A Low-Complexity Minimum Mean Square Error (MMSE) method for estimation of impulse response or channel response of Impulse-Radio Ultra-Wideband (IR-UWB) wireless channels which exploits the sparsity of the received signal profile and the structure of the sensing matrix. The method comprises of first sub-sampling a received signal profile; second finding a minimum mean square error estimate of the impulse-radio ultra-wideband communication channel by Bayesian estimation according to priori channel statistics; and third identifying one or more substantially orthogonal clusters in the received signal profile. Impulse response of the impulse-radio ultra-wideband communication channel is the sum of the total number of resolvable multipath components, each with a real valued fading gain, and delay, relative to the arrival of the first path and impulse is the Dirac delta function.