Turbo detection for MIMO systems: bit labeling and pre‐coding

Abstract

SUMMARYBit-interleaved coded modulation with iterative detection for multi-input multi-output (MIMO) systems demands an efficient APP detector that delivers soft information about the coded bits. The list-sequential detector is a reduced-complexity approximation to an exhaustive a posteriori probability (APP) detector. It uses a tree search employing the stack algorithm to find dominant terms of the log-likelihood ratio (LLR). The commonly used symbol-by-symbol Gray labeling is not necessarily the best approach to good performance of iterative systems. Therefore, we consider different bit labelings and differential pre-coding adapted to MIMO systems. With the help of extrinsic information transfer (EXIT) charts and bit error rate (BER) simulations, we show that symbol-by-symbol Gray labeling in combination with an outer Turbo code is a good compromise for fast convergence and low error floor of MIMO systems with iterative detection.

EXIT Charts for System Design and Analysis

“…Several papers studied the multi-dimensional constellation labelling demonstrating that it was beneficial to invoke multidimensional modulation in the context of both TCM and BICM [76,[86][87][88]. However, these papers did not quantify the achievable improvement, neither did they detail whether the improvement was merely due to the increased number of bits used by the combined symbols allowing for more flexibility in the design of the constellation , or due to the beneficial multi-dimensional labelling.…”

Design and performance of BICM-ID systems with hypercube constellations

“…Finally, we would like to point out that, after we submitted this paper, it was brought to our attention by the reviewers that the idea of multi-dimensional mapping was independently investigated in [17] for BICM-ID and in [18] for MIMO systems. The work in [17] is quite similar to what presented in this paper, but it only considers the AWGN channel model.…”

On Multidimensional BICM-ID Constellation Labelling

“…Accordingly, the benefits and flexibility offered by the bit-to-symbol mapping schemes in a higherdimensional space [14][15][16][17] may be linked to and hence represented by the slope of the AGM EXIT curve. For example, Figure 4-a shows both the GM and AGM EXIT curves of a BICM-ID schemes employing 16QAM modulation and operating at E b /N0 = 5.0dB.…”

“…However, the above-mentioned contributions [14][15][16][17] do not provide a quantitative definition of the f lexibility attained by the proposed bit-to-symbol mapping schemes in a higher-dimensional space. In addition, it is not clear, whether the achievable flexibility is due to expanding the constellation to a higher-dimensional space or accrues simply from increasing the number of bits per joint symbol.…”

“…Additionally, multi-dimensional labelling was also proposed for QPSK based BICM-ID for transmission over a single antenna [14]. Further improvements of multi-dimensional constellation labelling were proposed in [15,16]. More recently, multi-dimensional constellation labelling was also proposed for bit-interleaved space-time-coded modulation using iterative decoding in [17], where the labelling of the two 16-QAM symbols transmitted over two antennas in two consecutive time-slots was designed jointly and was optimised using the RTS technique [11].…”