An Enhanced DMT-optimality Criterion for STBC-schemes for Asymmetric MIMO Systems
K. Pavan Srinath, B. Sundar Rajan
备注：
To appear in the IEEE Transactions on Information Theory. The present version is a significantly revised version of arXiv:1201.1997v2. Manuscript length is 14 Pages, contains 1 Table and 4 figures
For any $n_t$ transmit, $n_r$ receive antenna ($n_t\times n_r$) MIMO system in a quasi-static Rayleigh fading environment, it was shown by Elia et al. that linear space-time block code-schemes (LSTBC-schemes) which have the non-vanishing determinant (NVD) property are diversity-multiplexing gain tradeoff (DMT)-optimal for arbitrary values of $n_r$ if they have a code-rate of $n_t$ complex dimensions per channel use. However, for asymmetric MIMO systems (where $n_r < n_t$), with the exception of a few LSTBC-schemes, it is unknown whether general LSTBC-schemes with NVD and a code-rate of $n_r$ complex dimensions per channel use are DMT-optimal. In this paper, an enhanced sufficient criterion for any STBC-scheme to be DMT-optimal is obtained, and using this criterion, it is established that any LSTBC-scheme with NVD and a code-rate of $\min\{n_t,n_r\}$ complex dimensions per channel use is DMT-optimal. This result settles the DMT-optimality of several well-known, low-ML-decoding-complexity LSTBC-schemes for certain asymmetric MIMO systems.
In this paper, a new method is proposed to obtain full-diversity, rate-2 (rate of 2 complex symbols per channel use) space-time block codes (STBCs) that are full-rate for multiple input, double output (MIDO) systems. Using this method, rate-2 STBCs for $4\times2$, $6 \times 2$, $8\times2$ and $12 \times 2$ systems are constructed and these STBCs are fast ML-decodable, have large coding gains, and STBC-schemes consisting of these STBCs have a non-vanishing determinant (NVD) so that they are DMT-optimal for their respective MIDO systems. It is also shown that the SR-code [R. Vehkalahti, C. Holla…
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 th…
This paper proposes a low decoding complexity, full-diversity and full-rate space-time block code (STBC) for 4 transmit and 2 receive ($4\times 2$) multiple-input multiple-output (MIMO) systems. For such systems, the best code known is the DjABBA code and recently, Biglieri, Hong and Viterbo have proposed another STBC (BHV code) which has lower decoding complexity than DjABBA but does not have full-diversity like the DjABBA code. The code proposed in this paper has the same decoding complexity as the BHV code for square QAM constellations but has full-diversity as well. Compared to the best co…
In this paper, Space-Time Block Codes (STBCs) with reduced Sphere Decoding Complexity (SDC) are constructed for two-user Multiple-Input Multiple-Output (MIMO) fading multiple access channels. In this set-up, both the users employ identical STBCs and the destination performs sphere decoding for the symbols of the two users. First, we identify the positions of the zeros in the $\textbf{R}$ matrix arising out of the Q-R decomposition of the lattice generator such that (i) the worst case SDC (WSDC) and (ii) the average SDC (ASDC) are reduced. Then, a set of necessary and sufficient conditions on t…
Full-rate (FR) and full-diversity (FD) are attractive features in MIMO systems. We refer to systems which achieve both FR and FD simultaneously as FRFD systems. Non-orthogonal STBCs can achieve FRFD without feedback, but their ML decoding complexities are high. V-BLAST without precoding achieves FR but not FD. FRFD can be achieved in V-BLAST through precoding given full channel state information at the transmitter (CSIT). However, with limited feedback precoding, V-BLAST achieves FD, but with some rate loss. Our contribution in this paper is two-fold: $i)$ we propose a limited feedback (LFB) p…
In this paper we investigate the criteria proposed by Coronel et al. for constructing MIMO MAC-DMT optimal codes over several classes of fading channels. We first give a counterexample showing their DMT result is not correct when the channel is frequency-selective. For the case of symmetric MIMO-MAC flat fading channels, their DMT result reduces to exactly the same as that derived by Tse et al., and we therefore focus on their criteria for constructing MAC-DMT optimal codes, especially when the number of receive antennas is sufficiently large. In such case, we show their criterion is equivalen…
Full-rate space-time block codes (STBCs) achieve high spectral-efficiency by transmitting linear combinations of information symbols through every transmit antenna. However, the coefficients used for the linear combinations, if not chosen carefully, results in ({\em i}) large number of processor bits for the encoder and ({\em ii}) high peak-to-average power ratio (PAPR) values. In this work, we propose a new class of full-rate STBCs called Integer STBCs (ICs) for multiple-input multiple-output (MIMO) fading channels. A unique property of ICs is the presence of integer coefficients in the code …
