M-PSK Constellations Research Articles

Adaptive Blind MPSK Constellation Recovery and Equalization for Cognitive Radio Applications

Cognitive radio is considered a relevant communication paradigm to deal with the increasing demands in modern communications systems. Adaptive schemes are required to recognize channel conditions and to properly adjust main transmission parameters to improve the quality of communications. In this direction, blind algorithms to recover constellation, from phase-modulated signals, represent a means to implement cognitive capabilities to allow automatic modulation recognition (AMR) on receivers. Commonly, the most popular approaches for blind constellation recovery are based on a two-step scheme. The first step uses to equalize channel effects and reduce inter-symbol interference (ISI). The second step carries out constellation recovery utilizing phase locked loop (PLL) systems like the Costas Loop, then to classify the incoming signal. This work proposes a novel single-step blind adaptive filter solution, inspired by an adaptive interference canceler, for joint equalization and constellation symbol recovery from received phase shift keying (PSK) waveforms. Furthermore, we propose new coefficients update mechanisms based on the constant amplitude of PSK signals. The proposed solution exhibits reduced computational complexity compared to the state of the art and a reduced time of convergence. Additionally, the proposed scheme does not require a training sequence to operate properly. The obtained results clearly show that the proposed scheme significantly improves accuracy regarding phase symbol estimation and ISI reduction.

Low-Complexity GSM Detection Based on Maximum Ratio Combining

Generalized spatial modulation (GSM) technology is an extension of spatial modulation (SM) technology, and one of its main advantages is to further improve band efficiency. However, the multiple active antennas for transmission also brings the demodulation difficulties at the receiver. To solve the problem of high computational complexity of the optimal maximum likelihood (ML) detection, two sub-optimal detection algorithms are proposed through reducing the number of transmit antenna combinations (TACs) detected at the receiver. One is the maximum ratio combining detection algorithm based on repetitive sorting strategy, termed as (MRC-RS), which uses MRC repetitive sorting strategy to select the most likely TACs in detection. The other is the maximum ratio combining detection algorithm, which is based on the iterative idea of the orthogonal matching pursuit, termed the MRC-MP algorithm. The MRC-MP algorithm reduces the number of TACs through finite iterations to reduce the computational complexity. For M-QAM constellation, a hard-limited maximum likelihood (HLML) detection algorithm is introduced to calculate the modulation symbol. For the M-PSK constellation, a low-complexity maximum likelihood (LCML) algorithm is introduced to calculate the modulation symbol. The computational complexity of these two algorithms for calculating the modulation symbol are independent of modulation order. The simulation results show that for GSM systems with a large number of TACs, the proposed two algorithms not only achieve almost the same bit error rate (BER) performance as the ML algorithm, but also can greatly reduce the computational complexity.

Performance analysis of receive diversity under time-varying and spatially correlated channels using partial CSI

In this paper, a single input multiple output system is considered with L receive antennas and the underlying channels are assumed to be time varying with temporal correlation coefficient a and spatially correlated with correlation coefficient $$\rho $$ . Further, the channel is assumed to be identically distributed using Rayleigh fading channels and characterized by first order autoregressive model. For the detection, we assume partial channel state information (CSI) available at the receiver. The partial CSI is in the form of a known preamble (one symbol) only before beginning of a frame of size N symbols. Further, the preamble is imperfectly known with a variance of error $$\sigma _e^2$$ . For the assumed system, closed form expressions of symbol error rate (SER) are derived for M-PSK and M-QAM constellations under the compound effect of spatially correlated channels, temporally correlated channels and partial CSI at the Receiver. The derived expressions are functions of average SNR per symbol, $$\rho $$ , a, $$\sigma _e^2$$ , N, L and modulation order M. Further, these expressions are reduced for some special cases and compared with prevailing results in literature. The analytical expressions are also validated by comparing them with the corresponding simulation results. The derived expressions are very useful to select N, L and M to overcome the deterioration in SER due to adverse effects of $$\rho $$ , a and $$\sigma _e^2$$ .

