International Telemetering Conference Proceedings / November 04-07, 1991 / Riviera Hotel and Convention Center, Las Vegas, Nevada / Methods to improve reception during multipath fading of telemetry data received aboard ships participating in missile exercises include various diversity techniques. Among these techniques are polarization, angle, height, and frequency diversity. In this paper, a two-ray multipath model is used to investigate the various techniques and determine the merits of each. Possible ways of implementing the promising ones are discussed.

We propose and analyze new finger assignment/management techniques that are applicable for RAKE receivers when they operate in the soft handover region. Two main criteria are considered: minimum use of additional network resources and minimum call drops. For the schemes minimizing the use of network resources, basic principles are to use the network resources only if necessary while minimum call drop schemes rely on balancing or distributing the signal strength/paths among as many base stations as possible. The analyses of these schemes require us to consider joint microscopic/macroscopic diversity techniques which have seldom been considered before and as such, we tackle the statistics of several correlated generalized selection combining output signal-to-noise ratios in order to obtain closed-form expressions for the statistics of interest. To provide a general comprehensive framework for the assessment of the proposed schemes, we investigate not only the complexity in terms of the average number of required path estimations/comparisons, the average number of combined paths, and the soft handover overhead but also the error performance of the proposed schemes over independent and identically distributed fading channels. We also examine via computer simulations the effect of path unbalance/correlation as well as outdated/imperfect channel estimations. We show through numerical exam ples that the proposed schemes which are designed for the minimum use of network resources can save a certain amount of complexity load and soft handover overhead with a very slight performance loss compared to the conventional generalized selection combining-based diversity systems. For the minimum call drop schemes, by accurately quantifying the average error rate, we show that in comparison to the conventional schemes, the proposed distributed schemes offer the better error performance when there is a considerable chance of loosing the signals from one of the active base stations.

Free-space optical (FSO) communication offers significant technical and operational advantages such as higher bandwidth capacity, robustness to electromagnetic interference, a high degree of spatial confinement (bringing virtually unlimited reuse and inherent security), low power requirements, and unregulated spectrum. FSO communication can be deployed as an efficient solution for a wide range of applications such as last-mile access, fiber backup, back-haul for wireless cellular networks, and disaster recovery among others. Although FSO system have many appealing features, they have rather disappointing performance for long links due to the degrading effects of atmospheric turbulence-induced fading. In this dissertation, we investigate different diversity techniques to boost the performance of FSO systems in the presence of the atmospheric turbulence-induced fading. In Chapter 3, we investigate receive diversity in coherent FSO systems considering both turbulence-induced amplitude and phase fluctuations under weak turbulence regime. To mitigate the wavefront phase distortion effect, modal compensation is deployed at the receiver. Under the assumption of Rician channel that models the combined effects of the atmospheric fading and modal compensation, we derive outage probability and diversity- multiplexing tradeoff of such systems. Our results show that, at high signal to noise ratio (SNR) regime, the diversity gain as great as the number of receiving apertures is achieved. Moreover, it is found that the modal compensation provides finite-SNR diversity advantages in coherent receivers. In Chapter 4, we investigate multi-hop transmission (serial relaying) as a form of diversity technique to combat atmospheric fading in coherent FSO systems. Utilizing the same channel model as in Chapter 3 and considering decode-and-forward relaying strategy, we quantify the outage probability and the finite-SNR diversity-multiplexing tradeoff of this relaying scheme. Exploiting the fact that fading variance is distance-dependent in the atmospheric channel, our results demonstrate that the multi-hop transmission takes advantage of the resulting shorter hops and yields significant performance improvements in the presence of fading. In Chapter 5, we study hybrid-ARQ protocols in coherent FSO communications over Gamma-Gamma atmospheric fading channels. We investigate and compare the performance of three hybrid-ARQ protocols in terms of the outage probability and throughput. Furthermore, we characterize the outage performance at high-SNR regime by diversity and coding gains. Our results provide insight into the performance mechanisms of different hybrid-ARQ protocols in coherent FSO systems and demonstrate that hybrid-ARQ significantly improves the outage performance of a coherent FSO system particularly in strong turbulence regime. In Chapter 6, we investigate parallel relaying in an intensity modulation/direct detection (IM/DD) FSO system. Assuming Gamma-Gamma fading model, we analyze both decode-and-forward and amplify-and-forward modes of cooperation. Focusing on high SNR regime, we investigate the outage probability and characterize it by the diversity and coding gains. The diversity-multiplexing tradeoff expression of each cooperation mode is also derived. Our performance analysis reveals that large energy savings can be achieved through the use of parallel relaying in FSO systems.

