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- All Subjects: Stochastic orders
- Creators: Kosut, Oliver
Description
This dissertation introduces stochastic ordering of instantaneous channel powers of fading channels as a general method to compare the performance of a communication system over two different channels, even when a closed-form expression for the metric may not be available. Such a comparison is with respect to a variety of performance metrics such as error rates, outage probability and ergodic capacity, which share common mathematical properties such as monotonicity, convexity or complete monotonicity. Complete monotonicity of a metric, such as the symbol error rate, in conjunction with the stochastic Laplace transform order between two fading channels implies the ordering of the two channels with respect to the metric. While it has been established previously that certain modulation schemes have convex symbol error rates, there is no study of the complete monotonicity of the same, which helps in establishing stronger channel ordering results. Toward this goal, the current research proves for the first time, that all 1-dimensional and 2-dimensional modulations have completely monotone symbol error rates. Furthermore, it is shown that the frequently used parametric fading distributions for modeling line of sight exhibit a monotonicity in the line of sight parameter with respect to the Laplace transform order. While the Laplace transform order can also be used to order fading distributions based on the ergodic capacity, there exist several distributions which are not Laplace transform ordered, although they have ordered ergodic capacities. To address this gap, a new stochastic order called the ergodic capacity order has been proposed herein, which can be used to compare channels based on the ergodic capacity. Using stochastic orders, average performance of systems involving multiple random variables are compared over two different channels. These systems include diversity combining schemes, relay networks, and signal detection over fading channels with non-Gaussian additive noise. This research also addresses the problem of unifying fading distributions. This unification is based on infinite divisibility, which subsumes almost all known fading distributions, and provides simplified expressions for performance metrics, in addition to enabling stochastic ordering.
ContributorsRajan, Adithya (Author) / Tepedelenlioğlu, Cihan (Thesis advisor) / Papandreou-Suppappola, Antonia (Committee member) / Bliss, Daniel (Committee member) / Kosut, Oliver (Committee member) / Arizona State University (Publisher)
Created2014
Description
Recently, the location of the nodes in wireless networks has been modeled as point processes. In this dissertation, various scenarios of wireless communications in large-scale networks modeled as point processes are considered. The first part of the dissertation considers signal reception and detection problems with symmetric alpha stable noise which is from an interfering network modeled as a Poisson point process. For the signal reception problem, the performance of space-time coding (STC) over fading channels with alpha stable noise is studied. We derive pairwise error probability (PEP) of orthogonal STCs. For general STCs, we propose a maximum-likelihood (ML) receiver, and its approximation. The resulting asymptotically optimal receiver (AOR) does not depend on noise parameters and is computationally simple, and close to the ML performance. Then, signal detection in coexisting wireless sensor networks (WSNs) is considered. We define a binary hypothesis testing problem for the signal detection in coexisting WSNs. For the problem, we introduce the ML detector and simpler alternatives. The proposed mixed-fractional lower order moment (FLOM) detector is computationally simple and close to the ML performance. Stochastic orders are binary relations defined on probability. The second part of the dissertation introduces stochastic ordering of interferences in large-scale networks modeled as point processes. Since closed-form results for the interference distributions for such networks are only available in limited cases, it is of interest to compare network interferences using stochastic. In this dissertation, conditions on the fading distribution and path-loss model are given to establish stochastic ordering between interferences. Moreover, Laplace functional (LF) ordering is defined between point processes and applied for comparing interference. Then, the LF orderings of general classes of point processes are introduced. It is also shown that the LF ordering is preserved when independent operations such as marking, thinning, random translation, and superposition are applied. The LF ordering of point processes is a useful tool for comparing spatial deployments of wireless networks and can be used to establish comparisons of several performance metrics such as coverage probability, achievable rate, and resource allocation even when closed form expressions for such metrics are unavailable.
ContributorsLee, Junghoon (Author) / Tepedelenlioğlu, Cihan (Thesis advisor) / Spanias, Andreas (Committee member) / Reisslein, Martin (Committee member) / Kosut, Oliver (Committee member) / Arizona State University (Publisher)
Created2014
Description
Multiple-input multiple-output systems have gained focus in the last decade due to the benefits they provide in enhancing the quality of communications. On the other hand, full-duplex communication has attracted remarkable attention due to its ability to improve the spectral efficiency compared to the existing half-duplex systems. Using full-duplex communications on MIMO co-operative networks can provide us solutions that can completely outperform existing systems with simultaneous transmission and reception at high data rates.
