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

Channel Estimation for Millimeter-Wave Massive MIMO with Hybrid Precoding over Frequency-Selective Fading Channels

Channel estimation for millimeter-wave (mmWave) massive MIMO with hybrid precoding is challenging, since the number of radio frequency (RF) chains is usually much smaller than that of antennas. To date, several channel estimation schemes have been proposed for mmWave massive MIMO over narrow-band channels, while practical mmWave channels exhibit the frequency-selective fading (FSF). To this end, this letter proposes a multi-user uplink channel estimation scheme for mmWave massive MIMO over FSF channels. Specifically, by exploiting the angle-domain structured sparsity of mmWave FSF channels, a distributed compressive sensing (DCS)-based channel estimation scheme is proposed. Moreover, by using the grid matching pursuit strategy with adaptive measurement matrix, the proposed algorithm can solve the power leakage problem caused by the continuous angles of arrival or departure (AoA/AoD). Simulation results verify that the good performance of the proposed solution.Comment: 4 pages, 3 figures, accepted by IEEE Communications Letters. This paper may be the first one that investigates the frequency selective fading channel estimation for mmWave massive MIMO systems with hybrid precoding. Key words: Millimeter-wave (mmWave) massive MIMO, frequency-selective fading, channel estimation, compressive sensing, hybrid precodin