Ergodic Capacity Analysis in Cognitive Radio Systems under Channel Uncertainty

In this paper, pilot-symbol-assisted transmission in cognitive radio systems over time selective flat fading channels is studied. It is assumed that causal and noncausal Wiener filter estimators are used at the secondary receiver with the aid of training symbols to obtain the channel side information (CSI) under an interference power constraint. Cognitive radio model is described together with detection and false alarm probabilities determined by using a Neyman-Person detector for channel sensing. Subsequently, for both filters, the variances of estimate errors are calculated from the Doppler power spectrum of the channel, and achievable rate expressions are provided considering the scenarios which are results of channel sensing. Numerical results are obtained in Gauss-Markov modeled channels, and achievable rates obtained by using causal and noncausal filters are compared and it is shown that the difference is decreasing with increasing signal-to-noise ratio (SNR). Moreover, the optimal probability of detection and false alarm values are shown, and the tradeoff between these two parameters is discussed. Finally, optimal power distributions are provided

On the Capacity and Energy Efficiency of Training-Based Transmissions over Fading Channels

In this paper, the capacity and energy efficiency of training-based communication schemes employed for transmission over a-priori unknown Rayleigh block fading channels are studied. In these schemes, periodically transmitted training symbols are used at the receiver to obtain the minimum mean-square-error (MMSE) estimate of the channel fading coefficients. Initially, the case in which the product of the estimate error and transmitted signal is assumed to be Gaussian noise is considered. In this case, it is shown that bit energy requirements grow without bound as the signal-to-noise ratio (SNR) goes to zero, and the minimum bit energy is achieved at a nonzero SNR value below which one should not operate. The effect of the block length on both the minimum bit energy and the SNR value at which the minimum is achieved is investigated. Flash training and transmission schemes are analyzed and shown to improve the energy efficiency in the low-SNR regime. In the second part of the paper, the capacity and energy efficiency of training-based schemes are investigated when the channel input is subject to peak power constraints. The capacity-achieving input structure is characterized and the magnitude distribution of the optimal input is shown to be discrete with a finite number of mass points. The capacity, bit energy requirements, and optimal resource allocation strategies are obtained through numerical analysis. The bit energy is again shown to grow without bound as SNR decreases to zero due to the presence of peakedness constraints. The improvements in energy efficiency when on-off keying with fixed peak power and vanishing duty cycle is employed are studied. Comparisons of the performances of training-based and noncoherent transmission schemes are provided

Pilot-symbol-assisted communications with noncausal and causal wiener filters

Abstract — In this paper, pilot-assisted transmission over timeselective flat fading channels is studied. It is assumed that noncausal and causal Wiener filters are employed at the receiver to perform channel estimation with the aid of training symbols sent periodically by the transmitter. For both filters, the variances of estimate errors are obtained from the Doppler power spectrum of the channel. Subsequently, achievable rate expressions are provided. The training period, and data and training power allocations are jointly optimized by maximizing the achievable rate expressions. Numerical results are obtained by modeling the fading as a Gauss-Markov process. The achievable rates of causal and noncausal filtering approaches are compared. For the particular ranges of parameters considered in the paper, the performance loss incurred by using a causal filter as opposed to a noncausal filter is shown to be small. The impact of aliasing that occurs in the undersampled version of the channel Doppler spectrum due to fast fading is analyzed. Finally, energy-per-bit requirements are investigated in the presence of noncausal and causal Wiener filters. I