In this paper, we tackle channel estimation in millimeter-wave hybrid multiple-input multiple-output systems by considering off-grid effects. In particular, we assume that spatial parameters can take any value in the angular domain, and need not fall on predefined discretized angles. Instead of increasing the number of discretized points to combat off-grid effects, we use implicit Dirichlet kernel structure in the Fourier domain, which conventional compressed sensing methods do not use. We propose greedy low-complexity algorithms based on orthogonal matching pursuit (OMP); our core idea is to traverse the Dirichlet kernel peak using estimates of the discrete Fourier transform. We demonstrate the efficacy of our proposed algorithms compared to standard OMP reconstruction. Numerical results show that our proposed algorithms obtain smaller reconstruction errors when off-grid effects are accounted for.
Interestingly, standard CS methods based on sparsity fail to leverage Dirichlet structure in the Fourier domain. We exploit this structure to improve the channel estimation process. In particular, we propose low-complexity algorithms based on OMP @cite_6 , owing to its computational tractability. Our numerical results show that while accounting for off-grid effects, our proposed algorithms obtain smaller channel reconstruction errors compared to standard OMP algorithms.
@cite_6
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This paper demonstrates theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal. This is a massive improvement over previous results, which require O(m2) measurements. The new results for OMP are comparable with recent results for another approach called basis pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems.