Precoder Index Modulation

Index modulation, where information bits are conveyed through antenna indices (spatial modulation) and subcarrier indices (subcarrier index modulation) in addition to information bits conveyed through conventional modulation symbols, is getting increased research attention. In this paper, we introduce {\em precoder index modulation}, where information bits are conveyed through the choice of a precoder matrix at the transmitter from a set of pre-determined pseudo-random phase precoder (PRPP) matrices. Combining precoder index modulation (PIM) and spatial modulation (SM), we introduce a PIM-SM scheme which conveys information bits through both antenna index as well as precoder index. Spectral efficiency (in bits per channel use) and bit error performance of these index modulation schemes are presented.Comment: arXiv admin note: substantial text overlap with arXiv:1401.654

Pseudo-random Phase Precoded Spatial Modulation

Spatial modulation (SM) is a transmission scheme that uses multiple transmit antennas but only one transmit RF chain. At each time instant, only one among the transmit antennas will be active and the others remain silent. The index of the active transmit antenna will also convey information bits in addition to the information bits conveyed through modulation symbols (e.g.,QAM). Pseudo-random phase precoding (PRPP) is a technique that can achieve high diversity orders even in single antenna systems without the need for channel state information at the transmitter (CSIT) and transmit power control (TPC). In this paper, we exploit the advantages of both SM and PRPP simultaneously. We propose a pseudo-random phase precoded SM (PRPP-SM) scheme, where both the modulation bits and the antenna index bits are precoded by pseudo-random phases. The proposed PRPP-SM system gives significant performance gains over SM system without PRPP and PRPP system without SM. Since maximum likelihood (ML) detection becomes exponentially complex in large dimensions, we propose low complexity local search based detection (LSD) algorithm suited for PRPP-SM systems with large precoder sizes. Our simulation results show that with 4 transmit antennas, 1 receive antenna, $5\times 20$ pseudo-random phase precoder matrix and BPSK modulation, the performance of PRPP-SM using ML detection is better than SM without PRPP with ML detection by about 9 dB at $10^{-2}$ BER. This performance advantage gets even better for large precoding sizes

Binary Continuous Phase Modulations Robust to a Modulation Index Mismatch

We consider binary continuous phase modulation (CPM) signals used in some recent low-cost and low-power consumption telecommunications standard. When these signals are generated through a low-cost transmitter, the real modulation index can end up being quite different from the nominal value employed at the receiver and a significant performance degradation is observed, unless proper techniques for the estimation and compensation are employed. For this reason, we design new binary schemes with a much higher robustness. They are based on the concatenation of a suitable precoder with binary input and a ternary CPM format. The result is a family of CPM formats whose phase state is constrained to follow a specific evolution. Two of these precoders are considered. We will discuss many aspects related to these schemes, such as the power spectral density, the spectral efficiency, simplified detection, the minimum distance, and the uncoded performance. The adopted precoders do not change the recursive nature of CPM schemes. So these schemes are still suited for serial concatenation, through a pseudo-random interleaver, with an outer channel encoder

MIMO Precoding with X- and Y-Codes

We consider a time division duplex (TDD) $n_t \times n_r$ multiple-input multiple-output (MIMO) system with channel state information (CSI) at both the transmitter and receiver. We propose X- and Y-Codes to achieve high multiplexing and diversity gains at low complexity. The proposed precoding schemes are based upon the singular value decomposition (SVD) of the channel matrix which transforms the MIMO channel into parallel subchannels. Then X- and Y-Codes are used to improve the diversity gain by pairing the subchannels, prior to SVD precoding. In particular, the subchannels with good diversity are paired with those having low diversity gains. Hence, a pair of channels is jointly encoded using a $2 \times 2$ real matrix, which is fixed {\em a priori} and does not change with each channel realization. For X-Codes these matrices are 2-dimensional rotation matrices parameterized by a single angle, while for Y-Codes, these matrices are 2-dimensional upper left triangular matrices. The complexity of the maximum likelihood decoding (MLD) for both X- and Y-Codes is low. Specifically, the decoding complexity of Y-Codes is the same as that of a scalar channel. Moreover, we propose X-, Y-Precoders with the same structure as X-, Y-Codes, but the encoding matrices adapt to each channel realization. The optimal encoding matrices for X-, Y-Codes/Precoders are derived analytically. Finally, it is observed that X-Codes/Precoders perform better for well-conditioned channels, while Y-Codes/Precoders perform better for ill-conditioned channels, when compared to other precoding schemes in the literature

Generalized Beamspace Modulation Using Multiplexing: A Breakthrough in mmWave MIMO

Spatial multiplexing (SMX) multiple-input multiple-output (MIMO) over the best beamspace was considered as the best solution for millimeter wave (mmWave) communications regarding spectral efficiency (SE), referred as the best beamspace selection (BBS) solution. The equivalent MIMO water-filling (WF-MIMO) channel capacity was treated as an unsurpassed SE upper bound. Recently, researchers have proposed various schemes trying to approach the benchmark and the performance bound. But, are they the real limit of mmWave MIMO systems with reduced radio-frequency (RF) chains? In this paper, we challenge the benchmark and the corresponding bound by proposing a better transmission scheme that achieves higher SE, namely the Generalized Beamspace Modulation using Multiplexing (GBMM). Inspired by the concept of spatial modulation, besides the selected beamspace, the selection operation is used to carry information. We prove that GBMM is superior to BBS in terms of SE and can break through the well known `upper bound'. That is, GBMM renews the upper bound of the SE. We investigate SE-oriented precoder activation probability optimization, fully-digital precoder design, optimal power allocation and hybrid precoder design for GBMM. A gradient ascent algorithm is developed to find the optimal solution, which is applicable in all signal-to-noise-ratio (SNR) regimes. The best solution is derived in the high SNR regime. Additionally, we investigate the hybrid receiver design and deduce the minimum number of receive RF chains configured to gain from GBMM in achievable SE. We propose a coding approach to realize the optimized precoder activation. An extension to mmWave broadband communications is also discussed. Comparisons with the benchmark (i.e., WF-MIMO channel capacity) are made under different system configurations to show the superiority of GBMM.Comment: Conference submitted to IC