Non‐coherent transmission for two‐way relaying systems with relay having large‐scale antennas

Without channel state information at the users and relay node, a non-coherent transmission scheme for the two-way relaying systems is investigated in this study. At the relay node, the authors first detect the uplink data with non-coherent maximum likelihood receiver by fully utilising the large receiving freedom of relay's large-scale antennas. Channel estimations can also be obtained by treating the detected uplink data as pilot symbols. Then, the relay node forwards the detected data by using beamforming. To assure the reliable detection of the users' transmitted symbols non-coherently, the authors propose a transmitting constellation design with the idea of searching an optimal angle for rotating one user's constellation. Specially, for M-PSK constellations, they derive the optimal rotation angle, which is highly consistent with the exhaustive searching results. In addition, they also analyse the lower bound of channel estimations in terms of normalised mean square error (NMSE). From simulation results, the proposed non-coherent transmission scheme achieves considerable error performance, and the NMSE lower bounds of channel estimations are also tight when the number of relay's antennas approaches to be large.

Intrinsic Secrecy of EGT and MRT Precoders for Proper and Improper Modulations

This paper makes an information theoretical analysis of the intrinsic secrecy level of M-QAM and M-PSK modulation schemes considering the use of equal gain transmission and maximum ratio transmission precoding techniques. In addition to the analysis of the conventional proper M-QAM and M-PSK constellations, a recently proposed family of improper versions of the M-QAM and M-PSK modulation schemes is also evaluated. With the exception of proper M-PSK, which verifies always full secrecy for the considered precoders, the main results show that for low order constellations, the amount of intrinsic secrecy provided by the combination of the precoder and modulation scheme is significant and, therefore, can be exploited in the design of a full secrecy solution. The theoretical derivations provided in this paper can be directly applied to quantify the minimal entropy that a secret key must have to fully secure the exchange of information for these transmission schemes.

Linear Transceiver Design for an Amplify-and-Forward Relay Based on the MBER Criterion

A design methodology based on the Minimum Bit Error Ratio (MBER) framework is proposed for a non-regenerative Multiple-Input Multiple-Output (MIMO) relay-aided system to determine various linear parameters. We consider both the Relay-Destination (RD) as well as the Source-Relay-Destination (SRD) link design based on this MBER framework, including the precoder, the Amplify-and-Forward (AF) matrix and the equalizer matrix of our system. It has been shown in the previous literature that MBER based communication systems are capable of reducing the Bit-Error-Ratio (BER) compared to their Linear Minimum Mean Square Error (LMMSE) based counterparts. We design a novel relay-aided system using various signal constellations, ranging from QPSK to the general M-QAM and M-PSK constellations. Finally, we propose its sub-optimal versions for reducing the computational complexity imposed. Our simulation results demonstrate that the proposed scheme indeed achieves a significant BER reduction over the existing LMMSE scheme.

Interference-Constrained Optimal Power-Adaptive Amplify-and-Forward Relaying and Selection for Underlay Cognitive Radios

In an underlay cognitive radio (CR) system, a secondary user can transmit when the primary is transmitting but is subject to tight constraints on the interference it causes to the primary receiver. Amplify-and-forward (AF) relaying is an effective technique that significantly improves the performance of a CR by providing an alternate path for the secondary transmitter's signal to reach the secondary receiver. We present and analyze a novel optimal relay gain adaptation policy (ORGAP) in which the relay is interference aware and optimally adapts both its gain and transmit power as a function of its local channel gains. ORGAP minimizes the symbol error probability at the secondary receiver subject to constraints on the average relay transmit power and on the average interference caused to the primary. It is different from ad hoc AF relaying policies and serves as a new and fundamental theoretical benchmark for relaying in an underlay CR. We also develop a near-optimal and simpler relay gain adaptation policy that is easy to implement. An extension to a multirelay scenario with selection is also developed. Our extensive numerical results for single and multiple relay systems quantify the power savings achieved over several ad hoc policies for both MPSK and MQAM constellations.

A Low-Complexity ML Detection Algorithm for Spatial Modulation Systems With <inline-formula> <tex-math notation="TeX">$M$</tex-math></inline-formula>PSK Constellation

Spatial modulation (SM), which is a novel transmission scheme, is employed for active transmit antenna indexes and modulated signals to convey the information. To recover the transmitted information bits, the maximum likelihood (ML) joint detector is often used. However, its complexity linearly grows with the number of transmit antennas and the size of the signal set. A reduced-complexity ML optimal algorithm for SM systems with M-QAM has been proposed. However, for M-PSK modulation, there are not similar low-complexity ML detection algorithms yet to our knowledge. In this paper, a low-complexity ML detection algorithm for SM systems with M-PSK modulation is proposed. By exploiting the features of M-PSK constellation, we give the ML-estimated values of the transmitted symbols. Therefore, the ML search complexity is independent of the constellation size. Simulation results show that the proposed algorithm has the same performance as the ML-optimum detector and significant reduction in computational complexity compared with existing detectors for SM systems with M-PSK modulation.

