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

Log-moment estimators of the Nakagami-lognormal distribution

[EN] In this paper, estimators of the Nakagami-lognormal (NL) distribution based on the method of log-moments have been derived and thoroughly analyzed. Unlike maximum likelihood (ML) estimators, the log-moment estimators of the NL distribution are obtained using straightforward equations with a unique solution. Also, their performance has been evaluated using the sample mean, confidence regions and normalized mean square error (NMSE). The NL distribution has been extensively used to model composite small-scale fading and shadowing in wireless communication channels. This distribution is of interest in scenarios where the small-scale fading and the shadowing processes cannot be easily separated such as the vehicular environment.This work has been funded in part by the Programa de Estancias de Movilidad de Profesores e Investigadores en Centros Extranjeros de Ensenanza Superior e Investigacion of the Ministerio de Educacion, Cultura y Deporte, Spain, PR2015-00151 and by the Ministerio de Economia, Industria y Competitividad of the Spanish Government under the national project TEC2017-86779-C2-2-R, through the Agencia Estatal de Investigacion (AEI) and the Fondo Europeo de Desarrollo Regional (FEDER).Reig, J.; Brennan, C.; Rodrigo Peñarrocha, VM.; Rubio Arjona, L. (2019). Log-moment estimators of the Nakagami-lognormal distribution. EURASIP Journal on Wireless Communications and Networking. 1-10. https://doi.org/10.1186/s13638-018-1328-6S110J. M. Ho, G. L. 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Mathiopoulos, in Adaptive M-QAM systems with diversity in correlated Nakagami-m fading and shadowing. IEEE Global Telecommunications Conference (GLOBECOM 2010) (IEEEMiami, 2010), pp. 1–5.Ö. Bulakci, A. B. Saleh, J. Hämäläinen, S. Redana, Performance analysis of relay site planning over composite fading/shadowing channels with cochannel interference. IEEE Trans. Veh. Technol.62(4), 1692–1706 (2013).W. Cheng, Y. Huang, On the performance of adaptive SC/MRC cooperative systems over composite fading channels. Chin. J. Electron.25(3), 533–540 (2016).M. G. Kibria, G. P. Villardi, W. Liao, K. Nguyen, K. Ishizu, F. Kojima, Outage analysis of offloading in heterogeneous networks: Composite fading channels. IEEE Trans. Veh. Technol.66(10), 8990–9004 (2017).K. Cho, J. Lee, C. G. Kang, Stochastic geometry-based coverage and rate analysis under Nakagami & log-normal composite fading channel for downlink cellular networks. IEEE Commun. Lett.21(6), 1437–1440 (2017).R. Singh, M. Rawat, Closed-form distribution and analysis of a combined Nakagami-lognormal shadowing and unshadowing fading channel. J Telecommun. Inf. Technol.4:, 81–87 (2016).J. Reig, L. Rubio, Estimation of the composite fast fading and shadowing distribution using the log-moments in wireless communications. IEEE Trans. Wireless. Commun.12(8), 3672–3681 (2013).S. Atapattu, C. Tellambura, H. Jiang, A mixture gamma distribution to model the SNR of wireless channels. IEEE Trans. Wireless Commun.10(12), 4193–4203 (2011).Q. Wang, H. Lin, P. Kam, Tight bounds and invertible average error probability expressions over composite fading channels. J. Commun. Netw.18(2), 182–189 (2016).J. M. Holtzmann, On using perturbation analysis to do sensitivity analysis: derivatives versus differences. IEEE Trans. Autom. Control. 37(2), 243–247 (1992).H. Suzuki, A statistical model for urban radio propagation. IEEE Trans. Commun.25(7), 673–680 (1977).M. D. 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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

Symbol level decoding of Reed-Solomon codes with improved reliability information over fading channels

