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Iterative Sphere Detectors for Imperfect Channel State Information

This manuscript presents an iterative detector based on a generalized Schnorr-Euchner enumeration for the case of imperfect channel state information. The detector determines the most contributive N∈{1,2} terms in each of the two log-sum-exponents. The objective function of the tree search is modified to account for (a) the channel estimation error variance and (b) the input a priories. Due to (a), the decomposition of the objective into the form used in conventional tree search is not possible. Moreover, both (a) and (b) invalidate the use of the progressive zigzag order. Because of this, a generalized Schnorr-Euchner enumeration is proposed where explicit sorting is done. Unlike the conventional tree search, the node weights are not computed in an additive way where the weight of a child node is the sum of the weights of the parent and the branch connecting them. The advantage of the proposed detectors compared to iterative channel estimation and decoding is that the repetition of the channel estimation and the QR decomposition is not needed. Also since they are based on the Schnorr-Euchner enumeration, they do not require an initial radius estimation and if channel estimation errors are small enough to be ignored, the search step becomes division- and square-root-free.