On the Capacity and Performance of Generalized Spatial Modulation

Generalized spatial modulation (GSM) uses $N$ antenna elements but fewer radio frequency (RF) chains ($R$) at the transmitter. Spatial modulation and spatial multiplexing are special cases of GSM with $R=1$ and $R=N$, respectively. In GSM, apart from conveying information bits through $R$ modulation symbols, information bits are also conveyed through the indices of the $R$ active transmit antennas. In this paper, we derive lower and upper bounds on the the capacity of a ($N,M,R$)-GSM MIMO system, where $M$ is the number of receive antennas. Further, we propose a computationally efficient GSM encoding (i.e., bits-to-signal mapping) method and a message passing based low-complexity detection algorithm suited for large-scale GSM-MIMO systems.Comment: Expanded version of the IEEE Communications Letters pape

Generalized Spatial Modulation in Indoor Wireless Visible Light Communication

In this paper, we investigate the performance of generalized spatial modulation (GSM) in indoor wireless visible light communication (VLC) systems. GSM uses $N_t$ light emitting diodes (LED), but activates only $N_a$ of them at a given time. Spatial modulation and spatial multiplexing are special cases of GSM with $N_{a}=1$ and $N_{a}=N_t$, respectively. We first derive an analytical upper bound on the bit error rate (BER) for maximum likelihood (ML) detection of GSM in VLC systems. Analysis and simulation results show that the derived upper bound is very tight at medium to high signal-to-noise ratios (SNR). The channel gains and channel correlations influence the GSM performance such that the best BER is achieved at an optimum LED spacing. Also, for a fixed transmission efficiency, the performance of GSM in VLC improves as the half-power semi-angle of the LEDs is decreased. We then compare the performance of GSM in VLC systems with those of other MIMO schemes such as spatial multiplexing (SMP), space shift keying (SSK), generalized space shift keying (GSSK), and spatial modulation (SM). Analysis and simulation results show that GSM in VLC outperforms the other considered MIMO schemes at moderate to high SNRs; for example, for 8 bits per channel use, GSM outperforms SMP and GSSK by about 21 dB, and SM by about 10 dB at $10^{-4}$ BER

On the Capacity of Generalized Quadrature Spatial Modulation

In this letter, the average mutual information (AMI) of generalized quadrature spatial modulation (GQSM) is first derived for continuous-input continuous-output channels. Our mathematical analysis shows that the calculation error induced by Monte Carlo integration increases exponentially with the signal-to-noise ratio. This nature of GQSM is resolved by deriving a closed-form expression. The derived AMI is compared with other related SM schemes and evaluated for different antenna activation patterns. Our results show that an equiprobable antenna selection method slightly decreases AMI of symbols, while the method significantly improves AMI in total.Comment: 5 pages, 5 figure

Peregrine comb: multiple compression points for Peregrine rogue waves in periodically modulated nonlinear Schr{\"o}dinger equations

It is shown that sufficiently large periodic modulations in the coefficients of a nonlinear Schr{\"o}dinger equation can drastically impact the spatial shape of the Peregrine soliton solutions: they can develop multiple compression points of the same amplitude, rather than only a single one, as in the spatially homogeneous focusing nonlinear Schr{\"o}dinger equation. The additional compression points are generated in pairs forming a comb-like structure. The number of additional pairs depends on the amplitude of the modulation but not on its wavelength, which controls their separation distance. The dynamics and characteristics of these generalized Peregrine soliton are analytically described in the case of a completely integrable modulation. A numerical investigation shows that their main properties persist in nonintegrable situations, where no exact analytical expression of the generalized Peregrine soliton is available. Our predictions are in good agreement with numerical findings for an interesting specific case of an experimentally realizable periodically dispersion modulated photonic crystal fiber. Our results therefore pave the way for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in the wide class of physical systems modeled by the nonlinear Schr{\"o}dinger equation

