Stopping Condition for Greedy Block Sparse Signal Recovery

For greedy block sparse recovery with unknown sparsity level, we theoretically derive a stopping condition to terminate the iteration process and thus to estimate the sparsity level. Focused on the block orthogonal matching pursuit (BOMP) algorithm, we model the energy of residual signals from a probabilistic perspective and we use its distribution to derive a threshold, the iteration process is terminated when the residual energy is below the given threshold. Specifically, a communication scenario of small packet transmission is considered, which uses the interference cancellation based BOMP (ICBOMP) algorithm to recover sparse signal, we apply the stopping condition to terminate the iterations, and thus to estimate the number of active users. Simulation results show that our derived condition can accurately estimate the sparsity level and at the same time guarantees a favorable recovery accuracy, both for the BOMP and ICBOMP recoveries.