Rakshith Rajashekar

Antenna Selection in Spatial Modulation Systems

Novel transmit antenna selection techniques are conceived for Spatial Modulation (SM) systems and their symbol error rate (SER) performance is investigated. Specifically, low-complexity Euclidean Distance optimized Antenna Selection (EDAS) and Capacity Optimized Antenna Selection (COAS) are studied. It is observed that the COAS scheme gives a better SER performance than the EDAS scheme. We show that the proposed antenna selection based SM systems are capable of attaining a significant gain in signal-to-noise ratio (SNR) compared to conventional SM systems, and also outperform the conventional MIMO systems employing antenna selection at both low and medium SNRs.

Reduced-Complexity ML Detection and Capacity-Optimized Training for Spatial Modulation Systems

Spatial Modulation (SM) is a recently developed low-complexity Multiple-Input Multiple-Output scheme that jointly uses antenna indices and a conventional signal set to convey information. It has been shown that the Maximum-Likelihood (ML) detector of an SM system involves joint detection of the transmit antenna index and of the transmitted symbol, hence, the ML search complexity grows linearly with the number of transmit antennas and the size of the signal set. To circumvent the problem, we show that the ML search complexity of an SM system may be rendered independent of the constellation size, provided that the signal set employed is a square- or a rectangular-QAM. Furthermore, we derive bounds for the capacity of the SM system and derive the optimal power allocation between the data and the training sequences by maximizing the worst-case capacity bound of the SM system operating with imperfect channel state information. We show, with the aid of our simulation results, that the proposed detector is ML-optimal, despite its lowest complexity amongst the existing detectors. Furthermore, we show that employing the proposed optimal power allocation provides a substantial gain in terms of the SM systems capacity as well as signal-to-noise ratio compared to its equal-power-allocation counterpart. Finally, we compare the performance of the SM system to that of the conventional Multiple-Input Multiple-Output (MIMO) system and show that the SM system is capable of outperforming the conventional MIMO system by a significant margin, when both the systems are employing optimal power splitting.

Spatial Modulation Aided Zero-Padded Single Carrier Transmission for Dispersive Channels

In this paper, we consider spatial modulation (SM) operating in a frequency-selective single-carrier (SC) communication scenario and propose zero-padding instead of the cyclic-prefix considered in the existing literature. We show that the zero-padded single-carrier (ZP-SC) SM system offers full multipath diversity under maximum-likelihood (ML) detection, unlike the cyclic-prefix based SM system. Furthermore, we show that the order of ML detection complexity in our proposed ZP-SC SM system is independent of the frame length and depends only on the number of multipath links between the transmitter and the receiver. Thus, we show that the zero-padding applied in the SC SM system has two advantages over the cyclic prefix: 1) achieves full multipath diversity, and 2) imposes a relatively low ML detection complexity. Furthermore, we extend the partial interference cancellation receiver (PIC-R) proposed by Guo and Xia for the detection of space-time block codes (STBCs) in order to convert the ZP-SC system into a set of narrowband subsystems experiencing flat-fading. We show that full rank STBC transmissions over these subsystems achieves full transmit, receive as well as multipath diversity for the PIC-R. Furthermore, we show that the ZP-SC SM system achieves receive and multipath diversity for the PIC-R at a detection complexity order which is the same as that of the SM system in flat-fading scenario. Our simulation results demonstrate that the symbol error ratio performance of the proposed linear receiver for the ZP-SC SM system is significantly better than that of the SM in cyclic prefix based orthogonal frequency division multiplexing as well as of the SM in the cyclic-prefixed and zero-padded single carrier systems relying on zero-forcing/minimum mean-squared error equalizer based receivers.

Modulation diversity for Spatial Modulation using Complex Interleaved Orthogonal Design

In this paper, we propose modulation diversity techniques for Spatial Modulation (SM) system using Complex Interleaved Orthogonal Design (CIOD). Specifically, we show that the standard SM scheme can achieve a transmit diversity order of two by using the CIOD meant for two transmit antenna system without incurring any additional system complexity or bandwidth requirement. Furthermore, we propose a low-complexity maximum likelihood detector for our CIOD based SM schemes by exploiting the structure of the CIOD. We show with our simulation results that the proposed schemes offer transmit diversity order of two and give a better symbol error rate performance than the conventional SM scheme.

Quantifying the Transmit Diversity Order of Euclidean Distance Based Antenna Selection in Spatial Modulation

In this letter, we quantify the transmit diversity order of the SM system operating in a closed-loop scenario. Specifically, the SM system relying on Euclidean distance based antenna subset selection (EDAS) is considered and the achievable diversity gain is evaluated. Furthermore, the resultant trade-off between the achievable diversity gain and switching gain is studied. Simulation results confirm our theoretical results. Specifically, switching gain is studied. Simulation results confirm our theoretical results. Specifically, at a symbol error rate of about 10-4 the signal-to-noise ratio gain achieved by EDAS is about 7 dBat a symbol error rate of about 10-4 the signal-to-noise ratio gain achieved by EDAS is about 7 dB in case of 16-QAM and about 5 dB in case of 64-QAM.

Generalized-Spatial-Modulation-Based Reduced-RF-Chain Millimeter-Wave Communications

A generalized spatial modulation (GSM)-based millimeter-wave communications system is proposed. The GSM transmitter is characterized by a lower number of radio frequency (RF) chains than the number of transmit antennas; hence, it is capable of reducing both the transmitter cost and the energy consumption. The antenna array alignment is optimized so as to maximize the rank of the channel matrix encountered. Furthermore, we employ an array of analog beamformers, which allows us to benefit both from the beamforming gain and from the GSM schemes high rate. It is demonstrated that the constrained capacity of the GSM transmitter equipped with as few as two RF chains is capable of approaching the performance of the full-RF spatial multiplexing having eight RF chains.

