Correlation-based techniques used for frame synchronization can suffer significant performance degradation over multi-path frequency-selective channels. In this paper, we propose a joint frame synchronization and channel estimation (JFSCE) framework as a remedy to this problem. This framework, however, increases the size of the resulting combined channel vector which should capture both the channel impulse response (CIR) vector and the frame boundary offset and, therefore, its estimation becomes more challenging. On the other hand, because the combined channel vector is sparse, sparse channel estimation methods can be applied. We propose several JFSCE methods using popular sparse signal recovery (SSR) algorithms which exploit the sparsity of the combined channel vector. Subsequently, the sparse channel vector estimate is used to design a sparse equalizer. Our simulation results and experimental measurements using software defined radios (SDRs) show that in some scenarios our proposed method improves the overall system performance significantly, in terms of the mean square error (MSE) between the transmitted and the equalized symbols compared to the conventional method.
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