Combining Beamforming and Space-Time Coding Using Noisy Quantized Feedback

The goal of combining beamforming and space-time coding in this work is to obtain full-diversity order and to provide additional received power (array gain) compared to conventional space-time codes. In our system, we consider a quasi-static fading environment and we incorporate both high-rate and low-rate feedback channels with possible feedback errors. To utilize feedback information, a class of code constellations is proposed, inspired from orthogonal designs and precoded space-time block codes, which is called generalized partly orthogonal designs or generalized PODs. Furthermore, to model feedback errors, we assume that the feedback bits go through binary symmetric channels (BSCs). Two cases are studied: first, when the BSC bit error probability is known a priori to the transmission ends and second, when it is not known exactly. In the first case, we derive a minimum pairwise error probability (PEP) design criterion for generalized PODs. Then we design the quantizer for the erroneous feedback channel and the precoder codebook of PODs based on this criterion. The quantization scheme in our system is a channel optimized vector quantizer (COVQ). In the second case, the design of the quantizer and the precoder codebook is based on similar approaches, however with a worst-case design strategy. The attractive property of our combining scheme is that it converges to conventional space-time coding with low-rate and erroneous feedback and to directional beamforming with high-rate and error-free feedback. This scheme shows desirable robustness against feedback channel modeling mismatch.Comment: In revision for IEEE Transactions on Communications, April 200

Generalized Spatial Modulation Aided MmWave MIMO with Sub-Connected Hybrid Precoding Scheme

Due to the high cost and low energy efficiency of the dedicated radio frequency (RF) chains, the number of RF chains in a millimeter wave (mmWave) multiple-input multiple-output (MIMO) system is usually limited from a practical point of view. In this case, the maximum number of independent data streams is also restricted by the number of RF chains, which consequently leads to limiting the potentially attainable spatial multiplexing gain. In order to address this issue, in this paper, a novel generalized spatial modulation (GenSM) aided mmWave MIMO system is proposed, which enables the transmission of an extra data stream via the index of the active antennas group and requires no extra RF chain. Moreover, a two-step algorithm is also proposed to optimize the hybrid precoder design with respect to spectral efficiency (SE) maximization. Finally, numerical simulation results demonstrate the superior SE performance achieved by the proposed scheme

Spatial Modulation for More Spatial Multiplexing: RF-Chain-Limited Generalized Spatial Modulation Aided MmWave MIMO with Hybrid Precoding

The application of hybrid precoding in millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems has been proved effective for reducing the number of radio frequency (RF) chains. However, the maximum number of independent data streams is conventionally restricted by the number of RF chains, which leads to limiting the spatial multiplexing gain. To further improve the achievable spectral efficiency (SE), in this paper we propose a novel generalized spatial modulation (GenSM) aided mmWave MIMO system to convey an extra data stream via the index of the active antennas group, while no extra RF chain is required. Moreover, we also propose a hybrid analog and digital precoding scheme for SE maximization. More specifically, a closed-form lower bound is firstly derived to quantify the achievable SE of the proposed system. By utilizing this lower bound as the cost function, a two-step algorithm is proposed to optimize the hybrid precoder. The proposed algorithm not only utilizes the concavity of the cost function over the digital power allocation vector, but also invokes the convex $\ell_\infty$ relaxation to handle the non-convex constraint imposed by analog precoding. Finally, the proposed scheme is shown via simulations to outperform state-of-the-art mmWave MIMO schemes in terms of achievable SE

Hybrid Beamforming with Spatial Modulation in Multi-user Massive MIMO mmWave Networks

The cost of radio frequency (RF) chains is the biggest drawback of massive MIMO millimeter wave networks. By employing spatial modulation (SM), it is possible to implement lower number of RF chains than transmit antennas but still achieve high spectral efficiency. In this work, we propose a system model of the SM scheme together with hybrid beamforming at the transmitter and digital combining at the receiver. In the proposed model, spatially-modulated bits are mapped onto indices of antenna arrays. It is shown that the proposed model achieves approximately 5dB gain over classical multi-user SM scheme with only 8 transmit antennas at each antenna array. This gain can be improved further by increasing the number of transmit antennas at each array without increasing the number of RF chains

Reconsidering Linear Transmit Signal Processing in 1-Bit Quantized Multi-User MISO Systems

In this contribution, we investigate a coarsely quantized Multi-User (MU)-Multiple Input Single Output (MISO) downlink communication system, where we assume 1-Bit Digital-to-Analog Converters (DACs) at the Base Station (BS) antennas. First, we analyze the achievable sum rate lower-bound using the Bussgang decomposition. In the presence of the non-linear quanization, our analysis indicates the potential merit of reconsidering traditional signal processing techniques in coarsely quantized systems, i.e., reconsidering transmit covariance matrices whose rank is equal to the rank of the channel. Furthermore, in the second part of this paper, we propose a linear precoder design which achieves the predicted increase in performance compared with a state of the art linear precoder design. Moreover, our linear signal processing algorithm allows for higher-order modulation schemes to be employed