The effect of convolutional encoder memory on the sphere decoding search radius in MIMO systems

In the new generation communication systems Multiple-Input-Multiple-Output systems are frequently used. The processing load of the Maximum Likelihood (ML) Detector which is the optimum detector for these systems, increases exponentially as a function of system dimension and memory due to testing all possible points. Sphere Decoding (SD) method which tests only the probable points, decreases the processing load dramatically. System memory changes by system dimensions and length of the convolutional encoder. This, in turn, affects the radius of the hyper sphere centered at the observation in the observation space at which SD attains the performance of the ML detector. This effect is investigated via simulation studies. In these simulations, it is observed that the radius of the SD is relatively smaller than the one in ML, and the ratio between the radius values varies from 6,61 in the case of memoryless 2×2 MIMO system to 1,02 in the case of 8x8 MIMO system with memory K=10 according to increased antenna numbers and system memory. In addition to these, it is observed that the radius of the hyper sphere is directly proportional to the memory of the encoder.