Channel Estimation And Equalization Based On Semi-definite Programming

In practical OFDM systems, it is not usual that all the carriers are available to users, sothe non-continuous orthogonal frequency division multiplexing (NC-OFDM) technology isproposed. However, the spectrum of NC-OFDM is random and discontinuous, so the existingresearch results of OFDM system can’t be directly applied to the NC-OFDM systems. Withrespect to pilot design methods of NC-OFDM system, there are some existing research results,but still lack of a convex optimization model for joint pilot placement and power allocation.Based on the analysis and summary of existing work, we propose a joint pilot placement andpower allocation channel estimation algorithm which is used in NC-OFDM system. The LSapproach is applied for channel estimation at the receiver. We minimize the Mean SquareError (MSE) of channel estimation by adjusting the powers of the pilot tones. Thisoptimization problem is then reformulated as an problem of the eigenvalues of a semi-definitehermitian matrix, which is a typical semi-definite programming problem. Through thesimulation to demonstrated the effectiveness of the proposed schemes. The simulation resultshave shown that the new algorithm can improve the performance of the system, both inchannel estimation and BER.In addition, there are many algorithms about the equalizer technology, where theminimum mean square error algorithm is by far the most popular algorithm for linearequalizer design, because of its low computational complexity. But for practicalcommunication systems, designers are often more concerned about the bit error rateperformance of the system, rather than its mean square error performance. However, thetheoretical analysis of the minimum bit error rate filtering algorithm is not perfect, and thecomplexity of the algorithm is high. To solve these problems, this paper proposes asuboptimal linear equalizer design algorithm based on semi-definite programming. Thealgorithm considers minimizing the bit error rate (MBER) by using of the semi-definiteprogramming problem. The simulation results are presented to demonstrated the effectivenessof the proposed schemes. Simulation results show that the BER performance of the proposedalgorithm is as good as EMBER algorithm at high SNR. Moreover, the running time and thecomplexity of the proposed algorithm is much lower than the EMBER algorithm.