Transmit precoded spatial modulation: maximizing the minimum Euclidean distance versus minimizing the bit error ratio

Abstract

In this paper, we investigate a pair of transmit pre-coding (TPC) algorithms conceived for spatial modulation (SM) systems communicating over flat-fading multiple-input multiple-output (MIMO) channels. In order to retain all the benefits of conventional SM, we design the TPC matrix to be diagonal and introduce two design criteria for optimizing the elements of the TPC matrix. Specifically, we first investigate a TPC design based on maximizing the minimum Euclidean distance dmin (max-dmin) between the SM signal points at the receiver side. A closed-form solution of the optimal max-dmin based TPC matrix is derived. Then, another TPC design algorithm is proposed for directly minimizing the bit error ratio (BER) upper bound of SM, which is capable of jointly optimizing the overall Euclidean distance between all received signal points. In the minimum BER (min- BER) based TPC algorithm, the theoretical gradient of the BER with respect to the diagonal TPC matrix is derived and a simplified iterative conjugate gradient (SCG) algorithm is invoked for TPC optimization. Our simulation results demonstrate that the proposed maxdmin based TPC algorithm is optimal in terms of the minimum distance. However, increasing dmin does not achieve a further BER improvement. We also confirm that the min-BER based TPC outperforms the maxdmin based TPC schemes in terms of the achievable BER performance.

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Identifiers

ORCID for Lajos Hanzo: orcid.org/0000-0002-2636-5214

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