optimal multiple quadrature amplitude modulation (MQAM) constellation size for each transmission stream and the optimal packet size. By exploiting the intrinsic relationship among the constellation size, the packet size, the symbol error rate (SER) and delay, we propose an adaptive transmission mode for different delay demands. For the case of user's buffer overflow, we use the congestion control algorithm to schedule the average queue length, and maintain the optimal delay performance for energy efficiency. Simulations show that to maximize the energy efficiency and offer different Quality of Service (QoS) of delay simultaneously, the transmitter should adaptively choose the constellation size and the packet size as well as the transmission mode. In this framework, the tradeoff between energy efficiency and delay demand are well demonstrated.

Exact MGF-Based Performance Analysis of Dual-Hop AF-Relayed Optical Wireless Communication Systems

In this paper, we analyze the subcarrier intensity modulation-based-relayed optical wireless communication system in the presence of various channel impairments such as turbulence, path loss and pointing errors. The relay follows an amplify and forward relaying protocol and the optical links are modeled assuming independent but not necessarily identically distributed (i.n.i.d) gamma-gamma fading statistics. We derive the novel analytical expressions for the moment generating function and cumulative distribution function of the equivalent end-to-end signal to noise ratio (SNR) at the destination and utilize these results to obtain the exact analytical expressions for outage probability and average symbol error rate for M-ary phase shift keying and M-ary quadrature amplitude modulation constellations, respectively. The results are obtained in terms of special function such as generalized bivariate Meijer's G-function and to get insight further, we present asymptotic analysis at high SNR values to find the effect of various parameters on the system performance.

A low-latency high-throughput soft-output signal detector for spatial multiplexing MIMO systems

This paper presents a low latency, high throughput soft-output signal detector for a 4×4 64-QAM spatial-multiplexing MIMO system. To achieve high data-level parallelism and accurate soft information, the detector adopts a channel-adaptive node perturbation technique to generate a list of candidate vectors around an initial linear estimation. The detection algorithm provides a large range and convenient performance-complexity trade-off by adjusting the node perturbation parameter. A partial-parallel pipelined VLSI architecture is developed to implement the algorithm with high throughput, low processing latency, while offering the flexibility to support run-time performance tuning. Moreover, a fast and hardware-friendly node enumeration scheme is developed to further reduce the processing delay by exploiting the geometric property of the quadrature amplitude modulation (QAM) constellation. The detector was synthesized using Synopsys Design Compiler with a 65nm CMOS standard cell library. The core area is 0.58mm2 with 290K gates. The peak throughput is 3Gb/s at 500MHz clock frequency with a latency of 20ns. Compared to other reported soft-output MIMO detectors, this is a latency reduction of 71%. The corresponding energy consumption is 33pJ per bit detection.

Channel Estimation and Equalization of DVB-T in Fast Fading Multipath Channels

Early Terrestrial Digital Video Broadcasting Systems (DVB-T) were planned to work in Line-of-Sight (LOS) environments where a significantly high Signal to Noise Ratio (SNR) is guaranteed for all times. However, the recent DVB standards are sought to work in non-LOS conditions where the SNR is relatively low. Hence, in such environments, there is a need for a successful channel estimation and detection technique to take care of the fast channel fluctuations. This article is dealing with LS channel estimation and detection method for DVB-T signals over various multipath fading channel. The proposed method has been proven successful for up to 16 Quadrature Amplitude Modulation (QAM) constellations even when there is no LOS. However, the performance is found to be insufficient for an acceptable user experience for higher number of constellations. 

Fast Maximum-Likelihood Decoder for Quasi-Orthogonal Space-Time Block Code

Motivated by the decompositions of sphere and QR-based methods, in this paper we present an extremely fast maximum-likelihood (ML) detection approach for quasi-orthogonal space-time block code (QOSTBC). The proposed algorithm with a relatively simple design exploits structure of quadrature amplitude modulation (QAM) constellations to achieve its goal and can be extended to any arbitrary constellation. Our decoder utilizes a new decomposition technique for ML metric which divides the metric into independent positive parts and a positive interference part. Search spaces of symbols are substantially reduced by employing the independent parts and statistics of noise. Symbols within the search spaces are successively evaluated until the metric is minimized. Simulation results confirm that the proposed decoder’s performance is superior to many of the recently published state-of-the-art solutions in terms of complexity level. More specifically, it was possible to verify that application of the new algorithms with 1024-QAM would decrease the computational complexity compared to state-of-the-art solution with 16-QAM.