M-ary PSK Constellations Research Articles

Compressive sensing‐based low‐complexity detector for differential spatial modulation

Detection of differential spatial modulation (DSM) needs only the received symbols, unlike spatial modulation that requires channel state information at the receiver. The maximum likelihood (ML)-based DSM receiver, though works well for a small number of transmit antennas, is computationally prohibitive for higher number of antennas. The hard-limiter based ML (HL-ML) receiver has low search complexity in the higher signal-to-noise regions only. The authors propose a low-complexity detection technique using compressive sensing for DSM. The detection involves a two-step process, by first finding the antenna index number and then the M-ary phase-shift keying (MPSK) symbol transmitted from that antenna. After performing a correlation between the past and the present received symbol blocks, the index location of the largest elements of this operation reveals the order of antennas that were activated in a symbol duration. The MPSK symbol is found by a pseudo-inverse operation on the columns of the past and the present received symbol blocks, corresponding to the time index and antenna number, which is same as the above indices. The proposed receiver achieves a substantial reduction in computational complexity close to 63%, when compared to the HL-ML receiver and the performance penalty narrows down with higher order MPSK constellations.

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.

New BER Expression of MPSK

This paper provides a new, exact, and general expression involving 1-D and 2-D Q-functions for the bit error probability of M-ary phase-shift keying (MPSK) under additive white Gaussian noise (AWGN) and fading channels when Gray code bit mapping is employed. Regular patterns in the error probability expression of the kth bit are observed while developing the bit error rate (BER) expression. From these patterns, we then derive a new BER expression for the MPSK constellation.

Exact and Approximate Distributions of Instantaneous Power for Pulse-Shaped Single-Carrier Signals

We develop two approaches to calculating statistical distributions of instantaneous power of pulse-shaped single-carrier signals. Our first approach is to derive a formula that can calculate exact distributions of pulse-shaped signals with arbitrary constellations. The exact approach is versatile but turns out to be computationally demanding except for some cases where the constellation has circular symmetry. Our second approach is thus based on approximation, which is valid only for M-ary phase shift keying (MPSK) or phase-shifted MPSK constellations, but requires substantially less computation. The validity of the proposed approaches is confirmed by numerical analysis.

Analysis of Optimum Detector of Trellis Coded MPSK in Phase Noise Channels

This paper presents a novel analytical expression which approximates the bit error rate (BER) of the joint phase and symbol maximum a posteriori (JMAP) sequence estimator for: trellis code modulation (TCM) with M-ary phase shift keying (MPSK) modulation; any arbitrary phase noise model (i.e., not limited to the Wiener process); and either a matched or mismatched decoder. First, we derived convenient closed-form expressions for approximating the pairwise error probability of two code sequences for both matched and mismatched decoders. Since the expressions are formulated either in the time or in the frequency domain, it is possible to indicate the contribution of every frequency in the phase noise spectrum. We then applied the union bound on the code sequence pairwise errors. The analytical expression was tight (usually <;1dB) for MPSK constellations with M ≥ 4 and code rates ≥ 0.5. Once developed, the expressions will assist designers to consider the influence on receiver performance of the code characteristics, decoder implementation and RF synthesizer phase noise. It further enables joint optimization of the RF synthesizer, the code and the decoder for achieving the lowest error rate or other design targets.

Blind Feedforward Symbol-Timing Estimation With PSK Signals: A Constant-Modulus Approach

In this letter, the problem of blind symbol-timing estimation with M-ary phase-shift keying (M-PSK) signals is considered. An estimator exploiting the constant modulus (CM) property of M-PSK constellations and the structure of the received signal when the convolution of the transmitter's signaling pulse and the receiver filter satisfies the Nyquist criterion is proposed. Since the derived estimator, termed the CM estimator, requires a maximization with respect to a continuous variable, a closed-form approximate CM (ACM) algorithm, suitable for digital implementation, is proposed. Computer simulation results show that with small excess bandwidth factors, the derived ACM algorithm outperforms previously proposed algorithms at moderate and high signal-to-noise ratios

Geometrically uniform partitions of L*MPSK constellations and related binary trellis codes

The theory of geometrically uniform trellis codes is applied to the case of multidimensional PSK (phase shift keying) constellations. The symmetry group of an L*MPSK (M-ary PSK) constellation is completely characterized. Conditions for rotational invariance of geometrically uniform partitions of a signal constellation are given. Through suitable algorithms, geometrically uniform partitions of L*MPSK (M=4,8,16 and L=1,2,3,4) constellations are found, which present good characteristics in terms of the set of distances at a given partition level, the maximum obtainable rotational invariance, and the isomorphism of the quotient group associated with the partition. These partitions are used as starting points in a search for good geometrically uniform trellis codes based on binary convolutional codes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>