Optimum Low-Complexity Decoder for Spatial Modulation

Abstract

In this paper, a novel low-complexity detection algorithm for spatial modulation (SM), referred to as the minimum-distance of maximum-length (m-M) algorithm, is proposed and analyzed. The proposed m-M algorithm is a smart searching method that is applied for the SM tree-search decoders. The behavior of the m-M algorithm is studied for three different scenarios: i) perfect channel state information at the receiver side (CSIR), ii) imperfect CSIR of a fixed channel estimation error variance, and iii) imperfect CSIR of a variable channel estimation error variance. Moreover, the complexity of the m-M algorithm is considered as a random variable, which is carefully analyzed for all scenarios, using probabilistic tools. Based on a combination of the sphere decoder (SD) and ordering concepts, the m-M algorithm guarantees to find the maximum-likelihood (ML) solution with a significant reduction in the decoding complexity compared to SM-ML and existing SM-SD algorithms; it can reduce the complexity up to 94% and 85% in the perfect CSIR and the worst scenario of imperfect CSIR, respectively, compared to the SM-ML decoder. Monte Carlo simulation results are provided to support our findings as well as the derived analytical complexity reduction expressions. Index TermsMultiple-input multiple-output (MIMO) systems, spatial modulation (SM), maximum likelihood (ML) decoder, sphere decoder (SD), low-complexity algorithms, complexity analysis. ). I. INTRODUCTIONMultiple-input multiple-output (MIMO) systems, which is an integral part of modern wireless communication standards, activate all transmit antennas to increase the spectral efficiency and/or improve the bit-error-ratio (BER) performance [2]. On the other hand, activating all transmit antennas at the same time not only creates a strong inter-channel interference (ICI) but also requires multiple radio frequency chains. A promising technique called spatial modulation (SM) has been studied in recent years [3]-[5] to overcome these problems in next-generation systems. In SM [6]-[9], only one transmit antenna is activated during the transmission burst, where the active transmit antenna is chosen out of all transmit antennas according to a part of the input bit-stream. The active antenna transmits a phase shift keying (PSK) or quadrature amplitude modulation (QAM) symbol, through a wireless medium, based on the rest of the input bit-stream. At the receiver side, all receive antennas receive the delivered signal and forward it to the digital signal processor (DSP) unit for decoding. The maximum-likelihood (ML) detector is utilized to decode the received signal by attempting all possible combinations of the QAM/PSK symbols and the transmit antennas, where this process depends on the number of transmit antennas, receive antennas, and modulation order. Consequently, the ML algorithm is classified to be costly from the decoding complexity point of view, particularly for increasing number of transmit/receive antennas and constellation points. Low-latency communications and energy-ef...

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“…However, these schemes demand many hardware implementation resources. Other detection techniques for MIMO-SM-QSM were reported in [15,19,20]. These detectors were based on tree search and spherical detection.…”

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