Estimation in OFDM Based Cognitive Radio Systems BER Analysis for Fourier and Wavelet Transform Process

In this correspondence, sparse channel estimation is first introduced in orthogonal frequency-division multiplexing (OFDM)-based cognitive radio systems. Based on the results of spectrum sensing, the pilot design is studied by minimizing the coherence of the dictionary matrix used for sparse recovery. Then, it is formulated as an optimal column selection problem where a table is generated and the indexes of the selected columns of the table form a pilot pattern. A novel scheme using constrained cross-entropy optimization is proposed to obtain an optimized pilot pattern, where it is modeled as an independent Bernoulli random process. Comparison between the conventional FFT based OFDM systems with DWT based OFDM system have been made according to some conventional and non-conventional modulation methods over AWGN and Rayleigh fading channel. The different wavelet families have been used and compared with FFT based OFDM system and found that DWT based OFDM system is better than FFT based OFDM system with regards to the bit error rate (BER) performance. Finally, we provide numerical results in terms of both MSE estimation performance and Bit Error Rate (BER) of a coded OFDM system using the proposed channel estimators, to show that they indeed approach MMSE performance.