Syed Ali Hassan

A Quasi-Stationary Markov Chain Model of a Cooperative Multi-Hop Linear Network

We consider a quasi-stationary Markov chain as a model for a decode and forward wireless multi-hop cooperative transmission system that forms successive Opportunistic Large Arrays (OLAs). This paper treats a linear network topology, where the nodes form a one-dimensional horizontal grid with equal spacing. In this OLA approach, all nodes are intended to decode and relay. Therefore, the method has potential application as a high-reliability and low-latency approach for broadcasting in a line-shaped network, or unicasting along a pre-designated route. We derive the transition probability matrix of the Markov chain based on the hypoexponential distribution of the received power at a given time instant assuming that all the nodes have equal transmit power and the channel has Rayleigh fading and path loss with an arbitrary exponent. The state is represented as a ternary word, which indicates which nodes have decoded in the present hop, in a previous hop, or have not yet decoded. The Perron-Frobenius eigenvalue and the corresponding eigenvector of the sub-stochastic matrix indicates the signal-to-noise ratio (SNR) margin that enables a given hop distance.

Opportunistic large array with limited participation: An energy-efficient cooperative multi-hop network

This paper studies an energy-efficient scheme for cooperative multi-hop communications in a finite density opportunistic large array (OLA) network. In a cooperative OLA network, a group of nodes transmits the same message signal to another group of nodes, providing range extension and increased reliability by exploiting the spatial diversity in a wireless system. However, in this paper, it is shown that a particular coverage and reliability of the network can be achieved by limiting the node participation in an OLA network, thereby providing energy-efficiency. Two types of networks are studied; a one-dimensional linear network and a two-dimensional strip network where the nodes are aligned on a regular grid. The transmissions originating from one level to another are modeled as a Markov process and the underlying transition probability matrix has been derived. By invoking the Perron-Frobenius theorem, the coverage, reliability, and energy-efficiency of the network has been quantified for a given end-to-end success probability constraint and a given signal-to-noise ratio (SNR) margin.

SNR Estimation for M-ARY Non-Coherent Frequency Shift Keying Systems

This paper considers how to estimate the average signal-to-noise ratio (SNR) for a communication system employing orthogonal non-coherent M-ARY frequency shift keying (NCMFSK), in white Gaussian noise (AWGN) and over both symbol-by-symbol fading channels and block fading channels. The proposed algorithm finds its application in a variety of applications including a cooperative transmission system, which is the main motivation behind this study. The maximum likelihood estimator and one using data statistics have been derived and simulated for various scenarios including data-aided, non-data aided and joint estimation using both the data and pilot sequences. We also derive the Cramer-Rao bound for the estimators in the case of Rayleigh fading channels. The results show that for a particular region of interest (e.g. high SNR or low SNR) and depending upon the availability of pilot sequence, a particular SNR estimation scheme is suitable.

Stochastic Modeling of Cooperative Multi-Hop Strip Networks With Fixed Hop Boundaries

In this paper, a strip-shaped cooperative multi-hop wireless network is modeled stochastically with quasi-stationary Markov chain. The network is considered to be a fixed boundary decode-and-forward Opportunistic Large Array (OLA), where each level is of the same size and contains the same number of nodes placed randomly. The state of the system is represented by the number of nodes that decode the message in the current level. The distribution of the received power at a node is derived to formulate the transition probability matrix. For the distribution of power, a closed-form expression of the distribution of distance between a pair of nodes in disjoint levels is derived. It is seen that the distribution of distance can be well-approximated by the Weibull distribution. The Weibull approximation is then carried forward to find the distribution of the received power at a node assuming all nodes transmit with the same power and the channel has Rayleigh fading and path loss with an arbitrary exponent. The coverage and outage characteristics for various network sizes and path loss exponents are quantified. The signal-to-noise ratio (SNR) margin required for a given network coverage is determined by using the Perron-Frobenius theorem of non-negative matrices. Numerical simulations are performed to validate the theoretical results.

The Benefit of Co-Locating Groups of Nodes in Cooperative Line Networks

We consider two topologies for the deployment of nodes in a one-dimensional network. The first deployment scenario considers nodes equally spaced on a line, while the second topology has groups of co-located nodes, such that the groups are equally spaced on the line, and such that the two networks have equal average density. In both linear topologies, nodes transmit cooperatively, as opportunistic large arrays, in each hop. The difference is only that in the first topology, the cooperators have disparate path loss, while in the second they do not. We study the multi-hop transmission for both cases, where the one hop distance remains the same for both the topologies. We model both the scenarios with a quasi-stationary Markov chain and show that the co-located groups deployment gives better performance, especially for higher path loss exponents.

