**Channel Capacity Analysis Under Various Adaptation Policies and Diversity Techniques over Fading Channels**

Mihajlo Stefanović1, Jelena Anastasov1, Stefan Panić2, Petar Spalević3 and Ćemal Dolićanin3 *1Faculty of Electronic Engineering, University of Niš, 2Faculty of Natural Science and Mathematics, University of Priština, 3State University of Novi Pazar Serbia* 

## **1. Introduction**

280 Wireless Communications and Networks – Recent Advances

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The lack of available spectrum for expansion of wireless services requires more spectrally efficient communication in order to meet the consumer demand. Since the demand for wireless communication services have been growing in recent years at a rapid pace, conserving, sharing and using bandwidth efficiently is of primary concern in future wireless communications systems. Therefore, channel capacity is one of the most important concerns in the design of wireless systems, as it determines the maximum attainable throughput of the system [1]. It can be defined as the average transmitted data rate per unit bandwidth, for a specified average transmit power, and specified level of received outage or bit-error rate [2]. Skilful combination of bandwidth efficient coding and modulation schemes can be used to achieve higher channel capacities per unit bandwidth. However, mobile radio links are, due to the combination of randomly delayed reflected, scattered, and diffracted signal components, subjected to severe multipath fading, which leads to serious degradation in the link signal-to-noise ratio (SNR). An effective scheme that can be used to overcome fading influence is adaptive transmission. The performance of adaptation schemes is further improved by combining them with space diversity, since diversity combining is a powerful technique that can be used to combat fading in wireless systems resulting in improving link performance [3].

#### **1.1 Channel and system model**

Diversity combining is a powerful technique that can be used to combat fading in wireless systems [4]. The optimal diversity combining technique is maximum ratio combining (MRC). This combining technique involves co-phasing of the useful signal in all branches, multiplication of the received signal in each branch by a weight factor that is proportional to the estimated ratio of the envelope and the power of that particular signal and summing of the received signals from all antennas. By co-phasing, all the random phase fluctuations of the signal that emerged during the transmission are eliminated. For this process it is necessary to estimate the phase of the received signal, so this technique requires the entire amount of the channel state information (CSI) of the received signal, and separate receiver chain for each branch of the diversity system, which increases the complexity of the system [5].

One of the least complicated combining methods is selection combining (SC). While other combining techniques require all or some of the amount of the CSI of received signal and separate receiver chain for each branch of the diversity system which increase its complexity, selection combining (SC) receiver process only one of the diversity branches, and is much simpler for practical realization, in opposition to these combining techniques [4-7]. Generally, SC selects the branch with the highest SNR, that is the branch with the strongest signal, assuming that noise power is equally distributed over branches. Since receiver diversity mitigates the impact of fading, the question is whether it also increases the capacity of a fading channel.

Another effective scheme that can be used to overcome fading influence is adaptive transmission. Adaptive transmission is based on the receiver's estimation of the channel and feedback of the CSI to the transmitter. The transmitter then adapts the transmit power level, symbol/bit rate, constellation size, coding rate/scheme or any combination of these parameters in response to the changing channel conditions [8]. Adapting certain parameters of the transmitted signal to the fading channel can help better utilization of the channel capacity. These transmissions provide a much higher channel capacities per unit bandwidth by taking advantage of favorable propagation conditions: transmitting at high speeds under favorable channel conditions and responding to channel degradation through a smooth reduction of their data throughput. The source may transmit faster and/or at a higher power under good channel conditions and slower and/or at a reduced power under poor conditions. A reliable feedback path between that estimator and the transmitter and accurate channel estimation at the receiver is required for achieving good performances of adaptive transmission. Widely accepted adaptation policies include optimal power and rate adaptation (OPRA), constant power with optimal rate adaptation (ORA), channel inversion with fixed rate (CIFR), and truncated CIFR (TIFR). Results obtained for this protocols show the trade-off between capacity and complexity. The adaptive policy with transmitter and receiver side information requires more complexity in the transmitter (and it typically also requires a feedback path between the receiver and transmitter to obtain the side information). However, the decoder in the receiver is relatively simple. The non-adaptive policy has a relatively simple transmission scheme, but its code design must use the channel correlation statistics (often unknown), and the decoder complexity is proportional to the channel decorrelation time. The channel inversion and truncated inversion policies use codes designed for additive white Gaussian noise (AWGN) channels, and are therefore the least complex to implement, but in severe fading conditions they exhibit large capacity losses relative to the other techniques.

