Generalized Silver Codes

For an $n_t$ transmit, $n_r$ receive antenna system ($n_t \times n_r$ system), a {\it{full-rate}} space time block code (STBC) transmits $n_{min} = min(n_t,n_r)$ complex symbols per channel use. The well known Golden code is an example of a full-rate, full-diversity STBC for 2 transmit antennas. Its ML-decoding complexity is of the order of $M^{2.5}$ for square $M$-QAM. The Silver code for 2 transmit antennas has all the desirable properties of the Golden code except its coding gain, but offers lower ML-decoding complexity of the order of $M^2$. Importantly, the slight loss in coding gain is negligible compared to the advantage it offers in terms of lowering the ML-decoding complexity. For higher number of transmit antennas, the best known codes are the Perfect codes, which are full-rate, full-diversity, information lossless codes (for $n_r \geq n_t$) but have a high ML-decoding complexity of the order of $M^{n_tn_{min}}$ (for $n_r < n_t$, the punctured Perfect codes are considered). In this paper, a scheme to obtain full-rate STBCs for $2^a$ transmit antennas and any $n_r$ with reduced ML-decoding complexity of the order of $M^{n_t(n_{min}-(3/4))-0.5}$, is presented. The codes constructed are also information lossless for $n_r \geq n_t$, like the Perfect codes and allow higher mutual information than the comparable punctured Perfect codes for $n_r < n_t$. These codes are referred to as the {\it generalized Silver codes}, since they enjoy the same desirable properties as the comparable Perfect codes (except possibly the coding gain) with lower ML-decoding complexity, analogous to the Silver-Golden codes for 2 transmit antennas. Simulation results of the symbol error rates for 4 and 8 transmit antennas show that the generalized Silver codes match the punctured Perfect codes in error performance while offering lower ML-decoding complexity.Comment: Accepted for publication in the IEEE Transactions on Information Theory. This revised version has 30 pages, 7 figures and Section III has been completely revise

A Fast Decodable Full-Rate STBC with High Coding Gain for 4x2 MIMO Systems

In this work, a new fast-decodable space-time block code (STBC) is proposed. The code is full-rate and full-diversity for 4x2 multiple-input multiple-output (MIMO) transmission. Due to the unique structure of the codeword, the proposed code requires a much lower computational complexity to provide maximum-likelihood (ML) decoding performance. It is shown that the ML decoding complexity is only O(M^{4.5}) when M-ary square QAM constellation is used. Finally, the proposed code has highest minimum determinant among the fast-decodable STBCs known in the literature. Simulation results prove that the proposed code provides the best bit error rate (BER) performance among the state-of-the-art STBCs.Comment: 2013 IEEE 24th International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), London : United Kingdom (2013

Low ML-Decoding Complexity, Large Coding Gain, Full-Rate, Full-Diversity STBCs for 2 X 2 and 4 X 2 MIMO Systems

This paper (Part of the content of this manuscript has been accepted for presentation in IEEE Globecom 2008, to be held in New Orleans) deals with low maximum likelihood (ML) decoding complexity, full-rate and full-diversity space-time block codes (STBCs), which also offer large coding gain, for the 2 transmit antenna, 2 receive antenna ($2\times 2$) and the 4 transmit antenna, 2 receive antenna ($4\times 2$) MIMO systems. Presently, the best known STBC for the $2\times2$ system is the Golden code and that for the $4\times2$ system is the DjABBA code. Following the approach by Biglieri, Hong and Viterbo, a new STBC is presented in this paper for the $2\times 2$ system. This code matches the Golden code in performance and ML-decoding complexity for square QAM constellations while it has lower ML-decoding complexity with the same performance for non-rectangular QAM constellations. This code is also shown to be \emph{information-lossless} and \emph{diversity-multiplexing gain} (DMG) tradeoff optimal. This design procedure is then extended to the $4\times 2$ system and a code, which outperforms the DjABBA code for QAM constellations with lower ML-decoding complexity, is presented. So far, the Golden code has been reported to have an ML-decoding complexity of the order of $M^4$ for square QAM of size $M$. In this paper, a scheme that reduces its ML-decoding complexity to $M^2\sqrt{M}$ is presented.Comment: 28 pages, 5 figures, 3 tables, submitted to IEEE Journal of Selected Topics in Signal Processin