A thesis submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy in the School of Electrical and Information Engineering, 2016Reliable and e cient data transmission have been the subject of current research, most especially in realistic channels such as the Rayleigh fading channels. The focus of every new technique is to improve the transmission reliability and to increase the transmission capacity of the communication links for more information to be transmitted. Modulation schemes such as M-ary Quadrature Amplitude Modulation (M-QAM) and Orthogonal Frequency Division Multiplexing (OFDM) were developed to increase the transmission capacity of communication links without additional bandwidth expansion, and to reduce the design complexity of communication systems. On the contrary, due to the varying nature of communication channels, the message transmission reliability is subjected to a couple of factors. These factors include the channel estimation techniques and Forward Error Correction schemes (FEC) used in improving the message reliability. Innumerable channel estimation techniques have been proposed independently, and in combination with di erent FEC schemes in order to improve the message reliability. The emphasis have been to improve the channel estimation performance, bandwidth and power consumption, and the implementation time complexity of the estimation techniques. Of particular interest, FEC schemes such as Reed-Solomon (RS) codes, Turbo codes, Low Density Parity Check (LDPC) codes, Hamming codes, and Permutation codes, are proposed to improve the message transmission reliability of communication links. Turbo and LDPC codes have been used extensively to combat the varying nature of communication channels, most especially in joint iterative channel estimation and decoding receiver structures. In this thesis, attention is focused on using RS codes to improve the message reliability of a communication link because RS codes have good capability of correcting random and burst errors, and are useful in di erent wireless applications. This study concentrates on symbol level soft decision decoding of RS codes. In this regards, a novel symbol level iterative soft decision decoder for RS codes based on parity-check equations is developed. This Parity-check matrix Transformation Algorithm (PTA) is based on the soft reliability information derived from the channel output in order to perform syndrome checks in an iterative process. Performance analysis verify that this developed PTA outperforms the conventional RS hard decision decoding algorithms and the symbol level Koetter and Vardy (KV ) RS soft decision decoding algorithm. In addition, this thesis develops an improved Distance Metric (DM) method of deriving reliability information over Rayleigh fading channels for combined demodulation with symbol level RS soft decision decoding algorithms. The newly proposed DM method incorporates the channel state information in deriving the soft reliability information over Rayleigh fading channels. Analysis verify that this developed metric enhances the performance of symbol level RS soft decision decoders in comparison with the conventional method. Although, in this thesis, the performance of the developed DM method of deriving soft reliability information over Rayleigh fading channels is only veri ed for symbol level RS soft decision decoders, it is applicable to any symbol level soft decision decoding FEC scheme. Besides, the performance of the all FEC decoding schemes plummet as a result of the Rayleigh fading channels. This engender the development of joint iterative channel estimation and decoding receiver structures in order to improve the message reliability, most especially with Turbo and LDPC codes as the FEC schemes. As such, this thesis develops the rst joint iterative channel estimation and Reed- Solomon decoding receiver structure. Essentially, the joint iterative channel estimation and RS decoding receiver is developed based on the existing symbol level soft decision KV algorithm. Consequently, the joint iterative channel estimation and RS decoding receiver is extended to the developed RS parity-check matrix transformation algorithm. The PTA provides design ease and exibility, and lesser computational time complexity in an iterative receiver structure in comparison with the KV algorithm. Generally, the ndings of this thesis are relevant in improving the message transmission reliability of a communication link with RS codes. For instance, it is pertinent to numerous data transmission technologies such as Digital Audio Broadcasting (DAB), Digital Video Broadcasting (DVB), Digital Subscriber Line (DSL), WiMAX, and long distance satellite communications. Equally, the developed, less computationally intensive, and performance e cient symbol level decoding algorithm for RS codes can be use in consumer technologies like compact disc and digital versatile disc.GS201

Performance Analysis of Selection Combining Over Correlated Nakagami-m Fading Channels with Constant Correlation Model for Desired Signal and Cochannel Interference

A very efficient technique that reduces fading and channel interference influence is selection diversity based on the signal to interference ratio (SIR). In this pa¬per, system performances of selection combiner (SC) over correlated Nakagami-m channels with constant correlation model are analyzed. Closed-form expressions are obtained for the output SIR probability density function (PDF) and cumulative distribution function (CDF) which is main contribution of this paper. Outage probability and the average error probability for coherent, noncoherent modulation are derived. Numerical results presented in this paper point out the effects of fading severity and cor¬relation on the system performances. The main contribu¬tion of this analysis for multibranch signal combiner is that it has been done for general case of correlated co-channel interference (CCI)

Dual-hop transmissions with fixed-gain relays over Generalized-Gamma fading channels

In this paper, a study on the end-to-end performance of dual-hop wireless communication systems equipped with fixed-gain relays and operating over Generalized-Gamma (GG) fading channels is presented. A novel closed form expression for the moments of the end-to-end signal-to-noise ratio (SNR) is derived. The average bit error probability for coherent and non-coherent modulation schemes as well as the end-to-end outage probability of the considered system are also studied. Extensive numerically evaluated and computer simulations results are presented that verify the accuracy of the proposed mathematical analysis.\u