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To approach the potential MIMO capacity while optimizing the system performance, the joint Tx/Rx MMSE design has been proposed. It is the optimal linear scheme for spatial multiplexing MIMO systems assuming a fixed number of spatial streams p as well as fixed modulation and coding across these spatial streams. However, the number of spatial streams has been arbitrarily chosen and fixed, which may lead to an inefficient power allocation strategy and a high bit-error rate (BER). In this paper, we propose to relax the constraint of fixed number of streams p and optimize this value under the constraints of fixed average total transmit power PT and fixed spectral efficiency R. The resulting spatially optimized joint Tx/Rx MMSE design is shown to lead to a 5.7 dB SNR gain over its full spatial multiplexing counterpart for a (3, 3) MIMO set-up at BER = 10-2 and R = 12 bits/s/Hz over flat-fading channels. Such a significant improvement is due to the better exploitation of the MIMO spatial diversity and the more efficient power allocation enabled by the proposed spatial optimization.