Coded transmit diversity in CDMA over Nakagami-m fading channels

With applications such as video conferencing, extensive web browsing and live video streaming, future wireless systems become extremely demanding in terms of high data rates and improved signal quality. In this thesis the performance of a space-time spreading transmit diversity scheme is examined over a frequency-flat Nakagami- m fading channel. The Nakagami- m channel model is considered as it is well known for modeling signal fading conditions ranging from severe to moderate, to light fading or no fading, through its parameter m. We also propose in this thesis a coded transmit diversity scheme which is based on a combination of a convolutional code with a space-time transmit diversity scheme that uses direct-sequence code division multiple access (DS-CDMA) for multiuser access. Our focus will be on the uplink of the communication system. The space-time scheme employs N = 2 and N r antennas at the mobile station (MS) side and at the base station (BS) side respectively. DS-CDMA is used to support many users and a linear decorrelator detector is used to combat the effect of multiuser interference. We study the performance of both the uncoded and coded transmit diversity schemes over slow fading and fast fading channels. In all cases, the investigations start by determining the probability density function (PDF) of the signal to interference and noise ratio at the output of the space-time combiner at the BS receiver side. Using this PDF we derive a closed-form (or an approximation) expression for the bit error rate (BER) of the system under consideration. The accuracy of the PDF and BER expressions are verified when compared to simulation results for different values of the fading figure m and for different combinations of transmit and receive antennas. In the case of the coded space-time transmit diversity scheme, the pairwise error probability and the corresponding BER upper bounds are obtained for fast and slow fading channels. The derived error bounds, when compared to system simulations, are shown to be tight at high signal-to-noise ratios. Furthermore, our analytical results explicitly show the achieved system diversity in terms of the number of transmit and receive antennas and the fading figure m. When the coded space-time scheme is considered, its diversity is shown to be a function of the minimum free distance d free of the convolutional code used. Furthermore we show that the diversity of the different schemes considered is always independent of the system loa

Precoding for Outage Probability Minimization on Block Fading Channels

The outage probability limit is a fundamental and achievable lower bound on the word error rate of coded communication systems affected by fading. This limit is mainly determined by two parameters: the diversity order and the coding gain. With linear precoding, full diversity on a block fading channel can be achieved without error-correcting code. However, the effect of precoding on the coding gain is not well known, mainly due to the complicated expression of the outage probability. Using a geometric approach, this paper establishes simple upper bounds on the outage probability, the minimization of which yields to precoding matrices that achieve very good performance. For discrete alphabets, it is shown that the combination of constellation expansion and precoding is sufficient to closely approach the minimum possible outage achieved by an i.i.d. Gaussian input distribution, thus essentially maximizing the coding gain.Comment: Submitted to Transactions on Information Theory on March 23, 201

Error Rates of the Maximum-Likelihood Detector for Arbitrary Constellations: Convex/Concave Behavior and Applications

Motivated by a recent surge of interest in convex optimization techniques, convexity/concavity properties of error rates of the maximum likelihood detector operating in the AWGN channel are studied and extended to frequency-flat slow-fading channels. Generic conditions are identified under which the symbol error rate (SER) is convex/concave for arbitrary multi-dimensional constellations. In particular, the SER is convex in SNR for any one- and two-dimensional constellation, and also in higher dimensions at high SNR. Pairwise error probability and bit error rate are shown to be convex at high SNR, for arbitrary constellations and bit mapping. Universal bounds for the SER 1st and 2nd derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, an implication for fading channels ("fading is never good in low dimensions") and optimization of a unitary-precoded OFDM system. For example, the error rate bounds of a unitary-precoded OFDM system with QPSK modulation, which reveal the best and worst precoding, are extended to arbitrary constellations, which may also include coding. The reported results also apply to the interference channel under Gaussian approximation, to the bit error rate when it can be expressed or approximated as a non-negative linear combination of individual symbol error rates, and to coded systems.Comment: accepted by IEEE IT Transaction

Exploiting diversity in wireless channels with bit-interleaved coded modulation and iterative decoding (BICM-ID)

