Modulated Unit-Norm Tight Frames for Compressed Sensing

In this paper, we propose a compressed sensing (CS) framework that consists of three parts: a unit-norm tight frame (UTF), a random diagonal matrix and a column-wise orthonormal matrix. We prove that this structure satisfies the restricted isometry property (RIP) with high probability if the number of measurements $m = O(s \log^2s \log^2n)$ for $s$-sparse signals of length $n$ and if the column-wise orthonormal matrix is bounded. Some existing structured sensing models can be studied under this framework, which then gives tighter bounds on the required number of measurements to satisfy the RIP. More importantly, we propose several structured sensing models by appealing to this unified framework, such as a general sensing model with arbitrary/determinisic subsamplers, a fast and efficient block compressed sensing scheme, and structured sensing matrices with deterministic phase modulations, all of which can lead to improvements on practical applications. In particular, one of the constructions is applied to simplify the transceiver design of CS-based channel estimation for orthogonal frequency division multiplexing (OFDM) systems.Comment: submitted to IEEE Transactions on Signal Processin

Performance Analysis of Compressive Sensing based LS and MMSE Channel Estimation Algorithm

In this paper, we have developed and implemented Minimum Mean Square Channel Estimation with Compressive Sensing (MMSE-CS) algorithm in MIMO-OFDM systems. The performance of this algorithm is analyzed by comparing it with Least Square channel estimation with compressive sensing (LS-CS), Least Square (LS) and Minimum Mean Square Estimation (MMSE) algorithms. It is observed that the performance of MMSE-CS in terms of Bit Error Rate (BER) metric is definitely better than LS-CS and LS algorithms and it is at par with MMSE algorithm. Moreover the role of compressive sensing theory in channel estimation is accentuated by the fact that in MMSE-CS algorithm only a very small number of channel coefficients are sensed to recreate the transmitted data faithfully as compared to MMSE algorithm