Signal Shaping for Generalized Spatial Modulation and Generalized Quadrature Spatial Modulation

Abstract

This paper investigates generic signal shaping methods for multiple-data-stream generalized spatial modulation (GenSM) and generalized quadrature spatial modulation (Gen-QSM) based on the maximizing the minimum Euclidean distance (MMED) criterion. Three cases with different channel state information at the transmitter (CSIT) are considered, including no CSIT, statistical CSIT and perfect CSIT. A unified optimization problem is formulated to find the optimal transmit vector set under size, power and sparsity constraints. We propose an optimization-based signal shaping (OBSS) approach by solving the formulated problem directly and a codebook-based signal shaping (CBSS) approach by finding sub-optimal solutions in discrete space. In the OBSS approach, we reformulate the original problem to optimize the signal constellations used for each transmit antenna combination (TAC). Both the size and entry of all signal constellations are optimized. Specifically, we suggest the use of a recursive design for size optimization. The entry optimization is formulated as a non-convex large-scale quadratically constrained quadratic programming (QCQP) problem and can be solved by existing optimization techniques with rather high complexity. To reduce the complexity, we propose the CBSS approach using a codebook generated by quadrature amplitude modulation (QAM) symbols and a low-complexity selection algorithm to choose the optimal transmit vector set. Simulation results show that the OBSS approach exhibits the optimal performance in comparison with existing benchmarks. However, the OBSS approach is impractical for large-size signal shaping and adaptive signal shaping with instantaneous CSIT due to the demand of high computational complexity. As a lowcomplexity approach, CBSS shows comparable performance and can be easily implemented in large-size systems.

Improving Generalized Spatial Modulation Using Translation Patterns

“…Observe that the second term on the RHS of ( 9) is an increasing function of M and n a . Thus, substituting the smallest possible values for M and n a , i.e., M = 16 and n a = 2, in the RHS of (9) shows that δ(C T )/δ(C GSM ) is lower bounded by 60/49 (approximately 0.86 dB), for any m ≥ 2 and n a ≥ 2.…”

“…Several signal constellations have been proposed in the literature that improve the error performance of GSM [5]- [9], albeit with some design limitations. Enhanced Spatial Modulation (ESM) and its variants [5], [6] have been designed for limited choice of system parameters (for example, complex symbols must take values from 16-or 64-QAM and n a must be even for ESM-Type2 constellations [6]).…”

“…Note that, to minimize the cost of digital-to-analog conversion at the transmitter it is desirable to use signals that do not contain irrational components [10]. The signal design technique of [9] relies on a numerical optimization algorithm whose complexity increases exponentially in the spectral efficiency. The authors are with the Department of Electrical Engineering, IIT Hyderabad, Hyderabad 502285, India (e-mail: ee17btech11021@iith.ac.in; lakshminatarajan@iith.ac.in).…”

“…In comparison with [5]- [9], our technique allows a simple and explicit construction for any choice of alphabet size (for the complex symbols), and any choice of n t , n a ≥ 2. This flexibility allows us to achieve a wide range of spectral efficiencies, including the ability to encode integer number of information bits.…”

A Grouped Pre-Coding Aided Spatial Modulation for MIMO Systems

“…Spatial modulation (SM) has been considered as one promising paradigm for emerging multiple-antenna techniques [1]- [6], where only a single transmit antenna is activated in each time slot. Except for the conventional modulated symbol, in the SM system, the transmit antenna index is also employed to convey additional information.…”