Channel Quantization Using Constellation Based Codebooks for Multiuser MIMO-OFDM

In this paper, we propose clustered quantization techniques for multiuser multi-input/multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) using constellation based codebooks. Constellation based codebooks provide scalability and efficient codeword search capability, which are key features for practical multiuser MIMO-OFDM systems with a large number of antennas. The proposed clustered quantization scheme quantizes consecutive subcarriers into a single codeword that minimizes aggregated quantization errors. We base our new clustering techniques on two constellation based quantization methods, namely equal-magnitude angular quantization (EMAQ) and squared-lattice angular quantization. New efficient codebook search algorithms are proposed for the clustered quantization. In addition, we propose new constellations to guarantee different users quantize channels into distinct codewords. One is a rotated M-PSK constellation suitable for randomly-distributed user scenarios, and the other is a random phase equal-magnitude (RPEM) constellation suitable for ill-conditioned user scenarios. Thus, full spatial multiplexing gain can be achievable even with small number of users. Finally, a near-sphere codeword search algorithm is proposed for the RPEM. In simulations, the proposed clustered quantization shows up to 50% higher throughput compared to conventional fixed-pilot channel quantization. Also, we show our new constellations for EMAQ improve throughput almost 35% compared to the standard EMAQ.

SEP-Optimal Transmit Power Policy for Peak Power and Interference Outage Probability Constrained Underlay Cognitive Radios

In underlay cognitive radio (CR), a secondary user (SU) can transmit concurrently with a primary user (PU) provided that it does not cause excessive interference at the primary receiver (PRx). The interference constraint fundamentally changes how the SU transmits, and makes link adaptation in underlay CR systems different from that in conventional wireless systems. In this paper, we develop a novel, symbol error probability (SEP)-optimal transmit power adaptation policy for an underlay CR system that is subject to two practically motivated constraints, namely, a peak transmit power constraint and an interference outage probability constraint. For the optimal policy, we derive its SEP and a tight upper bound for MPSK and MQAM constellations when the links from the secondary transmitter (STx) to its receiver and to the PRx follow the versatile Nakagami-m fading model. We also characterize the impact of imperfectly estimating the STx-PRx link on the SEP and the interference. Extensive simulation results are presented to validate the analysis and evaluate the impact of the constraints, fading parameters, and imperfect estimates.

A Rate $$\text{ M }_{\mathrm{T}}$$ Full Diversity STF Block Coded $$4\times 4$$ MIMO-OFDM System with Reduced Complexity

Multiple input multiple output (MIMO) communication systems with orthogonal frequency division multiplexing (OFDM) has a great role to play for 4G broadband wireless communications. In this paper, a space time frequency (STF) code is presented with reduced decoder complexity and to achieve code rate $$\text{ M }_\mathrm{T}$$ with full diversity of $$\text{ M }_{\mathrm{T}} \text{ M }_{\mathrm{R}} \text{ N }_{\mathrm{b}}$$ L i.e., product of number of transmit antennas ( $$\text{ M }_\mathrm{T}$$ ), receive antennas $$(\text{ M }_{\mathrm{R}})$$ , fading blocks $$(\text{ N }_{\mathrm{b}})$$ and channel taps (L). The maximum achievable diversity with high rate of STF block coded MIMO-OFDM is analyzed and verified by simulation results. The decoder complexity is resolved by employing several approaches like maximum likelihood (ML), sphere decoder (SD) and array processing. The performance of STF code is compared with existing layered algebraic STF code in terms of decoder complexity and bit error rate (BER). Further, the closed form expressions for BER performance of STFBC MIMO-OFDM systems are derived and evaluated for frequency selective block fading channels with MPSK constellations.

