Communication Over MIMO Broadcast Channels Using Lattice-Basis Reduction

A simple scheme for communication over MIMO broadcast channels is introduced which adopts the lattice reduction technique to improve the naive channel inversion method. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. Simulation results show that the proposed scheme performs well, and as compared to the more complex methods (such as the perturbation method) has a negligible loss. Moreover, the proposed method is extended to the case of different rates for different users. The asymptotic behavior of the symbol error rate of the proposed method and the perturbation technique, and also the outage probability for the case of fixed-rate users is analyzed. It is shown that the proposed method, based on LLL lattice reduction, achieves the optimum asymptotic slope of symbol-error-rate (called the precoding diversity). Also, the outage probability for the case of fixed sum-rate is analyzed.Comment: Submitted to IEEE Trans. on Info. Theory (Jan. 15, 2006), Revised (Jun. 12, 2007

SCMA Codebook Design

Multicarrier CDMA is a multiple access scheme in which modulated QAM symbols are spread over OFDMA tones by using a generally complex spreading sequence. Effectively, a QAM symbol is repeated over multiple tones. Low density signature (LDS) is a version of CDMA with low density spreading sequences allowing us to take advantage of a near optimal message passing algorithm (MPA) receiver with practically feasible complexity. Sparse code multiple access (SCMA) is a multi-dimensional codebook-based non-orthogonal spreading technique. In SCMA, the procedure of bit to QAM symbol mapping and spreading are combined together and incoming bits are directly mapped to multi-dimensional codewords of SCMA codebook sets. Each layer has its dedicated codebook. Shaping gain of a multi-dimensional constellation is one of the main sources of the performance improvement in comparison to the simple repetition of QAM symbols in LDS. Meanwhile, like LDS, SCMA enjoys the low complexity reception techniques due to the sparsity of SCMA codewords. In this paper a systematic approach is proposed to design SCMA codebooks mainly based on the design principles of lattice constellations. Simulation results are presented to show the performance gain of SCMA compared to LDS and OFDMA.Comment: Accepted for IEEE VTC-fall 201

Lattice-Based Precoding And Decoding in MIMO Fading Systems

In this thesis, different aspects of lattice-based precoding and decoding for the transmission of digital and analog data over MIMO fading channels are investigated: 1) Lattice-based precoding in MIMO broadcast systems: A new viewpoint for adopting the lattice reduction in communication over MIMO broadcast channels is introduced. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. The new viewpoint helps us to generalize the idea of lattice-reduction-aided precoding for the case of unequal-rate transmission, and obtain analytic results for the asymptotic behavior of the symbol-error-rate for the lattice-reduction-aided precoding and the perturbation technique. Also, the outage probability for both cases of fixed-rate users and fixed sum-rate is analyzed. It is shown that the lattice-reduction-aided method, using LLL algorithm, achieves the optimum asymptotic slope of symbol-error-rate (called the precoding diversity). 2) Lattice-based decoding in MIMO multiaccess systems and MIMO point-to-point systems: Diversity order and diversity-multiplexing tradeoff are two important measures for the performance of communication systems over MIMO fading channels. For the case of MIMO multiaccess systems (with single-antenna transmitters) or MIMO point-to-point systems with V-BLAST transmission scheme, it is proved that lattice-reduction-aided decoding achieves the maximum receive diversity (which is equal to the number of receive antennas). Also, it is proved that the naive lattice decoding (which discards the out-of-region decoded points) achieves the maximum diversity in V-BLAST systems. On the other hand, the inherent drawbacks of the naive lattice decoding for general MIMO fading systems is investigated. It is shown that using the naive lattice decoding for MIMO systems has considerable deficiencies in terms of the diversity-multiplexing tradeoff. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the non-vanishing determinant property can not achieve the optimal diversity-multiplexing tradeoff. 3) Lattice-based analog transmission over MIMO fading channels: The problem of finding a delay-limited schemes for sending an analog source over MIMO fading channels is investigated in this part. First, the problem of robust joint source-channel coding over an additive white Gaussian noise channel is investigated. A new scheme is proposed which achieves the optimal slope for the signal-to-distortion-ratio (SDR) curve (unlike the previous known coding schemes). Then, this idea is extended to MIMO channels to construct lattice-based codes for joint source-channel coding over MIMO channels. Also, similar to the diversity-multiplexing tradeoff, the asymptotic performance of MIMO joint source-channel coding schemes is characterized, and a concept called diversity-fidelity tradeoff is introduced in this thesis