The performance of adaptation schemes is further improved by combining them with space diversity. The hypothesis that the variation of the combiner output SNR is tracked perfectly by the receiver and that the variation in SNR is sent back to the transmitter via an error-free feedback path will be assumed in the ongoing analysis [8]. Also, it is assumed that time delay in this feedback path is negligible compared to the rate of the channel variation.

process it is necessary to estimate the phase of the received signal, so this technique requires the entire amount of the channel state information (CSI) of the received signal, and separate receiver chain for each branch of the diversity system, which increases the

One of the least complicated combining methods is selection combining (SC). While other combining techniques require all or some of the amount of the CSI of received signal and separate receiver chain for each branch of the diversity system which increase its complexity, selection combining (SC) receiver process only one of the diversity branches, and is much simpler for practical realization, in opposition to these combining techniques [4-7]. Generally, SC selects the branch with the highest SNR, that is the branch with the strongest signal, assuming that noise power is equally distributed over branches. Since receiver diversity mitigates the impact of fading, the question is whether it also increases the

Another effective scheme that can be used to overcome fading influence is adaptive transmission. Adaptive transmission is based on the receiver's estimation of the channel and feedback of the CSI to the transmitter. The transmitter then adapts the transmit power level, symbol/bit rate, constellation size, coding rate/scheme or any combination of these parameters in response to the changing channel conditions [8]. Adapting certain parameters of the transmitted signal to the fading channel can help better utilization of the channel capacity. These transmissions provide a much higher channel capacities per unit bandwidth by taking advantage of favorable propagation conditions: transmitting at high speeds under favorable channel conditions and responding to channel degradation through a smooth reduction of their data throughput. The source may transmit faster and/or at a higher power under good channel conditions and slower and/or at a reduced power under poor conditions. A reliable feedback path between that estimator and the transmitter and accurate channel estimation at the receiver is required for achieving good performances of adaptive transmission. Widely accepted adaptation policies include optimal power and rate adaptation (OPRA), constant power with optimal rate adaptation (ORA), channel inversion with fixed rate (CIFR), and truncated CIFR (TIFR). Results obtained for this protocols show the trade-off between capacity and complexity. The adaptive policy with transmitter and receiver side information requires more complexity in the transmitter (and it typically also requires a feedback path between the receiver and transmitter to obtain the side information). However, the decoder in the receiver is relatively simple. The non-adaptive policy has a relatively simple transmission scheme, but its code design must use the channel correlation statistics (often unknown), and the decoder complexity is proportional to the channel decorrelation time. The channel inversion and truncated inversion policies use codes designed for additive white Gaussian noise (AWGN) channels, and are therefore the least complex to implement, but in severe fading conditions they exhibit large capacity

The performance of adaptation schemes is further improved by combining them with space diversity. The hypothesis that the variation of the combiner output SNR is tracked perfectly by the receiver and that the variation in SNR is sent back to the transmitter via an error-free feedback path will be assumed in the ongoing analysis [8]. Also, it is assumed that time delay in this feedback path is negligible compared to the rate of the channel variation.

complexity of the system [5].

capacity of a fading channel.

losses relative to the other techniques.

Following these assumptions, transmitter could adapt its power and/or rate relative to the actual channel state.

There are numerous published papers based on study of channel capacity evaluation. In [9], the capacity of Rayleigh fading channels under four adaptation policies and multibranch system with variable correlation is investigated. The capacity of Rayleigh fading channels under different adaptive transmission and different diversity combining techniques is also studied in [7], [10]. In [11], channel capacity of MRC over exponentially correlated Nakagami-*m* fading channels under adaptive transmission is analyzed. Channel capacity of adaptive transmission schemes using equal gain combining (EGC) receiver over Hoyt fading channels is presented in [12]. In [13], dual-branch SC receivers operating over correlative Weibull fading under three adaptation policies are analyzed.

In this chapter we will focus on more general and nonlinear fading distributions. We will perform an analytical study of the *κ*-*μ* fading channel capacity, e.g., under the OPRA, ORA, CIFR and TIFR adaptation policies and MRC and SC diversity techniques. To the best of authors' knowledge, such a study has not been previously considered in the open technical literature. The expressions for the proposed adaptation policies and diversity techniques will be derived. Capitalizing on them, numerically obtained results will be graphically presented, in order to show the effects of various system parameters, such as diversity order and fading severity on observed performances. In the similar manner an analytical study of the Weibull fading channel capacity, under the OPRA, ORA, CIFR and TIFR adaptation policies and MRC diversity technique will be performed.
