Iterative Sphere Detectors Based on the Schnorr-Euchner Enumeration

Two kinds of iterative sphere detectors based on modifications of the Schnorr-Euchner enumeration are presented. The first is capable of finding "good" candidate lattice points relatively soon. Its complexity and performance are controlled by an adaptive radius backlash update strategy. The second systematically searches for the most contributive term in each of the two log-sum-exponents. Both kinds require modifications to the original Schnorr-Euchner enumeration. The objective function must account for the input a priories and explicit sorting of the branches stemming from the tree nodes must be done because the simple zigzag order in this case is not valid. The impact of the a priories on the log-likelihood ratio clipping is also addressed. The advantages of the new detectors compared to the Fincke-Pohst-based ones are: i) No initial radius is required, ii) the search step is division- and square-root-free and iii) the average computational complexity is lower.