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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 a…
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In the landmark paper by Hassibi and Hochwald, it is claimed without proof that the upper triangular matrix R encountered during the sphere decoding of any linear dispersion code is full-ranked whenever the rate of the code is less than the minimum of the number of transmit and receive antennas. In this paper, we show that this claim is true only when the number of receive antennas is at least as much as the number of transmit antennas. We also show that all known families of high rate (rate greater than 1 complex symbol per channel use) multigroup ML decodable codes have rank-deficient R matr…
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In multiple-input multiple-output (MIMO) fading channels, the design criterion for full-diversity space-time block codes (STBCs) is primarily determined by the decoding method at the receiver. Although constructions of STBCs have predominantly matched the maximum-likelihood (ML) decoder, design criteria and constructions of full-diversity STBCs have also been reported for low-complexity linear receivers. A new receiver architecture called Integer-Forcing (IF) linear receiver has been proposed to MIMO channels by Zhan et al. which showed promising results for the high-rate V-BLAST encoding sche…
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A novel distributed space-time block code (STBC) for the next generation mobile TV broadcasting is proposed. The new code provides efficient performance within a wide range of power imbalance showing strong adaptivity to the single frequency network (SFN) broadcasting deployments. The new code outperforms existing STBCs with equivalent decoding complexity and approaches those with much higher complexities.
In multiple-input multiple-output (MIMO) fading channels, the design criterion for full-diversity space-time block codes (STBCs) is primarily determined by the decoding method at the receiver. Although constructions of STBCs have predominantly matched the maximum-likelihood (ML) decoder, design criteria and constructions of full-diversity STBCs have also been reported for low-complexity linear receivers. A new receiver architecture called Integer-Forcing (IF) linear receiver has been proposed to MIMO channels by Zhan et al. which showed promising results for the high-rate V-BLAST encoding sche…
This paper presents a novel unified performance analysis of Space-Time Block Codes (STBCs) operating in the Multiple Input Multiple Output (MIMO) network and subjected to generalized shadowed fading and noise scenarios. Specifically, we derive novel, simple and accurate average bit error rates (ABER) expressions for coherent modulation schemes in the generalized η-μ and shadowed κ-μ fading channels. The noise in the network is assumed to be modeled by the additive white generalized Gaussian noise (AWGGN), which encompasses the Laplacian and the Gaussian noise environments as special cases. The…
In this paper, we consider an intensity modulated direct detection MIMO optical wireless communication (OWC) system. For such a system, a novel super-rectangular cover theory is developed to characterize both the unique identifiability and full reliability. This theory states that a transmitted matrix signal can be uniquely identified if and only if the cover order is equal to the transmitter aperture number, i.e., full cover. In addition, we prove that full reliability is guaranteed for space-time block coded MIMO-OWC over commonly used log-normal fading channels with an ML detector if and on…
Multicasting $K$ independent messages via multiple-input multiple-output (MIMO) channels to multiple users where each user already has a subset of messages as side information is studied. A general framework of constructing layered space-time index coding (LSTIC) from a large class of space-time block codes (STBC), including perfect STBC, is proposed. We analyze the proposed LSTIC and show that it provides minimum determinant gains that are exponential with the amount of information contained in the side information for any possible side information. When constructed over a perfect STBC, the p…
We focus on full-rate, fast-decodable space-time block codes (STBCs) for 2x2 and 4x2 multiple-input multiple-output (MIMO) transmission. We first derive conditions for reduced-complexity maximum-likelihood decoding, and apply them to a unified analysis of two families of 2x2 STBCs that were recently proposed. In particular, we describe a reduced-complexity sphere decoding algorithm suitable for QAM signal constellations. Next, we derive a novel reduced-complexity 4x2 STBC, and show that it outperforms all previously known codes with certain constellations.
