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16 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 1, NO. 2, NOVEMBER 2010 [8] H. Gao, P. J. Smith, and M. Clark, “Theoretical reliability of MMSE linear diversity combining in rayleigh-fading additive interference channels,” IEEE Trans. Commun., vol. 46, no. 5, pp. 666–672, May 1998. [9] L. Yang, M. Chen, S. Cheng, and H. Wang, “Combined maximum likelihood and ordered successive interference cancellation grouped detection algorithm for multistream mimo,” in Proc. of 8th IEEE Int. Symposium on Spread Spectrum Techniques and Applications, Aug. 2004, pp. 250–254. Maciej Krasicki received the M.S. degree in Electronics and Telecommunications from Poznan University of Technology, Poland, in 2006. Since then he has been working towards the Ph.D. degree. His dissertation work concerns a new (‘boosted’) space-time diversity scheme, designed to support iterative decoding at the receiver of WLAN systems. His Ph.D. defense took place in 2010. From 2009 he has been with the Faculty of Electronics and Telecommunications, Poznan University of Technology, as a Research Assistant. His research interests include multi-antenna transmission, space-time coding and iterative signal processing. He has published several papers in journals (e.g. Electronics Letters) and conference proceedings.
ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 1, NO. 2, NOVEMBER 2010 17 Spectral Analysis of Boosted Space-Time Diversity Scheme Abstract—In this paper the asymptotic performance of a new intuitive space-time diversity scheme is analyzed. So called boosted scheme is compatible with today’s WLAN specifications with regard to convolutional coding and bit labelling, and minimizes the number of decoding iterations, required to obtain a reasonable Bit Error Rate. Good properties of the proposed scheme are proved by high asymptotic coding gain and advantageous distance spectrum. A simulation experiment is run to investigate the system performance in terms of poor channel state. The boosted scheme is compared with its ancestor – Bit-Interleaved Space-Time Coded Modulation with Iterative Decoding (BI-STCM-ID). Index Terms—Multiple-input multiple-output channels, bitinterleaved space-time coded modulation, Alamouti scheme, constellation labeling, block fading, distance spectrum, coding gain. I. INTRODUCTION WIRELESS Local Area Networks have recently become a very popular Internet access technique. Almost each notebook is equipped with an 802.11 card. Expectations for WLAN throughput are still growing. The new 802.11n [1] specification provides some promising techniques such as multi-antenna transmission with space-time block coding (STBC). The key issue is to make use of higher Multiple-Input Multiple-Output channel capacity. Reviewed in Section 2 BI- STCM-ID [2], that exploits iterative processing at the receiver, seems to be an excellent solution. Unfortunately, the 802.11n specification accepts only Gray constellation labelling, which makes iterative processing worthless [3]. On the opposite, there are some constellation labellings, optimized for the lowest Bit Error Rate (BER) in case of error-free feedback. The author is an advocate of a new intuitive approach to an overall mapping (constellation labelling and space-time coding) described in Section 3. The proposed boosted spacetime diversity scheme minimizes the number of passes while reasonable BER is kept. Theoretical analysis and simulation results are presented in Section 4. Section 5 of this paper is designed to conclude the work. A. System model II. BI-STCM-ID OVERVIEW A BI-STCM-ID system is shown in Fig. 1. In the first instance, information bits are encoded by a convolutional encoder of rate RC = 1/kc. Next, K interleaved encoded bits [v 1 t . . . v K t ] choose a vector [x 1 t . . . x q t ] of constellation M. Krasicki is with the Faculty of Electronics and Telecommunications, Poznan University of Technology, Poznan, Poland (phone: +48 61 665 39 36; fax: +48 61 665 38 23; e-mail: mkrasic@et.put.poznan.pl). Maciej Krasicki Fig. 1. Transmitter (a) and receiver (b) of BI-STCM-ID points, each of them according to labelling rule ω. Next, q constellation points form the space-time (ST) symbol Xt ∈ ℵ. The ST symbol consists of modified constellation points transmitted by Nt antennas within L time slots. As it can be noticed, each ST symbol is unequivocally associated with K encoded bits, so overall mapping rule ϖ : {0, 1} K → ℵ can be defined. In case of orthogonal 2 × 2 Alamouti scheme, q = 2, L = 2, and � x Xt = 1 t x2 � � � t 2 ∗ � � 1 ∗ . (1) −xt xt The signals received by Nr antennas within L time slots are expressed by Yt = XtHt + Wt Matrix Ht describes the channel, i.e. [hi,j]t is a temporal gain of the path between ith transmit- and jth receive antenna. Wt represents the Gaussian noise. Space-time demapper evaluates its output log-likelihood ratios (LLRs) [4] λ � v k t ; O � according to a priori LLRs λ � v k t ; I � and the information received from the channel. SISO decoder [5] increases LLR’s reliability according to max-log-MAP routine. B. BI-STCM-ID Asymptotic Performance When ideal interleaving is assumed, the union bound of bit error probability is given by [3]: Pb ≤ 1 kc d=df (2) ∞� WI(d)f (d, ϖ, ℵ), (3) where df is the free distance of the convolutional code, and WI(d) denotes the total input weight of error events at
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