Compressive sensing framework for signal processing in heterogeneous cellular networks

We consider a heterogeneous cellular network where each base station sends a unique training signal based on its physical layer cell identity. The received signal at the mobile terminal (MT) is a superposition of training signals from different base stations (BS). Neither the identities of BS nor their channel response is known apriori at the MT. For this scenario, we consider the problem of finding the identities of constituent BS from the superimposed components in the received signal. Though the number of BS with unique identities can be quite large in a cellular network, in any given scenario, the actual number of BS interfering at a MT is relatively few. By exploiting this sparseness, we show that our problem can be solved using block sparse signal reconstruction algorithms under compressive sensing framework where the sensing matrix in our model is block matrix with circulant blocks (BCB). We apply convex programming based ℓ₂/ℓ₁ mixed norm minimization approach and greedy based subspace matching pursuit approach to recover the identities of interfering BS. We characterize the block restricted isometry property and the mutual subspace incoherence of BCB matrices with i.i.d. Rademacher distributed entries and establish certain guarantees on the recovery. Our proposed approaches give significant improvements over conventional successive interference cancellation approach when used with both randomly generated training signals and 3GPP-LTE training signals. Our results offer new and promising avenues for signal processing problems in heterogeneous cellular networks.