This paper considers the problem of channel estimation for millimeter wave wireless communication channels. Many existing channel estimation approaches utilize the spatial sparsity of mmWave channels and employ compressive sensing based techniques to estimate the parameters of the channel, such as the Angles of Arrival (AoA) and Angles of Departure (AoD) of the channel paths. In this paper, we show how the problem of channel estimation can be converted into a fourth order tensor decomposition problem, which offers several benefits. Firstly, we do not need a grid-based search for the angles. More importantly, our algorithm is applicable for both uniform and non-uniform arrays at the transmitter and receiver. In particular, our method can exploit well-known benefits offered by the difference co-array of suitably designed sparse arrays and provably identify a larger number of channel paths compared to existing approaches.

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