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An integrated design of a joint distributed source coding and an adaptive signal processing scheme for a virtual multiple input multiple output (V-MIMO) communications-based, cooperative wireless sensor network is proposed. We employ a distributed coding scheme that exploits inherent correlations among sensor data and an adaptive correlation tracking technique based on recursive least squares (RLS) algorithm that provides improved energy efficiency compared to previously proposed such joint coding and signal processing schemes for single input single output (SISO) communications based systems. An integration scheme with virtual space-time block coding based M-ary quadrature amplitude modulation (M-QAM) communication is also developed. The system efficiency is analyzed for various transmission distances and various channel conditions. Our results show that the proposed system achieves significant energy savings compared to conventional designs beyond certain transmission distances. The achieved energy efficiencies and low decoding error rates justify the application of the proposed scheme in energy constrained wireless sensor networks.