Optimization of Spatiotemporal Apertures in Channel Sounding

In this paper, we investigate the impact of the spatiotemporal aperture of a channel sounding system equipped with antenna arrays at the transmitter and receiver on the accuracy of joint estimation of Doppler frequency and bidirection. The contribution of this paper is threefold. First, we state a spatiotemporal model that can describe parallel as well as switched sounding systems. The proposed model is applicable for arbitrary layouts of the spatial arrays. To simplify the derivations, we investigate the special case of linear spatial arrays. However, the results obtained for linear arrays can be generalized to arbitrary arrays. Secondly, we give the necessary and sufficient conditions for a spatiotemporal array to yield the minimum Cramer-Rao lower bound (CRLB) in the single-path case and Bayesian CRLB in the multipath case. The obtained conditions amount to an orthogonality condition on the spatiotemporal array. Thirdly, we define the Doppler-bidirection ambiguity function and derive the necessary and sufficient conditions for a linear spatiotemporal array to be ambiguous. Based on the ambiguity function, we define the normalized side-lobe level, which we propose to use as a figure of merit in the design of spatiotemporal arrays.