Subspace Blind Channel Estimation Methods in OFDM Systems under Multi-path Channels

Abstract

In this paper, we compare two methods of subspace blind channel estimation in orthogonal frequency division multiplexing (OFDM) systems using different guard intervals under a multi-path channel with an exponentially decaying power profile. In both methods, we propose the same solution to solve the scalar ambiguity problem, which is a common problem in subspace blind estimation methods, by using a single pilot signal. The bit error rate (BER) and the normalized mean square error (NMSE) of the estimated channel vector were compared under various signal-to-noise ratio (SNR) and different numbers of transmitted OFDM symbols. The impact of using different positions of the pilot signal is also demonstrated. The results of channel estimation, data detection, and system complexity show that the zero padding (ZP) model is superior to the model with a cyclic prefix (CP).

A Nonredundant SVD-based Precoding Matrix for Blind Channel Estimation in CP-OFDM Systems Over Channels with Memory

“…Where 𝑁(0,0.5𝜎 𝑙 2 ) represents a Gaussian random variable characterized by a zero-mean and a variance of 0.5𝜎 𝑙 2 , where denotes the expected value of the norm squared of the channel impulse 𝜎 𝑙 2 = 𝐸[‖ℎ 𝑙 ‖ 2 ], 𝑛 corresponds to the total number of realizations of the generated channel impulse response. The channel model parameters are 𝜏 𝑟𝑚𝑠 𝑇 𝑠 = 10 ⁄ , 𝑛 = 40.…”

“…. , 𝑑 𝑖,𝑁−1 ] 𝑇 is the data block and 𝒔 𝒊 (𝑘) = [𝑠 𝑖,0 (𝑘) ,..., s 𝑖,𝑁−1 (𝑘) ] 𝑇 , k = 1 ,2 and 3 are the data vectors after the precoder, respectively 𝑨 (1) , 𝑨 (2) and 𝑨 (3) . There is no redundancy introduced into the systems because all precoding matrices are of size 𝑁 × 𝑁.…”

“…Where 𝑟 𝑊 (𝑖) are the elements of the row vector 𝒓 𝑾 and w is an integer and defined between [1, N]. The two precoding matrices 𝑨 (2) and 𝑨 (3) are designed as follows:…”

“…The design of both 𝑨 𝒃 (2) and 𝑨 𝒃 (3) following the Equations (34), ( 35), ( 36) and (37), considering that 𝑨 (2) and 𝑨 (3) as the element of the final matrices. Appendix A established that the matrix 𝑨 (2) has full rank property because it shares the same general structure as 𝑨 (1) . A similar proof for the rank property of matrix 𝑨 (3) for w = N / 4 is mentioned in Appendix B.…”

“…Since the inverse of 𝑨 𝒇 , affects BER, which has to reduce the impact of noise vector on the data estimate, the data detection method must be improved in order to employ this kind of precoder in applications where data detection is necessary. In this case, we investigate the proposed OFDM system's channel estimate utilizing matrices 𝑨 (2) and 𝑨 (3) . The matrices 𝑨 (2) and 𝑨 (3) at 𝜌 = 0.1 outperform other curves in terms of NMSE, as seen in Figure 4.…”