Adaptive Constellation Rotation Scheme for Two-User Fading MAC with Quantized Fade State Feedback

With no Channel State Information (CSI) at the users, transmission over the two-user Gaussian Multiple Access Channel with fading and finite constellation at the input, will have high error rates due to multiple access interference (MAI). However, perfect CSI at the users is an unrealistic assumption in the wireless scenario, as it would involve extremely large feedback overheads. In this paper we propose a scheme which removes the adverse effect of MAI using only quantized knowledge of fade state at the transmitters such that the associated overhead is nominal. One of the users rotates its constellation relative to the other without varying the transmit power to adapt to the existing channel conditions, in order to meet certain pre-determined minimum Euclidean distance requirement in the equivalent constellation at the destination. The optimal rotation scheme is described for the case when both the users use symmetric M-PSK constellations at the input, where M=2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ</sup> , λ being a positive integer. The strategy is illustrated by considering the example where both the users use QPSK signal sets at the input. The case when the users use PSK constellations of different sizes is also considered. It is shown that the proposed scheme has considerable better error performance compared to the conventional non-adaptive scheme, at the cost of a feedback overhead of just ⌈ log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /8 - M/4 + 2)⌉ + 1 bits, for the M-PSK case.

ML Decoder for Decode-and-Forward Based Cooperative Communication System

Decode-and-forward (DF) protocol based cooperative communication is vulnerable to the erroneous relaying by the relay. In this paper, we derive a maximum-likelihood (ML) decoder for the DF protocol utilizing arbitrary complex-valued constellations including M-PSK, M-PAM, and M-QAM. A set-up of a single pair of source and destination with one relay is studied. The source and the relay utilize orthogonal uncoded transmissions. The relay performs ML decoding and forwards the decoded symbol to the destination, and it might commit errors in decoding the data. The ML decoder at the destination is obtained by maximizing the probability density function (p.d.f.) of the data received during two orthogonal transmissions at the destination under the assumption that the average probability of error of the source-relay link is known at the destination. The proposed ML decoder is a generalized decoder which is applicable to arbitrary constellations, whereas, one existing DF cooperative decoder is applicable to the real valued constellations like BPSK and M-PAM. One existing decoder is also applicable to M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -QAM constellations. We also derive a low-complexity piecewise linear (PL) decoder for arbitrary complex-valued M-point constellations which performs similar to the ML decoder for all signal-to-noise ratio values. An approximate expression of the symbol error rate (SER) of the PL decoder for M-PSK constellation is derived. By using the approximate SER expressions, it is proved that the proposed ML and PL decoders achieve full diversity of two in the cooperative system studied.

Error Rate for PSK and QAM Modulations for Non-Ideal OFDM Systems with Noisy Channel Estimates and Receive Diversity

This paper characterizes the SER for a non-ideal OFDM system with either M-PSK or M-QAM constellations operating over a frequency-selective, time-varying, Rayleigh fading channel. The imperfections that we consider are inter-carrier interference (ICI) and/or inter-symbol interference (ISI), imperfect time and frequency synchronization, and noisy channel estimates. We consider an MRC receiver with L diversity branches. We present SER characterizations with and without ISI, and show that the effect of ISI, especially for higher order modulation schemes, e.g., 8PSK and above, can be very severe, irrespective of the number of diversity branches.

Performance of Filter Bank Modulation with Phase Noise

We study the effect of phase noise in filter bank modulation systems. In particular, we analyze the FMT (Filtered Multitone) and the DMT (Discrete Multitone) system. While DMT uses a rectangular shape sub-channel pulse, the FMT system uses a frequency confined pulse. Approximated symbol error rate expressions for M-PSK and M-QAM constellations are derived for two types of receivers: the non-coherent receiver, and the one-tap coherent receiver. The results show that FMT with a root-raised-cosine pulse has some more robustness to phase noise w.r.t. DMT, although both systems are affected by phase noise especially with high order modulation.

Differential Decoder for MAC Based Two-User Communication Systems

We derive a decoder for differential data of two multiple access channel (MAC) based uplink users. Both users utilize differential modulation for transmitting their data. It is assumed that the users cannot exchange their information. In addition, it is assumed that the users transmit data over multiple access uplink channels simultaneously in the same frequency band and without any orthogonal signatures (no CDMA). Their transmissions are assumed to be perfectly synchronized in time, phase, and frequency. The decoder is obtained by maximizing the joint probability distribution function (p.d.f.) of consecutively received data samples. We first obtain a partially differential decoder which avoids the knowledge of channel of one user at the base-station. Then we derive a heuristic differential decoder which completely avoids the knowledge of the channels of both users. For the heuristic differential decoder to work properly, both users must use rotated constellations. Optimized values of rotation angles for different M-PSK constellations are numerically obtained. It is further shown by simulations that the proposed differential decoders perform better than a same rate existing TDMA based two-user transmission scheme.

