In this paper, we present a non-coherent energy detection scheme for spatial modulation (SM) systems. In particular, the use of SM is motivated by its low-complexity implementation in comparison to multiple-input multiple-output (MIMO) systems, achieved through the activation of a single antenna during transmission. Moreover, energy detection-based communications restrict the channel state information to the magnitude of the fading gains. This consideration makes the design applicable for low-cost low-powered devices since phase estimation and its associated circuitry are avoided. We derive an energy detection metric for a multi-antenna receiver based on the maximum-likelihood (ML) criterion. By considering a biased pulse amplitude modulation, we develop an analytical framework for the SM symbol error rate at high signal-to-noise ratios. Numerical results show that the diversity order is proportional to half the number of receive antennas; this result stems from having partial receiver channel knowledge. In addition, we compare the performance of the proposed scheme with that of the coherent ML receiver and show that the SM energy detector outperforms its coherent counterpart in certain scenarios, particularly when utilizing non-negative constellations. Ultimately, we implement an SM testbed using software-defined radio devices and provide experimental error rate measurements that validate our theoretical contribution.

翻译：本文提出了一种用于空间调制（SM）系统的非相干能量检测方案。与多输入多输出（MIMO）系统相比，SM通过单天线激活传输实现了低复杂度的实现，这一特性是其应用的主要动机。此外，基于能量检测的通信将信道状态信息限制在衰落增益的幅度上。这一设计避免了相位估计及其相关电路，因此适用于低成本、低功耗设备。我们基于最大似然（ML）准则推导了多天线接收机的能量检测度量。通过考虑有偏脉冲幅度调制，我们建立了高信噪比下SM符号错误率的分析框架。数值结果表明，分集阶数与接收天线数的一半成正比，这一结果源于部分接收信道知识。此外，我们将所提方案的性能与相干ML接收机进行了比较，并表明在某些场景下，特别是使用非负星座时，SM能量检测器优于其相干对应方案。最终，我们利用软件无线电设备实现了SM实验平台，并提供了验证理论贡献的实验误码率测量结果。