Hybrid Beamforming in mm-Wave MIMO Systems Having a Finite Input Alphabet

Recently, there has been significant research effort toward achieving high data rates in the millimeter wave bands by employing large antenna systems. These systems are considered to have only a fraction of the RF chains compared with the total number of antennas and employ analog phase shifters to steer the transmit and receive beams in addition to the conventional beamforming (BF)/combining invoked in the baseband domain. This scheme, which is popularly known as hybrid BF, has been extensively studied in the literature. To the best of our knowledge, all the existing schemes focus on obtaining the BF/combining matrices that maximize the system capacity computed using a Gaussian input alphabet. However, this choice of matrices may be suboptimal for practical systems, since they employ a finite input alphabet, such as quadrature amplitude modulation/phase-shift keying constellations. Hence, in this paper, we consider a hybrid BF/combining system operating with a finite input alphabet and optimize the analog as well as digital BF/combining matrices by maximizing the mutual information (MI). This is achieved by an iterative gradient ascent algorithm that exploits the relationship between the minimum mean-squared error and the MI. Furthermore, an iterative algorithm is proposed for designing a codebook for the analog and digital BF/combining matrices based on a vector quantization approach. Our simulation results demonstrate that the proposed gradient ascent algorithm achieves an ergodic rate improvement of up to 0.4 bits per channel use (bpcu) compared with the Gaussian input scenario. Furthermore, the gain in the ergodic rate achieved by employing the vector quantization-based codebook is about 0.5 bpcu compared with the Gaussian input scenario.

Full-Diversity Dispersion Matrices From Algebraic Field Extensions for Differential Spatial Modulation

We consider differential spatial modulation (DSM) operating in a block fading environment and propose sparse unitary dispersion matrices (DMs) using algebraic field extensions. The proposed DM sets are capable of exploiting full transmit diversity and, in contrast to the existing schemes, can be constructed for systems having an arbitrary number of transmit antennas. More specifically, two schemes are proposed: 1) field-extension-based DSM (FE-DSM), where only a single conventional symbol is transmitted per space–time block; and 2) FE-DSM striking a diversity–rate tradeoff (FE-DSM-DR), where multiple symbols are transmitted in each space–time block at the cost of a reduced transmit diversity gain. Furthermore, the FE-DSM scheme is analytically shown to achieve full transmit diversity, and both proposed schemes are shown to impose decoding complexity, which is independent of the size of the signal set. It is observed from our simulation results that the proposed FE-DSM scheme suffers no performance loss compared with the existing DM-based DSM (DM-DSM) scheme, whereas FE-DSM-DR is observed to give a better bit-error-ratio performance at higher data rates than its DM-DSM counterpart. Specifically, at data rates of 2.25 and 2.75 bits per channel use, FE-DSM-DR is observed to achieve about 1- and 2-dB signal-to-noise ratio (SNR) gain with respect to its DM-DSM counterpart.

Field Extension Code Based Dispersion Matrices for Coherently Detected Space-Time Shift Keying

Motivated by the recent Coherent Space-Time Shift Keying (CSTSK) philosophy, we construct new dispersion matrices for rotationally invariant PSK signaling sets. Given a specific PSK signal constellation, the dispersion matrices of the existing CSTSK scheme were chosen by maximizing the mutual information over randomly generated sets of dispersion matrices. In this contribution we propose a general method for constructing a set of structured dispersion matrices for arbitrary PSK signaling sets using Field Extension (FE) codes and then study the attainable Symbol Error Rate (SER) performance of some example constructions. We demonstrate that the proposed dispersion scheme is capable of outperforming the existing dispersion arrangement at medium to high SNRs.

Iterative Matrix Decomposition Aided Block Diagonalization for mm-Wave Multiuser MIMO Systems

Considering the dearth for spectrum in the congested microwave band, the next generation of cellular communication systems is envisaged to incorporate part of the millimeter wave (mm-wave) band. Hence, recently, there has been a significant interest in beamforming aided mm-wave systems. We consider a downlink multiuser mm-wave system employing a large number of antennas combined with fewer radio frequency chains both at the base station (BS) and at each of the user equipments (UEs). The BS and each of the UE are assumed to have a hybrid beamforming architecture, where a set of analog phase shifters is followed by digital precoding/combining blocks. In this paper, we propose an iterative matrix decomposition based hybrid beamforming (IMD-HBF) scheme for a single-user scenario, which accurately approximates the unconstrained beamforming solution, we show that the knowledge of the angle of departure (AoD) of the various channel paths is sufficient for the block diagonalization (BD) of the downlink mm-wave channel and hence for achieving interference free channels for each of the UEs, we propose a novel subspace projection based AoD aided BD (SP-AoD-BD) that achieves significantly better performance than the conventional BD, while still only requiring the knowledge of the AoD of various channel paths, and we use IMD-HBF in order to employ SP-AoD-BD in the hybrid beamforming architecture and study its performance with respect to the unconstrained system. We demonstrate using simulation results that the proposed IMD-HBF gives the same spectral efficiency as that of the unconstrained system in the single user scenario. Furthermore, we study the achievable sum rate of the users, when employing SP-AoD-BD with the aid of IMD-HBF and show that the loss in the performance with respect to the unconstrained system as well as the existing schemes is negligible, provided that the number of users is not excessive.