Beamspace Channel Estimation for the Millimeter-wave Massive MIMO Systems: Dual Loops-based Iteration Reduction Algorithms

In the millimeter-wave (mmWave) massive multipleinput multiple-output (MIMO) channel estimation problem blue employing lens antenna arrays, conventional compressed sensing algorithms demand numerous matrix-vector multiplications per iteration, thereby incurring substantial computational complexity. To address this challenge, we propose dual-loop beamspace channel estimation strategies that leverage the sparsity of the mmWave beamspace channel, formulating the estimation problem as a sparse signal recovery task. First, we design an effective dual-loop algorithm based on the ℓ₁ minimization problem to tackle the channel estimation problem. In the outer loop, an ℓ₁- based iterative reduction algorithm (ℓ₁-IRA) reduces the largescale channel estimation problem to a series of small-scale subproblems by exploiting the sparsity of the beamspace channel. In the inner loop, the fast iterative shrinkage thresholding algorithm with backtracking (FISTAB) algorithm is used to solve these subproblems efficiently. Furthermore, conventional compressed sensing algorithms exhibit favorable performance in weakly correlated systems but suffer from significant performance degradation in strongly correlated scenarios. To mitigate this limitation, we design an ℓ₁₋₂ minimization problem-based IRA (ℓ₁₋₂-IRA) for the beamspace channel estimation problem. Finally, simulation results show that the proposed dual loop methods significantly reduce pilot overhead and improve beamspace channel estimation accuracy compared to conventional channel estimation techniques.