Optimization of Fast-Decodable Full-Rate STBC with Non-Vanishing Determinants

Full-rate STBC (space-time block codes) with non-vanishing determinants achieve the optimal diversity-multiplexing tradeoff but incur high decoding complexity. To permit fast decoding, Sezginer, Sari and Biglieri proposed an STBC structure with special QR decomposition characteristics. In this paper, we adopt a simplified form of this fast-decodable code structure and present a new way to optimize the code analytically. We show that the signal constellation topology (such as QAM, APSK, or PSK) has a critical impact on the existence of non-vanishing determinants of the full-rate STBC. In particular, we show for the first time that, in order for APSK-STBC to achieve non-vanishing determinant, an APSK constellation topology with constellation points lying on square grid and ring radius \sqrt{m^2+n^2} (m,n\emph{\emph{integers}}) needs to be used. For signal constellations with vanishing determinants, we present a methodology to analytically optimize the full-rate STBC at specific constellation dimension.Comment: Accepted by IEEE Transactions on Communication

A New Low-Complexity Decodable Rate-5/4 STBC for Four Transmit Antennas with Nonvanishing Determinants

The use of Space-Time Block Codes (STBCs) increases significantly the optimal detection complexity at the receiver unless the low-complexity decodability property is taken into consideration in the STBC design. In this paper we propose a new low-complexity decodable rate-5/4 full-diversity 4 x 4 STBC. We provide an analytical proof that the proposed code has the Non-Vanishing-Determinant (NVD) property, a property that can be exploited through the use of adaptive modulation which changes the transmission rate according to the wireless channel quality. We compare the proposed code to the best existing low-complexity decodable rate-5/4 full-diversity 4 x 4 STBC in terms of performance over quasi-static Rayleigh fading channels, worst- case complexity, average complexity, and Peak-to-Average Power Ratio (PAPR). Our code is found to provide better performance, lower average decoding complexity, and lower PAPR at the expense of a slight increase in worst-case decoding complexity.Comment: 5 pages, 2 figures and 1 table; IEEE Global Telecommunications Conference (GLOBECOM 2011), 201

A Low-Complexity, Full-Rate, Full-Diversity 2 X 2 STBC with Golden Code's Coding Gain

This paper presents a low-ML-decoding-complexity, full-rate, full-diversity space-time block code (STBC) for a 2 transmit antenna, 2 receive antenna multiple-input multiple-output (MIMO) system, with coding gain equal to that of the best and well known Golden code for any QAM constellation. Recently, two codes have been proposed (by Paredes, Gershman and Alkhansari and by Sezginer and Sari), which enjoy a lower decoding complexity relative to the Golden code, but have lesser coding gain. The $2\times 2$ STBC presented in this paper has lesser decoding complexity for non-square QAM constellations, compared with that of the Golden code, while having the same decoding complexity for square QAM constellations. Compared with the Paredes-Gershman-Alkhansari and Sezginer-Sari codes, the proposed code has the same decoding complexity for non-rectangular QAM constellations. Simulation results, which compare the codeword error rate (CER) performance, are presented.Comment: Submitted to IEEE Globecom - 2008. 6 pages, 3 figures, 1 tabl

A New Low-Complexity Decodable Rate-1 Full-Diversity 4 x 4 STBC with Nonvanishing Determinants

Space-time coding techniques have become common-place in wireless communication standards as they provide an effective way to mitigate the fading phenomena inherent in wireless channels. However, the use of Space-Time Block Codes (STBCs) increases significantly the optimal detection complexity at the receiver unless the low complexity decodability property is taken into consideration in the STBC design. In this letter we propose a new low-complexity decodable rate-1 full-diversity 4 x 4 STBC. We provide an analytical proof that the proposed code has the Non-Vanishing-Determinant (NVD) property, a property that can be exploited through the use of adaptive modulation which changes the transmission rate according to the wireless channel quality. We compare the proposed code to existing low-complexity decodable rate-1 full-diversity 4 x 4 STBCs in terms of performance over quasi-static Rayleigh fading channels, detection complexity and Peak-to-Average Power Ratio (PAPR). Our code is found to provide the best performance and the smallest PAPR which is that of the used QAM constellation at the expense of a slight increase in detection complexity w.r.t. certain previous codes but this will only penalize the proposed code for high-order QAM constellations.Comment: 5 pages, 3 figures, and 1 table; IEEE Transactions on Wireless Communications, Vol. 10, No. 8, AUGUST 201