Diversity-Integration Tradeoffs in MIMO Detection

In this paper, a multiple-input multiple-output (MIMO) detection problem is considered. At first, we derive the generalized likelihood ratio test (GLRT) for arbitrary transmitted signals and arbitrary time-correlation of the disturbance. Then, we investigate design criteria for the transmitted waveforms in both power-unlimited and power-limited systems and we derive closed-form formulas for the probability of false alarm and the detection probability. Finally, we study the interplay among the rank of the optimized space-time code (i.e., the number of linearly independent transmitted waveforms), the number of transmit diversity paths generated in the signal space, and the amount of energy integrated along each path. The results confirm that there is an inherent tradeoff between diversity and integration, and that no uniformly optimum waveform design strategy exists.