Beyond Codebook-Based Analog Beamforming at mmWave: Compressed Sensing and Machine Learning Methods

Analog beamforming is the predominant approach for millimeter wave (mmWave) communication given its favorable characteristics for limited-resource devices. In this work, we aim at reducing the spectral efficiency gap between analog and digital beamforming methods. We propose a method for refined beam selection based on the estimated raw channel. The channel estimation, an underdetermined problem, is solved using compressed sensing (CS) methods leveraging angular domain sparsity of the channel. To reduce the complexity of CS methods, we propose dictionary learning iterative soft-thresholding algorithm, which jointly learns the sparsifying dictionary and signal reconstruction. We evaluate the proposed method on a realistic mmWave setup and show considerable performance improvement with respect to code-book based analog beamforming approaches

Analog coding for delay-limited applications

In this paper, we consider the problem of sending an analog source over an additive white Gaussian noise channel. The traditional analog coding schemes suffer from the threshold effect. We introduce two robust schemes for analog conding. Unlike the previous methods, the new methods asymptotically achieve the optimal scaling of the signal-to-distortion-ratio (SDR) without being affected by the threshold effect. Also, we show that approximated versions of these techniques perform well for the practical applications, with a low complexity in encoding/decoding

A New code for high-rate differential space-time transmission

In [1], a differential space-time modulation scheme (based on unitary matrices) are presented that can be used without knowledge of the Channel State Information (CSI) at the receiver. This is suitable for mobile communication applications where fading coefficients change rapidly with time. All previous differential space-time codes have been designed to produce full diversity. However, by sacrificing the diversity, one can increase the rate per channel use of the space-time modulation [2]. For very high values of Signal-to-Noise-Ratio (SNR), the performance of multiple-antenna systems is determined by diversity product. However, maximizing the diversity product is not the appropriate criterion for high-rate communications operating in practical ranges of SNR for the case of using multiple receive antennas. Indeed, for reasonable range of SNR values, when the number of receive antennas is greater than or equal to the number of transmit antennas, the diversity sum (minimum squared Euclidean distance) is more important than the diversity product. In this paper, we present a practical sub-optimum solution to the problem of high-rate non-coherent communication over a Multiple-Input Multiple-Output (MIMO) fading channel with M transmit antennas. We use a differential transmission scheme with unitary codewords in the form of V=D1AD2 where D1 and D2 are diagonal matrices with unit-norm elements and A is a fixed unitary matrix. To have a good distance distribution for the codewords, we show that A must have equal-norm elements [3], e.g., A can be selected as the Vandermonde matrix with M’th roots of unity, i.e., ⎡1

Spectrally-Efficient Differential Space-Time Coding Using Non-Full-Diverse Constellations

A method to construct spectral-efficient unitary space-time codes is proposed for high-rate differential communications over multiple-antenna channels. Unlike most of the known methods which are designed to maximize the diversity product (minimum determinant distance), we aim at increasing the spectral efficiency. Simulation results indicate that for high spectral efficiency and for more than one receive antenna, the new method significantly outperforms the other known alternatives. In the special case of two transmit antennas, which is the main focus of this paper, the relation between the proposed code and the Alamouti scheme helps us to provide an efficient maximum likelihood decoding algorithm. We also show that similar ideas can be applied to more than two transmit antennas. As an example, we present a construction for 4 by 4 unitary constellations which has a good performance as compared to the other known codes

Spectral-Efficient Differential Space-Time Coding Using Non-Full-Diverse Constellations

In this paper, a method is proposed to construct spectral-efficient unitary space-time codes for high-rate differential communications over multiple-antenna channels. Unlike most of the known methods which are designed to maximize the diversity product (the minimum determinant distance), our objective is to increase the spectral efficiency. The simulation results indicate that for high spectral efficiency and for more than one receive antenna, the new method significantly outperforms the existing alternatives. In the special case of two transmit antennas, which is the main focus of this paper, the relation between the proposed code and the Alamouti scheme helps us to provide an efficient Maximum Likelihood (ML) decoding algorithm. Also, we demonstrate that similar ideas can be applied for designing codes for more than two transmit antennas. As an example, we present a construction for 4 by 4 unitary constellations which has a good performance as compared to the other known codes