###### Abstract
In a MIMO-OFDM system, where a receiver should address the effects of co-antenna interference, in addition to ISI, the concept of turbo equalization can be used to mitigate iteratively the co-antenna interference. Among different equalization methods, MIMO minimum mean-squared error (MMSE) is a prominent low-complexity suboptimal algorithm [6;7]. Using the MMSE algorithm in an iterative scheme compensates sub-optimality and leads to an error-rate performance near enough to the performance achieved when the optimal high-complexity maximum-likelihood (ML) algorithm is used [8;9]. Iterative demapping was proposed firstly in [10] based on bit interleaved coded modulation (BICM) with additional soft feedback from the SISO convolutional decoder to the constellation demapper. For a system with convolutional code, BICM and 8-PSK modulation, 1 dB and 1.5 dB gains for BER performance were reported for Rayleigh flat fading channels and channels with AWGN, respectively. In [11], the use of iterative demapping shows performance improvement of 1.2 dB at BER of \(10^{-6}\) for the QAM BICM scheme with the ow-density parity-check (LDPC) channel decoder over a flat fading Rayleigh channel with 15% of erasures. The symbol-by-symbol maximum a posteriori (MAP) algorithm is the optimal algorithm for obtaining the outputs of the demapper. The MAP algorithm is likely to be considered of high complexity for hardware implementation in a real system basically because of the numerical representation of probabilities, non-linear functions and because of mixed multiplications and the additions of these values [12]. Implementing the MAP algorithm in its logarithmic domain instead of the probabilistic form reduces the computational complexity. The Max-Log-MAP demapping algorithm is a suboptimal direct transformation of the MAP algorithm into the logarithmic domain; hence, the values and operations are easier to handle. Figure 1 presents the MIMO-OFDM receiver block diagram, which uses MMSE turbo-equalization and turbo-demapping. In previous work, presented in [13; 14], flexible application-specific processors dedicated for turbo-equalization and turbo-demapping have been proposed. The first task in realizing a flexible multi-standard hardware component is to define the flexibility parameters. The equalizer module is based on the MMSE algorithm, and it is affected by flexibility parameters, which are extracted from the following requirements:  
1. The ability to support various MIMO schemes reaching to a 4 \(\times\) 4 antenna dimension
2. The capability of using efficiently the implemented hardware resources for different time diversity channel types (block fading, quasi-static and fast fading)
3. The possibility to execute in both iterative and no-iterative modes  
Regarding turbo-demapping, the demapper implements the Max-Log-MAP algorithm. It embraces all flexibility requirements for recent wireless digital communication standards. It can execute in iterative and non-iterative processing schemes and support different mapping styles, modulation types and signal space diversity (SSD) with rotated constellation. Such wide flexibility becomes crucial in the current trend toward the convergence of wireless communication services [15] and the requirement of multi-standard terminals. In addition, the demonstration of the ability of designing highly flexible, yet efficient, hardware architectures can prompt the proposition of new processing schemes and parameters that better meet the environment conditions and applications. Such novel schemes, associated with efficient flexible implementations, can then constitute potential candidates for adoption in next generation communication systems. In addition to the requirements of efficiency and productivity, the emergent flexibility requirement sets up a new design metric.