Chapter 10
Reduced-Complexity Iterative Sphere Detection for Channel-Coded SDMA-OFDM Systems
10.1 Introduction1
The radio spectrum is a scarce resource. Therefore, one of the most important objectives in the design of future communications systems is the efficient exploitation of the available spectrum, in order to accommodate the ever-increasing traffic demands. Any effort to achieve bandwidth-efficient transmissions over hostile wireless channels typically requires advanced channel coding. Powerful turbo codes were introduced by Berrou in [565, 566] in the context of iteratively decoding two parallel concatenated convolutional codes. His work was later extended to serially concatenated codes [567] and then found its way gradually into iterative detector designs, such as for example iterative multiuser detectors [568]. Despite their modest complexity, iterative detection and decoding mechanisms are capable of approaching the capacity limits for transmission over wireless MIMO channels.
10.1.1 Iterative Detection and Decoding Fundamentals
10.1.1.1 System Model
Before introducing the channel coding blocks in our MIMO system model, let us briefly review the mathematical model of an SDMA system supporting U users and having N receive antennas at the BS, which is formulated as
(10.1) 
where y, H, s and n are the (N × 1)-element received signal column vector, the (N × U)-element FD-CTF ...
