Space Shift Keying (SSK—) MIMO with Practical Channel Estimates

Abstract

Abstract-In this paper, we study the performance of space modulation for Multiple-Input-Multiple-Output (MIMO) wireless systems with imperfect channel knowledge at the receiver. We focus our attention on two transmission technologies, which are the building blocks of space modulation: i) Space Shift Keying (SSK) modulation; and ii) Time-Orthogonal-Signal-Design (TOSD-) SSK modulation, which is an improved version of SSK modulation providing transmit-diversity. We develop a singleintegral closed-form analytical framework to compute the Average Bit Error Probability (ABEP) of a mismatched detector for both SSK and TOSD-SSK modulations. The framework exploits the theory of quadratic-forms in conditional complex Gaussian Random Variables (RVs) along with the Gil-Pelaez inversion theorem. The analytical model is very general and can be used for arbitrary transmit-and receive-antennas, fading distributions, fading spatial correlations, and training pilots. The analytical derivation is substantiated through Monte Carlo simulations, and it is shown, over independent and identically distributed (i.i.d.) Rayleigh fading channels, that SSK modulation is as robust as single-antenna systems to imperfect channel knowledge, and that TOSD-SSK modulation is more robust to channel estimation errors than the Alamouti scheme. Furthermore, it is pointed out that only few training pilots are needed to get reliable enough channel estimates for data detection, and that transmitand receive-diversity of SSK and TOSD-SSK modulations are preserved even with imperfect channel knowledge.Index Terms-Imperfect channel knowledge, "massive" multiple-input-multiple-output (MIMO) systems, mismatched receiver, performance analysis, single-RF MIMO design, space shift keying (SSK) modulation, spatial modulation (SM), transmit-diversity.

Single-Carrier SM-MIMO: A Promising Design for Broadband Large-Scale Antenna Systems

“…However, in order 36 to satisfy the ever-growing demands for higher capacity, larger 37 coverage area and better reliability, further improved MIMO 38 transceivers should be designed [6]. 39 Pursuing this research objective, the concept of large-scale 40 MIMO (LS-MIMO) techniques has been proposed [6]- [12], 41 which employs tens to hundreds of transmit/receive anten- 42 nas for dramatically improving the attainable link reliability, 43 spectral efficiency and cellular coverage. Usually, the multiple-44 antenna front-end architecture requires a separate radio fre-45 quency (RF) chain.…”

Adaptive generalized space shift keying

“…This way, the achievable transmit-diversity gain with the proposed design, which is denoted as SSK-time orthogonal signal design (SSK-TOSD), is equal to two. The realization of practical time-orthogonal shaping filters is discussed in [26]. In addition, the same authors apply in [22] their time-orthogonal shaping filter design to GSSK systems and they prove that the achievable transmit-diversity gains are equal to the minimum number of different channel links among all the possible pairs of constellation points.…”

“…Consequently, the question that comes into our mind is: could we somehow enhance the AGSSK method by avoiding the negative term inside the argument of the Q-function? The answer is affirmative by considering the properties of time-orthogonal waveforms [26]. Specifically, assuming two time-orthogonal waveforms u i (t) and u p (t), then:…”

End-to-end BER analysis of space shift keying in decode-and-forward cooperative relaying

“…Several of these performance analysis works consider point-to-point fading channels, and only few of them consider relay channels. For example, BER analysis of SSK in various point-to-point fading scenarios have been reported in [2]- [6]; analysis for i.i.d.…”

“…Rayleigh fading MIMO in [2], Nakagami-m fading MISO in [3], [4], Rician fading MIMO in [5], and Rayleigh fading MIMO with imperfect CSI in [6]. Likewise, BER analyses of SM in point-to-point fading have been reported in [7], [8]; analysis for i.i.d.…”