On the performance of cooperative diversity with amplify-and-forward relays over weibull fading channels

The wireless communication channel suffers from much channel impairments such as noise, path loss, fading, shadowing and interference .Among all those degrading factors, fading which is produced by multipath is the most severe due to the interference between two or more versions of the transmitted signal which arriving at the destination at slightly different times and the rapid random fluctuation of those signal amplitude over a short period of time resulting to the drastic degradation of the reliability and the performance of the overall system and the reliability . For this reason, during the last decade wireless communication performance improvement has been the subject of lot of investigation, different methods and techniques have been implemented in order to mitigate the effect of multipath fading and improve the wireless channels. One of the efficient technique proposed by researchers was the so called multiple input multiple output systems commonly abbreviated by MIMO. This technique is also referred as antenna space diversity and represents a powerful means of mitigating the deleterious effects of fading in wireless communication, the basic ideas behind MIMO is the use of multiple antennas at the transmitting and the receiving nodes in order to create diversity, the receiver is supplied multiple replicas of the transmitting signals instead of one signal, so the likelihood that all replicas of the signals will fade simultaneously is extremely reduced. another major advantage of MIMO is potentially increase in the channel capacity without any expansion in the required bandwidth or increase in the transmit power. Despite all these assets, MIMO has practical constraints on its deployment in modern wireless devices due the size of equipment, computational capacity requirements and power consumption. To counteract these constraints an alternative technique that can use single antenna at the transmitting and receiving nodes was proposed, cooperative communication takes advantage of the broadcasting nature of wireless medium and allowing neighboring relay nodes to cooperate in communication by forwarding information from source nodes to destination nodes, cooperative communication provides space diversity gain equivalent to MIMO systems, enhance coverage and substantial increase channel capacity without increase the power of the transmitter. A cooperative phase consists of two time-slots. In the first time-slot, the source broadcasts a symbol to the relays and to the destination. In the second time-slot, the relays process the received symbol and forward them to the destination according to some specifics relay strategy or protocol. Nowadays it exists a whole gamut of different relaying strategies but they can globally be classified into two big groups: Decode-and-Forward (DF) or non-regenerative and the Amplify-and-Forward (AF) or regenerative, in the literatures another classification can be found but throughput this thesis we shall consider the above-mentioned classification and we shall also assume that the relay strategy operate in orthogonal channels mode and Time Duplex Division is used due to the limitation of the terminals to transmit and receive the symbols in the same time at the same frequency. The Amplified-and-forward (AF) is the most popular and the simplest cooperative signaling strategy that can be used at the relay to amplify the received signal from the source node and retransmits it to the destination node without doing any specific decoding, in fact it acts as analog repeaters by retransmitting an amplified version of their received signals for this reason it is also called non regenerative relaying , the amplification process which is the multiplication with an amplification parameter is used to normalize the received power. The main advantage of this strategy is its low -complexity implementation and its power constraints, the disadvantage of this strategy is the fact that, the relay nodes amplified the received noise at the same time. Recent research has shown that AF cooperative diversity leads to significantly lower bit error rate (BER) than DF strategy and direct non-cooperative communication. On the other hand, in DF strategy the complexity at the receiver is higher in comparison to that in the AF strategy, the relay node decodes the received signal transmitted by the source node, re-encode it and then retransmit it to destination node noting that during the decoding process the additive noise is removed but symbol at the relay node may be incorrect, therefore, the overall system performance depends on the success of the symbol decoding. Although DF strategy has the advantage over the latter relay strategy in reducing the additive noise at the relay, it suffers from the error propagation issues due the incorrect detection of the relay. The scope of this thesis is to discuss all the above issues, cooperative communication network multiple-relays is considered in order to mitigate the problem of channel impairments and improve performance of overall system through diversity techniques. Diversity techniques consist of transmitting independently two or more copies of the same signal multiple times, the expectation is that at least one of these replicas will be received correctly, or at least one of the diversity branches will have the higher instantaneous signal-to-noise ratio. One alternative to have diversity in wireless communication system without increasing the number of the receiver and transmitter antennas is through the use of cooperative diversity. In this thesis, we shall analyze the performance of cooperative communication with Amplified-and-forward relays strategy over i.i.d (independent and identical distributed) Weibull fading channels using maximum ratio combining (MRC), a closed form expression for the moment generating function (MGF) of the total SNR at the destination node is derived. The fundamental idea behind maximum ratio combining (MRC) is to combine the signals coming from the Lth relaying branch and maximize the receiver SNR, in other words the instantaneous signal-to-noise ratio of the L branch diversity with the combining technique MRC is the sum of the individual signal-to-noise ratio for each branch. Among all the combining techniques MRC is the optimal in the absence of interference however its implementation requires exact information of the instantaneous SNR on each cooperative diversity branch, which sometimes can be difficult to find, because we shall deal the probability density function of sum of Weibull distribution even if the channel coefficients of the links are mutually independent and identical, to overcome this cumbersome task, we use the Moment Generating based-approach (MGF) and the algorithm of the best relay which consist selecting the relay with the highest instantaneous signal-to-noise ratio among the L branch from the Kth relays to the destination source, so only the best relay node (out of K relays) is used at any time. In fact, the algorithm maximizes the minimum signal strength and reduce the number of required channel and maintain full diversity order. At the end, after applying the MRC, we deal only with the direct link from the source to the destination and a link which has the highest instantaneous SNR. For the analyses of the performance metrics in cooperative wireless communication system the moment generating function based-approach, these approach is gaining popularity as a approach to unified error rate analysis of digital communications un fading channels, the performance metrics like as the outage probability and symbol error rates can be expressed in terms of the MGF of the SNR at the output of a diversity combiner in a multiple-channel receiver system, so it is used in order to greatly simplify our analysis of performance metrics, the use of MGF in diversity analysis of the moment generating come from the difficulty in computing the sum of probability density function of the instantaneous SNR and also when computing outage probability and the average probability of error which require integration over the distribution of the sum of the instantaneous SNR , the distribution of this sum is often not in closed-form for any number of branches of diversity with the same or different fading distribution on each branch , even when it is in closed form it can be difficult to evaluate numerically, another motivation of using the Moment Generating-based approach is that expressing the average error probability in terms of the MGF for the sum of instantaneous SNR instead of its probability density function eliminates these tedious integration Specifically, when the diversity branch are independent non identical (i.n,d ). The performance of the maximum ratio combing diversity of cooperative communication over fading channels has gained much interest, many papers in the recent literature could be found discussing the performance of cooperative system with multiple-relay, most of the model for these systems typically assume either Rayleigh fading channels or independent identically distributed Nakagami or even Rician fading channels , these fading models may not be an appropriate fading channel model, we choose Weibull fading channel because it is a flexible statistical model for describing multipath fading channels in both indoor and out-door radio propagation environments and mobile communication systems. This thesis analyzes the performance of the outage probability and the average symbol error rates of the amplify-and-forward relay strategy over independent and identical distributed Weibull fading channels, the maximum ratio combining technique has been used, in order to combine the instantaneous SNR of the direct link i.e. from the source to the destination, and the indirect link and the best relay selection criteria at the destination is used. The closed-form expression of the MGF for the end -to-to SNR at the destination is derived with the help of Meijer G-function/Generalized hypergeometric function which is available in common mathematical software package such as MATLAB, MATHEMATICA, MAPLE. This derived of the total MGF is helpful in analyzing the performance metrics.