Distributed versus cluster-based cooperative linear networks: A range extension study in Suzuki fading environments

This paper studies two topologies for cooperative multi-hop linear networks; a distributed equi-distant node topology and a co-located group of nodes topology such that both topologies operate under composite shadowing-fading environment. The transmission from one hop to another in both topologies is modeled as a Markov process where the underlying channel model is drawn from a Suzuki distribution. The distribution of the sum of multiple Suzuki random variables (RVs) is obtained by a moment generating function (MGF)-based approximation technique. It is shown that the coverage of both topologies is different contingent upon the severity of shadowing and the transmit power of the radios. The optimal level of cooperation between nodes is shown to have a dependency on the path loss exponent such that a large number of cooperators is optimal for a small path loss exponent and vice versa for obtaining the maximum range of the network. Monte Carlo simulations are performed to validate the analytical model.

Performance Analysis of Linear Cooperative Multi-Hop Networks Subject to Composite Shadowing-Fading

We consider a cooperative multi-hop line network, where a group of nodes cooperatively transmits the same message to another group of nodes, and model the transmission from one group to another as a discrete-time quasi-stationary Markov process. We derive the transition probability matrix of the Markov chain by considering the wireless channel exhibiting composite shadowing-fading. The shadowing is modeled as a log-normal random variable (RV) and the multipath fading as a Rayleigh RV, where the multiplicative model for the mixture distribution known as Suzuki (Rayleigh-lognormal) distribution has been considered. The sum distribution of the multiple Suzuki RVs is approximated by a single log-normal RV by using the moment generating function (MGF)-based technique. This MGF-based technique uses Gauss-Hermite integration to present the sum distribution in closed form. We quantify the signal-to-noise ratio (SNR) margin required to achieve a certain quality of service (QoS) under standard deviation of the shadowing. We also provide the optimal level of cooperation required for obtaining maximum coverage of a line network under a given QoS. Two topologies for linear network are considered and the performance of each topology under various system parameters is provided. The analytical results have been validated by matching with the simulation results.

On the modeling of randomized distributed cooperation for linear multi-hop networks

A one-dimensional cooperative network is modeled stochastically, such that the nodes are randomly placed according to a Bernoulli process. A discrete time quasi-stationary Markov chain model is considered to characterize the multi-hop transmissions and its transition probability matrix has been derived. By the Perron-Frobenious theorem, the eigen-decomposition of the matrix gives useful information about the coverage of the network and signal-to-noise (SNR) margin that is required for obtaining a given quality of service or packet delivery ratio. An SNR penalty for the random placement of nodes, compared to regular placement, is quantified.

SNR Estimation for a Non-Coherent M-FSK Receiver in a Slow Flat Fading Environment

Estimation of the signal-to-noise ratio (SNR) is considered for a non-coherent M-ary frequency shift keying (NC-MFSK) receiver. It has been assumed that the transmitted symbols undergo a slow flat fading channel where a block of data is corrupted by an independent constant fade and additive white Gaussian noise. Two approaches for SNR estimation are reported in this paper: an approximate maximum likelihood approach and another using the data statistics, both for data aided and non-data aided systems. It has been shown that for a particular SNR region of interest and depending upon the availability of pilot symbols, a particular approach is suitable for SNR estimation.

Performance of Multi-Hop Cooperative Networks Subject to Timing Synchronization Errors

In this paper, we propose a mathematical model for timing synchronization errors in a cascaded virtual multi-hop multiple-input multiple-output (MIMO) system that incorporates cooperation at each hop using decode-and-forward (DF) algorithm. Specifically, the DF relays are grouped to form clusters and one cluster transmits the same data to the next cluster over orthogonal fading channels. The proposed error model is used to study the statistics of the timing error from one cluster to the next and it has been shown that the variance of the timing errors gradually increases as the data traverse the multi-hop network. The effects of the timing errors on the bit error probability (BEP) performance of the system have been quantified. For that purpose, the closed-form expressions of the BEP for the network are derived for every hop with a particular number of nodes per hop. The results indicate that the BEP performance of the system degrades as the data propagates from hop to hop. We quantify the minimum required SNR and the optimal number of relays per cluster that guarantee successful traversal of data to a specified number of hop while keeping overall BEP below a defined threshold.