Free-space optical (FSO) communication offers significant technical and operational advantages such as higher bandwidth capacity, robustness to electromagnetic interference, a high degree of spatial confinement (bringing virtually unlimited reuse and inherent security), low power requirements, and unregulated spectrum. FSO communication can be deployed as an efficient solution for a wide range of applications such as last-mile access, fiber backup, back-haul for wireless cellular networks, and disaster recovery among others. Although FSO system have many appealing features, they have rather disappointing performance for long links due to the degrading effects of atmospheric turbulence-induced fading. In this dissertation, we investigate different diversity techniques to boost the performance of FSO systems in the presence of the atmospheric turbulence-induced fading. In Chapter 3, we investigate receive diversity in coherent FSO systems considering both turbulence-induced amplitude and phase fluctuations under weak turbulence regime. To mitigate the wavefront phase distortion effect, modal compensation is deployed at the receiver. Under the assumption of Rician channel that models the combined effects of the atmospheric fading and modal compensation, we derive outage probability and diversity- multiplexing tradeoff of such systems. Our results show that, at high signal to noise ratio (SNR) regime, the diversity gain as great as the number of receiving apertures is achieved. Moreover, it is found that the modal compensation provides finite-SNR diversity advantages in coherent receivers. In Chapter 4, we investigate multi-hop transmission (serial relaying) as a form of diversity technique to combat atmospheric fading in coherent FSO systems. Utilizing the same channel model as in Chapter 3 and considering decode-and-forward relaying strategy, we quantify the outage probability and the finite-SNR diversity-multiplexing tradeoff of this relaying scheme. Exploiting the fact that fading variance is distance-dependent in the atmospheric channel, our results demonstrate that the multi-hop transmission takes advantage of the resulting shorter hops and yields significant performance improvements in the presence of fading. In Chapter 5, we study hybrid-ARQ protocols in coherent FSO communications over Gamma-Gamma atmospheric fading channels. We investigate and compare the performance of three hybrid-ARQ protocols in terms of the outage probability and throughput. Furthermore, we characterize the outage performance at high-SNR regime by diversity and coding gains. Our results provide insight into the performance mechanisms of different hybrid-ARQ protocols in coherent FSO systems and demonstrate that hybrid-ARQ significantly improves the outage performance of a coherent FSO system particularly in strong turbulence regime. In Chapter 6, we investigate parallel relaying in an intensity modulation/direct detection (IM/DD) FSO system. Assuming Gamma-Gamma fading model, we analyze both decode-and-forward and amplify-and-forward modes of cooperation. Focusing on high SNR regime, we investigate the outage probability and characterize it by the diversity and coding gains. The diversity-multiplexing tradeoff expression of each cooperation mode is also derived. Our performance analysis reveals that large energy savings can be achieved through the use of parallel relaying in FSO systems.

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Simulation methods are used when closed-form solutions do not exist. An interesting simulation method that has been widely used in many scientific fields is the Monte Carlo method. Not only it is a simple technique that enables to estimate the quantity of interest, but it can also provide relevant information about the value to be estimated through its confidence interval. However, the use of classical Monte Carlo method is not a reasonable choice when dealing with rare event probabilities. In fact, very small probabilities require a huge number of simulation runs, and thus, the computational time of the simulation increases significantly. This observation lies behind the main motivation of the present work. In this thesis, we propose efficient importance sampling estimators to evaluate rare events probabilities. In the first part of the thesis, we consider a variety of turbulence regimes, and we study the outage probability of free-space optics communication systems under a generalized pointing error model with both a nonzero boresight component and different horizontal and vertical jitter effects. More specifically, we use an importance sampling approach,based on the exponential twisting technique to offer fast and accurate results. We also show that our approach extends to the multihop scenario. In the second part of the thesis, we are interested in assessing the outage probability achieved by some diversity techniques over generalized fading channels. In many circumstances, this is related to the difficult question of analyzing the statistics of the sum of random variables. More specifically, we propose robust importance sampling schemes that efficiently evaluate the outage probability of diversity receivers over Gamma-Gamma, α − µ, κ − µ, and η − µ fading channels. The proposed estimators satisfy the well-known bounded relative error criterion for both maximum ratio combining and equal gain combining cases. We show the accuracy and the efficiency of our approach compared to naive Monte Carlo via some selected numerical simulations in both case studies. In the last part of this thesis, we propose efficient importance sampling estimators for the left tail of positive Gaussian quadratic forms in both real and complex settings. We show that these estimators possess the bounded relative error property. These estimators are then used to estimate the outage probability of maximum ratio combining diversity receivers over correlated Nakagami-m or correlated Rician fading channels

<p>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.</p> <p>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.</p> <p>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.</p> <p>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.</p> <p>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.</p> <p>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.</p> <p>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.</p>

<p>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.</p> <p>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.</p> <p>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.</p> <p>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.</p> <p>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.</p> <p>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.</p> <p>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.</p>