Generalized Spatial Modulation in Large-Scale Multiuser MIMO Systems

Generalized spatial modulation (GSM) uses $n_t$ transmit antenna elements but fewer transmit radio frequency (RF) chains, $n_{rf}$. Spatial modulation (SM) and spatial multiplexing are special cases of GSM with $n_{rf}=1$ and $n_{rf}=n_t$, respectively. In GSM, in addition to conveying information bits through $n_{rf}$ conventional modulation symbols (for example, QAM), the indices of the $n_{rf}$ active transmit antennas also convey information bits. In this paper, we investigate {\em GSM for large-scale multiuser MIMO communications on the uplink}. Our contributions in this paper include: ($i$) an average bit error probability (ABEP) analysis for maximum-likelihood detection in multiuser GSM-MIMO on the uplink, where we derive an upper bound on the ABEP, and ($ii$) low-complexity algorithms for GSM-MIMO signal detection and channel estimation at the base station receiver based on message passing. The analytical upper bounds on the ABEP are found to be tight at moderate to high signal-to-noise ratios (SNR). The proposed receiver algorithms are found to scale very well in complexity while achieving near-optimal performance in large dimensions. Simulation results show that, for the same spectral efficiency, multiuser GSM-MIMO can outperform multiuser SM-MIMO as well as conventional multiuser MIMO, by about 2 to 9 dB at a bit error rate of $10^{-3}$. Such SNR gains in GSM-MIMO compared to SM-MIMO and conventional MIMO can be attributed to the fact that, because of a larger number of spatial index bits, GSM-MIMO can use a lower-order QAM alphabet which is more power efficient.Comment: IEEE Trans. on Wireless Communications, accepte

On the Performance of MIMO FSO Communications over Double Generalized Gamma Fading Channels

A major performance degrading factor in free space optical communication (FSO) systems is atmospheric turbulence. Spatial diversity techniques provide a promising approach to mitigate turbulence-induced fading. In this paper, we study the error rate performance of FSO links with spatial diversity over atmospheric turbulence channels described by the Double Generalized Gamma distribution which is a new generic statistical model covering all turbulence conditions. We assume intensity modulation/direct detection with on-off keying and present the BER performance of single-input multiple-output (SIMO), multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) FSO systems over this new channel model.Comment: 6 Pages, 4 figure, IEEE ICC conference 201

Downlink Precoding for Massive MIMO Systems Exploiting Virtual Channel Model Sparsity

In this paper, the problem of designing a forward link linear precoder for Massive Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, we employ a novel and efficient methodology that allows for a sparse representation of multiple users and groups in a fashion similar to Joint Spatial Division and Multiplexing. Then, the method is generalized to include Orthogonal Frequency Division Multiplexing (OFDM) for frequency selective channels, resulting in Combined Frequency and Spatial Division and Multiplexing, a configuration that offers high flexibility in Massive MIMO systems. A challenge in such system design is to consider finite alphabet inputs, especially with larger constellation sizes such as $M\geq 16$. The proposed methodology is next applied jointly with the complexity-reducing Per-Group Processing (PGP) technique, on a per user group basis, in conjunction with QAM modulation and in simulations, for constellation size up to $M=64$. We show by numerical results that the precoders developed offer significantly better performance than the configuration with no precoder or the plain beamformer and with $M\geq 16$

Complex Quadrature Spatial Modulation

In this paper, we propose a spatial modulation (SM) scheme referred to as complex quadrature spatial modulation (CQSM). In contrast to quadrature spatial modulation (QSM), CQSM transmits two complex signal constellation symbols on the real and quadrature spatial dimensions at each channel use, increasing the spectral efficiency. To this end, signal symbols transmitted at any given time instant are drawn from two different modulation sets. The first modulation set is any of the conventional QAM/PSK alphabets, while the second is a rotated version of it. The optimal rotation angle is obtained through simulations for several modulation schemes and analytically proven for the case of QPSK, where both results coincide. Simulation results showed that CQSM outperformed QSM and generalized SM (GSM) by approximately 5 and 4.5 dB, respectively, for the same transmission rate. Its performance was similar to that of QSM; however, it achieved higher transmission rates. It was additionally shown numerically and analytically that CQSM outperformed QSM for a relatively large number of transmit antennas.Comment: 11 pages, 3 tables, 11 figures. ETRI Journal, 201