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We examine power spectrum estimation from wide-sense stationary signals received at different wireless sensors. We organize multiple sensors into several groups, where each group estimates the temporal correlation only at particular lags, which are different from group to group. A fusion centre collects all the correlation estimates from different groups of sensors, and uses them to estimate the power spectrum. This reduces the required sampling rate per sensor. We further investigate the conditions required for the system matrix to have full column rank, which allows for a least-squares reconstruction method.