Adaptive modulation and diversity combining represent very important adaptive solutions for future generations of wireless communication systems. Indeed, to improve the performance and the efficiency of these systems, these two techniques recently have been used jointly in new schemes named joint adaptive modulation and diversity combining (JAMDC) schemes. Considering the problem of finding lowcomplexity, bandwidth-efficient, and processing-power efficient transmission schemes for a downlink scenario and capitalizing on some of these recently proposed JAMDC schemes, we propose and analyze three fully joint adaptive modulation, diversity combining, and power control (FJAMDC) schemes. More specifically, the modulation constellation size, the number of combined diversity paths, and the needed power level are determined jointly to achieve the highest spectral efficiency with the lowest possible combining complexity, given the fading channel conditions and the required bit error rate (BER) performance. The performance of these three FJAMDC schemes is analyzed in terms of their spectral efficiency, processing power consumption, and error-rate performance. Selected numerical examples show that these schemes considerably increase the spectral efficiency of the existing JAMDC schemes with a slight increase in the average number of combined paths for the low signal to noise ratio range while maintaining compliance with the BER performance and a low radiated power resulting in a substantial decrease in interference to co-existing systems/users.

Generalized fading has been an imminent part and parcel of wireless communications. It not only characterizes the wireless channel appropriately but also allows its utilization for further performance analysis of various types of wireless communication systems. Under the umbrella of generalized fading channels, a unified performance analysis of a free-space optical (FSO) link over the Malaga (M) atmospheric turbulence channel that accounts for pointing errors and both types of detection techniques (i.e. indirect modulation/direct detection (IM/DD) as well as heterodyne detection) is presented. Specifically, unified exact closed-form expressions for the probability density function (PDF), the cumulative distribution function (CDF), the moment generating function (MGF), and the moments of the end-to-end signal-to-noise ratio (SNR) of a single link FSO transmission system are presented, all in terms of the Meijer's G function except for the moments that is in terms of simple elementary functions. Then capitalizing on these unified results, unified exact closed-form expressions for various performance metrics of FSO link transmission systems are offered, such as, the outage probability (OP), the higher-order amount of fading (AF), the average error rate for binary and M-ary modulation schemes, and the ergodic capacity (except for IM/DD technique, where closed-form lower bound results are presented), all in terms of Meijer's G functions except for the higher-order AF that is in terms of simple elementary functions. Additionally, the asymptotic results are derived for all the expressions derived earlier in terms of the Meijer's G function in the high SNR regime in terms of simple elementary functions via an asymptotic expansion of the Meijer's G function. Furthermore, new asymptotic expressions for the ergodic capacity in the low as well as high SNR regimes are derived in terms of simple elementary functions via utilizing moments. All the presented results are verified via computer-based Monte-Carlo simulations. Besides addressing the pointing errors with zero boresight effects as has been addressed above, a unified capacity analysis of a FSO link that accounts for nonzero boresight pointing errors and both types of detection techniques (i.e. heterodyne detection as well as IM/DD) is also addressed. Specifically, an exact closed-form expression for the moments of the end-to-end SNR of a single link FSO transmission system is presented in terms of well-known elementary functions. Capitalizing on these new moments expressions, approximate and simple closed-form results for the ergodic capacity at high and low SNR regimes are derived for lognormal (LN), Rician-LN (RLN), and M atmospheric turbulences. All the presented results are verified via computer-based Monte-Carlo simulations. Based on the fact that FSO links are cost-effective, license-free, and can provide even higher bandwidths compared to the traditional radio-frequency (RF) links, the performance analysis of a dual-hop relay system composed of asymmetric RF and FSO links is presented. This is complemented by the performance analysis of a dual-branch transmission system composed of a direct RF link and a dual-hop relay composed of asymmetric RF and FSO links. The performance of the later scenario is evaluated under the assumption of the selection combining (SC) diversity and the maximal ratio combining (MRC) schemes. RF links are modeled by Rayleigh fading distribution whereas the FSO link is modeled by a unified GG fading distribution. More specifically, in this work, new exact closed-form expressions for the PDF, the CDF, the MGF, and the moments of the end-to-end SNR are derived. Capitalizing on these results, new exact closed-form expressions for the OP, the higher-order AF, the average error rate for binary and M-ary modulation schemes, and the ergodic capacity are offered. Cognitive radio networks (CRN) have also proved to improve the performance of wireless communication systems and hence based on this, the hybrid system analyzed above is extended with CRN technology wherein the outage and error performance analysis of a dual-hop transmission system composed of asymmetric RF channel cascaded with a FSO link is presented. For the RF link, an underlay cognitive network is considered where the secondary users share the spectrum with licensed primary users. Indoor femtocells act as a practical example for such networks. Specifically, it is assumed that the RF link applies power control to maintain the interference at the primary network below a predetermined threshold. While the RF channel is modeled by the Rayleigh fading distribution, the FSO link is modeled by a unified Gamma-Gamma turbulence distribution. The FSO link accounts for pointing errors and both types of detection techniques (i.e. heterodyne detection as well as IM/DD). With this model, a new exact closed-form expression is derived for the OP and the error rate of the end-to-end SNR of these systems in terms of the Meijer's G function and the Fox's H functions under amplify-and-forward relay schemes. All new analytical results are verified via computer-based Monte-Carlo simulations and are illustrated by some selected numerical results.