This thesis considers a full-duplex MIMO relay which amplifies and forwards the received signals, between a source and a destination that do not a have line of sight. Full-duplex mode raises the problem of self-interference. Though all the links in the system undergo frequency flat fading, the end-to-end effective channel is frequency selective. This is due to the imperfect cancellation of the self-interference at the relay and this residual self-interference acts as intersymbol interference at the destination which is treated by equalization. This also leads to complications in form of recursive equations to determine the input-output relationship of the system. This also leads to complications in the form of recursive equations to determine the input-output relationship of the system.
To overcome this, a signal flow graph approach using Mason's gain formula is proposed, where the effective channel is analyzed with keen notice to every loop and path the signal traverses. This gives a clear understanding and awareness about the orders of the polynomials involved in the transfer function, from which desired conclusions can be drawn. But the complexity of Mason's gain formula increases with the number of antennas at relay which can be overcome by the proposed linear algebraic method. Input-output relationship derived using simple concepts of linear algebra can be generalized to any number of antennas and the computation complexity is comparatively very low.
For a full-duplex amplify-and-forward MIMO relay system, assuming equalization at the destination, new mechanisms have been implemented at the relay that can compensate the effect of residual self-interference namely equal-gain transmission and antenna selection. Though equal-gain transmission does not perform better than the maximal ratio transmission, a trade-off can be made between performance and implementation complexity. Using the proposed antenna selection strategy, one pair of transmit-receive antennas at the relay is selected based on four selection criteria discussed. Outage probability analysis is performed for all the strategies presented and detailed comparison has been established. Considering minimum mean-squared error decision feedback equalizer at the destination, a bound on the outage probability has been obtained for the antenna selection case and is used for comparisons. A cross-over point is observed while comparing the outage probabilities of equal-gain transmission and antenna selection techniques, as the signal-to-noise ratio increases and from that point antenna selection outperforms equal-gain transmission and this is explained by the fact of reduced residual self-interference in antenna selection method.
This thesis considers a full-duplex MIMO relay which amplifies and forwards the received signals, between a source and a destination that do not a have line of sight. Full-duplex mode raises the problem of self-interference. Though all the links in the system undergo frequency flat fading, the end-to-end effective channel is frequency selective. This is due to the imperfect cancellation of the self-interference at the relay and this residual self-interference acts as intersymbol interference at the destination which is treated by equalization. This also leads to complications in form of recursive equations to determine the input-output relationship of the system. This also leads to complications in the form of recursive equations to determine the input-output relationship of the system.
To overcome this, a signal flow graph approach using Mason's gain formula is proposed, where the effective channel is analyzed with keen notice to every loop and path the signal traverses. This gives a clear understanding and awareness about the orders of the polynomials involved in the transfer function, from which desired conclusions can be drawn. But the complexity of Mason's gain formula increases with the number of antennas at relay which can be overcome by the proposed linear algebraic method. Input-output relationship derived using simple concepts of linear algebra can be generalized to any number of antennas and the computation complexity is comparatively very low.
For a full-duplex amplify-and-forward MIMO relay system, assuming equalization at the destination, new mechanisms have been implemented at the relay that can compensate the effect of residual self-interference namely equal-gain transmission and antenna selection. Though equal-gain transmission does not perform better than the maximal ratio transmission, a trade-off can be made between performance and implementation complexity. Using the proposed antenna selection strategy, one pair of transmit-receive antennas at the relay is selected based on four selection criteria discussed. Outage probability analysis is performed for all the strategies presented and detailed comparison has been established. Considering minimum mean-squared error decision feedback equalizer at the destination, a bound on the outage probability has been obtained for the antenna selection case and is used for comparisons. A cross-over point is observed while comparing the outage probabilities of equal-gain transmission and antenna selection techniques, as the signal-to-noise ratio increases and from that point antenna selection outperforms equal-gain transmission and this is explained by the fact of reduced residual self-interference in antenna selection method.
ContributorsJonnalagadda, Geeta Sankar Kalyan (Author) / Tepedelenlioğlu, Cihan (Thesis advisor) / Bliss, Daniel (Committee member) / Kosut, Oliver (Committee member) / Arizona State University (Publisher)
Created2018