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

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

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

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

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 Novel Construction of Multi-group Decodable Space-Time Block Codes

Complex Orthogonal Design (COD) codes are known to have the lowest detection complexity among Space-Time Block Codes (STBCs). However, the rate of square COD codes decreases exponentially with the number of transmit antennas. The Quasi-Orthogonal Design (QOD) codes emerged to provide a compromise between rate and complexity as they offer higher rates compared to COD codes at the expense of an increase of decoding complexity through partially relaxing the orthogonality conditions. The QOD codes were then generalized with the so called g-symbol and g-group decodable STBCs where the number of orthogonal groups of symbols is no longer restricted to two as in the QOD case. However, the adopted approach for the construction of such codes is based on sufficient but not necessary conditions which may limit the achievable rates for any number of orthogonal groups. In this paper, we limit ourselves to the case of Unitary Weight (UW)-g-group decodable STBCs for 2^a transmit antennas where the weight matrices are required to be single thread matrices with non-zero entries in {1,-1,j,-j} and address the problem of finding the highest achievable rate for any number of orthogonal groups. This special type of weight matrices guarantees full symbol-wise diversity and subsumes a wide range of existing codes in the literature. We show that in this case an exhaustive search can be applied to find the maximum achievable rates for UW-g-group decodable STBCs with g>1. For this purpose, we extend our previously proposed approach for constructing UW-2-group decodable STBCs based on necessary and sufficient conditions to the case of UW-g-group decodable STBCs in a recursive manner.Comment: 12 pages, and 5 tables, accepted for publication in IEEE transactions on communication

An Adaptive Conditional Zero-Forcing Decoder with Full-diversity, Least Complexity and Essentially-ML Performance for STBCs

A low complexity, essentially-ML decoding technique for the Golden code and the 3 antenna Perfect code was introduced by Sirianunpiboon, Howard and Calderbank. Though no theoretical analysis of the decoder was given, the simulations showed that this decoding technique has almost maximum-likelihood (ML) performance. Inspired by this technique, in this paper we introduce two new low complexity decoders for Space-Time Block Codes (STBCs) - the Adaptive Conditional Zero-Forcing (ACZF) decoder and the ACZF decoder with successive interference cancellation (ACZF-SIC), which include as a special case the decoding technique of Sirianunpiboon et al. We show that both ACZF and ACZF-SIC decoders are capable of achieving full-diversity, and we give sufficient conditions for an STBC to give full-diversity with these decoders. We then show that the Golden code, the 3 and 4 antenna Perfect codes, the 3 antenna Threaded Algebraic Space-Time code and the 4 antenna rate 2 code of Srinath and Rajan are all full-diversity ACZF/ACZF-SIC decodable with complexity strictly less than that of their ML decoders. Simulations show that the proposed decoding method performs identical to ML decoding for all these five codes. These STBCs along with the proposed decoding algorithm outperform all known codes in terms of decoding complexity and error performance for 2,3 and 4 transmit antennas. We further provide a lower bound on the complexity of full-diversity ACZF/ACZF-SIC decoding. All the five codes listed above achieve this lower bound and hence are optimal in terms of minimizing the ACZF/ACZF-SIC decoding complexity. Both ACZF and ACZF-SIC decoders are amenable to sphere decoding implementation.Comment: 11 pages, 4 figures. Corrected a minor typographical erro

Asymptotically-Optimal, Fast-Decodable, Full-Diversity STBCs

For a family/sequence of STBCs $\mathcal{C}_1,\mathcal{C}_2,\dots$, with increasing number of transmit antennas $N_i$, with rates $R_i$ complex symbols per channel use (cspcu), the asymptotic normalized rate is defined as $\lim_{i \to \infty}{\frac{R_i}{N_i}}$. A family of STBCs is said to be asymptotically-good if the asymptotic normalized rate is non-zero, i.e., when the rate scales as a non-zero fraction of the number of transmit antennas, and the family of STBCs is said to be asymptotically-optimal if the asymptotic normalized rate is 1, which is the maximum possible value. In this paper, we construct a new class of full-diversity STBCs that have the least ML decoding complexity among all known codes for any number of transmit antennas $N>1$ and rates $R>1$ cspcu. For a large set of $\left(R,N\right)$ pairs, the new codes have lower ML decoding complexity than the codes already available in the literature. Among the new codes, the class of full-rate codes ($R=N$) are asymptotically-optimal and fast-decodable, and for $N>5$ have lower ML decoding complexity than all other families of asymptotically-optimal, fast-decodable, full-diversity STBCs available in the literature. The construction of the new STBCs is facilitated by the following further contributions of this paper:(i) For $g > 1$, we construct $g$-group ML-decodable codes with rates greater than one cspcu. These codes are asymptotically-good too. For $g>2$, these are the first instances of $g$-group ML-decodable codes with rates greater than $1$ cspcu presented in the literature. (ii) We construct a new class of fast-group-decodable codes for all even number of transmit antennas and rates $1 < R \leq 5/4$.(iii) Given a design with full-rank linear dispersion matrices, we show that a full-diversity STBC can be constructed from this design by encoding the real symbols independently using only regular PAM constellations.Comment: 16 pages, 3 tables. The title has been changed.The class of asymptotically-good multigroup ML decodable codes has been extended to a broader class of number of antennas. New fast-group-decodable codes and asymptotically-optimal, fast-decodable codes have been include