Multiple-symbol differential sphere decoding for unitary space-time modulation

Abstract

Abstract-We consider multiple-symbol differential detection (MSDD) for multiple-input multiple-output (MIMO) Rayleighfading channels. MSDD, which jointly processes blocks of AE received symbols to detect AE ½ data symbols, allows for power-efficient transmission over rapid-fading channels. However, the complexity of the straightforward approach to find the maximum-likelihood (ML) MSDD solution is exponential in AE , the number of transmit antennas AEÌ and the rate Ê. In this paper, we introduce an MSDD algorithm based on sphere decoding whose average complexity is not exponential in AE for interesting ranges of signal-to-noise ratio (SNR) and aribtrary unitary signal constellations. For the interesting special cases of diagonal and orthogonal constellations we achieve a similar complexity reduction in AEÌ and Ê. Based on an error-rate analysis for MSDD we also propose a variant of MSDD that considerably improves power efficiency in relatively fast fading at a very moderate increase in complexity.

Multiple symbol differential detection based on sphere decoding for unitary space-time modulation

“…Ref. [5] indicates that for static channels, the conditions required by dominant error events are that only one transmitted matrix S(n) is wrong asS(n), andS(n) maximizes Re tr(S H (n)S(n)). As long as the fading bandwidth is not too wide, the dominant error events over CF channels may be the same as that over static channels [17] .…”

“…Recalling that the ML metric with QS assumption excludes a "ln det" term in (5) [5] , and QS assumption is an approximation of CF assumption, we infer that this term can be omitted without much performance degradation if the fading channel varies slowly [12] . We refer tod 1 as approximate ML (AML) metric.…”

“…Based on the former, decision-feedback detection (DFD), noncoherent sequence detection (NSD), and multiple symbol differential sphere decoding (MSDSD) were proposed in refs. [3][4][5], respectively. These algorithms provide major design approaches of MSDD.…”

Multiple-Symbol Joint Signal Processing for Differentially Encoded Single- and Multi-Carrier Communications: Principles, Designs and Applications

“…Inspired by above contributions, the SD algorithm was first introduced by Lampe et al in [73] for mitigating the complexity of the ML-MSDD [74,75] in the context of a differentially modulated SISO system, leading to the multiple-symbol differential sphere detection (MSDSD) concept. More recently, the employment of MSDSD is further extended to the family of co-located and distributed MIMO systems by Pauli and Lampe in [69] as well as by Wang and Hanzo in [68], respectively. Basically, the transplantation of the SD mechanism into the MSDD relies on the fact that S d of (3) formed in the context of both the colocated and distributed MIMO systems considered is unitary, owing to the employment of conventional DPSK schemes or unitary space-time codes.…”

Multiple-Symbol Differential Sphere Detection for the Amplify-and-Forward Cooperative Uplink

“…However, the performance of the former scheme rapidly degrades, as the channel connecting the multiple terminals becomes more time-selective and/or dispersive. Recently, in order to mitigate the error floor encountered by differentially encoded direct transmission combined with CDD employing an observation window size of N wind = 2, a multiplesymbol based differential sphere detection (MSDSD) technique using N wind > 2 has been proposed in [4,5]. In the light of the above observations, our main contribution in this paper is the design of a MSDSD scheme proposed for multipath channels using multidimensional tree search [6], which is capable of making DAFaided cooperative systems significantly more robust to time-selective propagation environments.…”