This dissertation studies a state-of-the-art bandwidth-efficient coded modulation technique, known as bit interleaved coded modulation with iterative decoding (BICM-ID), together with various diversity techniques to dramatically improve the performance of digital communication systems over wireless channels. For BICM-ID over a single-antenna frequency non-selective fading channel, the problem of mapping over multiple symbols, i.e., multi-dimensional (multi-D) mapping, with 8-PSK constellation is investigated. An explicit algorithm to construct a good multi-D mapping of 8-PSK to improve the asymptotic performance of BICM-ID systems is introduced. By comparing the performance of the proposed mapping with an unachievable lower bound, it is conjectured that the proposed mapping is the global optimal mapping. The superiority of the proposed mapping over the best conventional (1-dimensional complex) mapping and the multi-D mapping found previously by computer search is thoroughly demonstrated. In addition to the mapping issue in single-antenna BICM-ID systems, the use of signal space diversity (SSD), also known as linear constellation precoding (LCP), is considered in BICM-ID over frequency non-selective fading channels. The performance analysis of BICM-ID and complex N-dimensional signal space diversity is carried out to study its performance limitation, the choice of the rotation matrix and the design of a low-complexity receiver. Based on the design criterion obtained from a tight error bound, the optimality of the rotation matrix is established. It is shown that using the class of optimal rotation matrices, the performance of BICM-ID systems over a frequency non-selective Rayleigh fading channel approaches that of the BICM-ID systems over an additive white Gaussian noise (AWGN) channel when the dimension of the signal constellation increases. Furthermore, by exploiting the sigma mapping for any M-ary quadrature amplitude modulation (QAM) constellation, a very simple sub-optimal, yet effective iterative receiver structure suitable for signal constellations with large dimensions is proposed. Simulation results in various cases and conditions indicate that the proposed receiver can achieve the analytical performance bounds with low complexity. The application of BICM-ID with SSD is then extended to the case of cascaded Rayleigh fading, which is more suitable to model mobile-to-mobile communication channels. By deriving the error bound on the asymptotic performance, it is first illustrated that for a small modulation constellation, a cascaded Rayleigh fading causes a much more severe performance degradation than a conventional Rayleigh fading. However, BICM-ID employing SSD with a sufficiently large constellation can close the performance gap between the Rayleigh and cascaded Rayleigh fading channels, and their performance can closely approach that over an AWGN channel. In the next step, the use of SSD in BICM-ID over frequency selective Rayleigh fading channels employing a multi-carrier modulation technique known as orthogonal frequency division multiplexing (OFDM) is studied. Under the assumption of correlated fading over subcarriers, a tight bound on the asymptotic error performance for the general case of applying SSD over all N subcarriers is derived and used to establish the best achievable asymptotic performance by SSD. It is then shown that precoding over subgroups of at least L subcarriers per group, where L is the number of channel taps, is sufficient to obtain this best asymptotic error performance, while significantly reducing the receiver complexity. The optimal joint subcarrier grouping and rotation matrix design is subsequently determined by solving the Vandermonde linear system. Illustrative examples show a good agreement between various analytical and simulation results. Further, by combining the ideas of multi-D mapping and subcarrier grouping, a novel power and bandwidth-efficient bit-interleaved coded modulation with OFDM and iterative decoding (BI-COFDM-ID) in which multi-D mapping is performed over a group of subcarriers for broadband transmission in a frequency selective fading environment is proposed. A tight bound on the asymptotic error performance is developed, which shows that subcarrier mapping and grouping have independent impacts on the overall error performance, and hence they can be independently optimized. Specifically, it is demonstrated that the optimal subcarrier mapping is similar to the optimal multi-D mapping for BICM-ID in frequency non-selective Rayleigh fading environment, whereas the optimal subcarrier grouping is the same with that of OFDM with SSD. Furthermore, analytical and simulation results show that the proposed system with the combined optimal subcarrier mapping and grouping can achieve the full channel diversity without using SSD and provide significant coding gains as compared to the previously studied BI-COFDM-ID with the same power, bandwidth and receiver complexity. Finally, the investigation is extended to the application of BICM-ID over a multiple-input multiple-output (MIMO) system equipped with multiple antennas at both the transmitter and the receiver to exploit both time and spatial diversities, where neither the transmitter nor the receiver knows the channel fading coefficients. The concentration is on the class of unitary constellation, due to its advantages in terms of both information-theoretic capacity and error probability. The tight error bound with respect to the asymptotic performance is also derived for any given unitary constellation and mapping rule. Design criteria regarding the choice of unitary constellation and mapping are then established. Furthermore, by using the unitary constellation obtained from orthogonal design with quadrature phase-shift keying (QPSK or 4-PSK) and 8-PSK, two different mapping rules are proposed. The first mapping rule gives the most suitable mapping for systems that do not implement iterative processing, which is similar to a Gray mapping in coherent channels. The second mapping rule yields the best mapping for systems with iterative decoding. Analytical and simulation results show that with the proposed mappings of the unitary constellations obtained from orthogonal designs, the asymptotic error performance of the iterative systems can closely approach a lower bound which is applicable to any unitary constellation and mapping