Double-differential orthogonal space-time block codes for arbitrarily correlated Rayleigh channels with carrier offsets

The presence of carrier offsets in the multiple-input multiple-output (MIMO) channels is an important practical and theoretical problem. Double-differential coding is a technique which allows the receiver to decode the data without any channel or carrier offset knowledge. We propose a double-differential (DD) coding scheme which is applicable to square orthogonal space-time block codes (OSTBC) using M-PSK constellation. The main advantages of our proposed DD coding scheme are: 1) The previously proposed DD codes are applicable only to the specific class of space-time block codes which follow the diagonal unitary group property, whereas our DD coding is applicable to any square OSTBC. 2) We propose a suboptimal decoder which preserves the linear decoding property of the OSTBC. 3) A theoretical analysis is performed to find a pairwise error probability (PEP) upper bound of the proposed double-differential orthogonal space-time block codes (DDOSTBC). 4) In order to improve the performance of DDOSTBC over the arbitrarily correlated Rayleigh channels we propose a precoder which minimizes an upper bound of the PEP. The proposed DDOSTBC are able to achieve higher coding gain than the similar rate existing DD coding scheme. In addition, the proposed precoded DDOSTBC achieves performance gain for correlated channels as compared to the unprecoded DDOSTBC.

Distributed GABBA space-time codes in amplify-and-forward relay networks

Cooperative communications via distributed space-time codes has been recently proposed as a way to form virtual multiple-antennas that provide dramatic gains in slow fading wireless environments. In this paper, we consider the design of practical distributed space-time codes for wireless relay networks using the amplify-and-forward (AF) scheme, where each relay transmits a scaled version of the linear combinations of the received symbols and their complex conjugate. We employ GABBA codes, which are systematically constructed, orthogonally decodable, full-rate, full-diversity space-time block codes, in a distributed fashion. Our scheme is valid for any number of relays with linear orthogonal decoding in the destination, which make it feasible to employ large numbers of potential relays to improve the diversity order. We generalize the distributed space-time codes in AF mode when the source-destination link contributes in both phases of the transmission. Assuming MPSK or M-QAM constellations and maximum likelihood (ML) detection, we derive an approximate formula for the symbol error probability of the investigated scheme in Rayleigh fading channels. The analytical results are confirmed by simulations, indicating both the accuracy of the analysis, and the fact that low-complexity, flexible, and high-performing distributed space-time block codes can be designed based on GABBA codes.

Performance analysis of transmit beamforming for MISO systems with imperfect feedback

In this paper, we analyze the performance of transmit beamforming on multiple-antenna Rayleigh fading channels with imperfect channel feedback. We characterize the feedback imperfections in terms of noisy channel estimation, feedback delay, and finite-rate channel quantization. We develop a general framework, that is valid for an arbitrary two-dimensional linear modulation, to capture the aforementioned imperfections and derive the symbol and bit error probability expressions for both M-PSK and M-ary rectangular QAM constellations with Gray code mapping. We show that the proposed analytical formulation is valid for a frequency-domain duplexing system with/without finite-rate channel quantization and a time-domain duplexing system. We validate the accuracy of the analysis through simulations, and assess the relative effects of channel estimation inaccuracy, feedback delay, and finite-rate quantization on the symbol and bit error performances for various constellations.

Symbol and bit error probabilities of orthogonal space-time block codes with antenna selection over keyhole fading channels

The symbol error rate (SER) and the bit error rate (BER) of orthogonal space-time block codes (OSTBCs) with antenna selection over keyhole fading channels are examined. Considered are receive antenna selection, transmit antenna selection, and joint antenna selection at both the transmitter and the receiver. The exact SERs of OSTBCs for M-PSK and square MQAM constellations are obtained using the technique of moment generating function (MGF). By applying the Bonferroni-type bounds, tight lower and upper bounds for both the SER and BER are provided in closed-form expressions with finite-range single integrals. The bounds can be applied to arbitrary constellations and mappings. Numerical results show that the bounds can be used to provide practically the exact SER and BER over a wide range of the signal-to-noise ratio.