Sparse channel estimation of pulse-shaping multiple-input–multiple-output orthogonal frequency division multiplexing systems with an approximate gradient l2 – Sl0 reconstruction algorithm

Most of the existing compressed channel-sensing methods for multiple-input-multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems did not take into account the pulse-shaping filter in the transmitter and matched filter in the receiver. However, these two filters are commonly used in digital communication systems. The compressed channel-sensing problem of pulse-shaping MIMO-OFDM systems is first formulated. A new signal-reconstruction algorithm in the compressed sensing framework is then proposed. The algorithm is based on minimising a smoothed l₀-norm regularised least-square (LS) (l₂ - Sl₀) objective function, and the unconstrained optimisation involved is performed by an approximate gradient method. Further, the proposed l₂ - Sl₀ algorithm is applied to reconstruct the channel impulse response. A number of computer simulation-based experiments are conducted, showing a better reconstruction accuracy of the l₂ - Sl₀ algorithm as compared with the smoothed l₀-norm (Sl₀) algorithm. The proposed channel estimation approach can save nearly 25% pilot signals to maintain the same mean square error and bit error rate performances as given by the conventional LS method.