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01-06-2015 | Issue 3/2015

Wireless Personal Communications 3/2015

Regularized Lattice Sphere Decoding for Block Data Transmission Systems

Journal:
Wireless Personal Communications > Issue 3/2015
Authors:
Mahmoud A. M. Albreem, Mohd Fadzli Mohd Salleh

Abstract

This paper presents Lattice Sphere Decoding (LSD) with regularization techniques for block data transmission systems. It has shown that a small condition number (\(\tau \)) results in better detection performance. This paper aims to reduce this value to its smallest possible value. Regularization technique offers reduction in condition number (\(\tau \)) that improves LSD performance. In this work, two regularization techniques are utilized on LSD. First, \(\hbox {L}_{1}\)-regularization method is introduced, which sums the mixed norms. Second, \(\hbox {L}_{2}\)- regularization method, which is the most commonly used method of regularization for ill-conditioned problems in mathematics. We derive the exact relationship between the LSD performance and condition number (\(\tau \)) as well as the relationship between LSD initial radius (d) and condition number (\(\tau \)). The derived equations show their convergence to the fact that the performance increases as the radius (d) increases. Simulation results show that the LSD with \(\hbox {L}_{1}\)-regularization technique offers smaller condition number (\(\tau \)), and therefore, produces better system performance. From the performance results and the complexity analysis, it is apparent that the proposed techniques achieve a good balance between complexity and performance.

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