Performance evaluation of communication systems with transmit diversity

Transmit diversity is a key technique to combat fading with multiple transmit antennae for next-generation wireless communication systems. Space-time block code (STBC) is a main component of this technique. This dissertation consists of four parts: the first three discuss performance evaluation of STBCs in various circumstances, the fourth outlines a novel differential scheme with full transmit diversity. In the first part, closed-form expressions for the bit error rate (BER) are derived for STBC based on Alamouti\u27s scheme and utilizing M-ary phase shift keying (MPSK) modulation. The analysis is carried out for a slow, flat Rayleigh fading channel with coherent detection and with non-coherent differential encoding/decoding. The BER expression for coherent detection is exact. But for differential detection it is an approximation appropriate for a high signal-to-noise ratio. Numerical results are provided for analysis and simulations for BPSK and QPSK modulations. A signal-to-noise ratio loss of approximately 3 dB always occurs with conventional differential detection for STBC compared to coherent detection. In the second part of this dissertation, a multiple-symbol differential detection (MSDD) technique is proposed for MPSK STBCs, which greatly reduces this performance loss by extending the observation interval for decoding. The technique uses maximum likelihood block sequence detection instead of traditional block-by-block detection and is carried out on the slow, flat Rayleigh fading channel. A generalized decision metric for an observation interval of N blocks is derived. It is shown that for a moderate number of blocks, MSDD provides more than 1.0 dB performance improvement corresponding to conventional differential detection. In addition, a closed-form pairwise error probability for differential BPSI( STBC is derived for an observation interval of N blocks, and an approximate BER is obtained to evaluate the performance. In the third part, the BER performance of STBC over a spatio-temporal correlated channel with coherent and noncoherent detection is illustrated, where a general space-time correlation model is utilized. The simulation results demonstrate that spatial correlation negatively effects the performance of the STBC scheme with differential detection but temporal correlation positively impacts it. However, with coherent detection, spatial correlation still has negative effect on the performance but temporal correlation has no impact on it. In the final part of this dissertation, a differential detection scheme for DS/CDMA MIMO link is presented. The transmission provides for full transmit and receive diversity gain using a simple detection scheme, which is a natural extension of differential detection combined with an orthogonal transmit diversity (OTD) approach. A capacity analysis for this scheme is illustrated

Digital communications over fading channels

In this report, the probabilities of bit error for the most commonly used digital modulation techniques are analyzed. Analytic solutions are developed for the probability of bit error when the signal is affected by the most commonly encountered impairment to system performance for a wireless channel, the transmission of the signal over a fading channel. In this report, the effect of a slow, flat Ricean fading channel on communications systems performance is examined. Since channel fading significantly degrades the performance of a communication system, the performance of digital communication systems that also use forward error correction channel coding is analyzed for hard decision decoding and, where appropriate, for soft decision decoding. Diversity, another technique to mitigate the effect of fading channels on digital communication systems performance, is also discussed. Also included is a discussion of the effect of narrowband noise interference, both continuous and pulsed, on digital communication systems. We then discuss the analysis of the probability of bit error for the combination of error correction coding and diversity. Following this, we briefly discuss spread spectrum systems. Next, we examine the link budget analysis and various models for channel loss. Finally, we examine in detail the second generation digital wireless standard Global System for Mobile (GSM).Approved for public release; distribution is unlimited

Design and performance analysis of quadratic-form receivers for fading channels

Ph.DDOCTOR OF PHILOSOPH