In this two-part paper, we consider the multiantenna multihop relay channels in which the source signal arrives at the destination through N independent relaying hops in series. The main concern of this work is to design relaying strategies that utilize efficiently the relays in such a way that the diversity is maximized. In part I, we focus on the amplify-and-forward (AF) strategy with which the relays simply scale the received signal and retransmit it. More specifically, we characterize the diversity-multiplexing tradeoff (DMT) of the AF scheme in a general multihop channel with arbitrary nu…
This paper introduces a new and unified bit error rates performance analysis of space-time block codes (STBC) deployed in wireless systems with spatial diversity in generalized shadowed fading and noise scenarios. Specifically, we derive a simple and a very accurate approximate expressions for the average error rates of coherent modulation schemes in generalized $η-μ$ and $κ-μ$ shadowed fading channels with multiple input multiple output (MIMO) systems. The noise in the network is assumed to be modeled using the additive white generalized Gaussian noise (AWGGN), which encompasses the classical…
In this paper the performance limits and design principles of rateless codes over fading channels are studied. The diversity-multiplexing tradeoff (DMT) is used to analyze the system performance for all possible transmission rates. It is revealed from the analysis that the design of such rateless codes follows the design principle of approximately universal codes for parallel multiple-input multiple-output (MIMO) channels, in which each sub-channel is a MIMO channel. More specifically, it is shown that for a single-input single-output (SISO) channel, the previously developed permutation codes …
Currently for the nt x nr MIMO channel, any explicitly constructed space-time (ST) designs that achieve optimality with respect to the diversity multiplexing tradeoff (DMT) are known to do so only when decoded using maximum likelihood (ML) decoding, which may incur prohibitive decoding complexity. In this paper we prove that MMSE regularized lattice decoding, as well as the computationally efficient lattice reduction (LR) aided MMSE decoder, allows for efficient and DMT optimal decoding of any approximately universal lattice-based code. The result identifies for the first time an explicitly co…
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 constellatio…
Fading MIMO relay channels are studied analytically, when the source and destination are equipped with multiple antennas and the relays have a single one. Compact closed-form expressions are obtained for the outage probability under i.i.d. and correlated Rayleigh-fading links. Low-outage approximations are derived, which reveal a number of insights, including the impact of correlation, of the number of antennas, of relay noise and of relaying protocol. The effect of correlation is shown to be negligible, unless the channel becomes almost fully correlated. The SNR loss of relay fading channels …
Multiple Input Multiple Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) is a promising transmission scheme for high performance broadband wireless communications. However, this technique suffers from a major drawback which is the high Peak to Average Power Ratio (PAPR) of the output signals. In order to overcome this issue, several methods that require the transmission of explicit Side Information (SI) bits have been proposed. In fact, the transmitted bits must be channel-encoded as they are particularly critical to the performance of the considered OFDM system. This channel-en…
High-rate space-time block codes (STBC with code rate > 1) in multi-input multi-output (MIMO) systems are able to provide both spatial multiplexing gain and diversity gain, but have high maximum likelihood (ML) decoding complexity. Since group-decodable (quasi-orthogonal) code structure can reduce the decoding complexity, we present in this paper systematic methods to construct group-decodable high-rate STBC with full symbol-wise diversity gain for arbitrary transmit antenna number and code length. We show that the proposed group-decodable STBC can achieve high code rate that increases almost …
A partial interference cancellation (PIC) group decoding based space-time block code (STBC) design criterion was recently proposed by Guo and Xia, where the decoding complexity and the code rate trade-off is dealt when the full diversity is achieved. In this paper, two designs of STBC are proposed for any number of transmit antennas that can obtain full diversity when a PIC group decoding (with a particular grouping scheme) is applied at receiver. With the PIC group decoding and an appropriate grouping scheme for the decoding, the proposed STBC are shown to obtain the same diversity gain as th…
In this short note we will prove that non-vanishing determinant (NVD) criterion is not enough for an asymmetric space-time block code (STBC) to achieve the optimal diversity-multiplexing gain trade-off (DMT). This result is in contrast to the recent result made by Srinath and Rajan. In order to clarify the issue further the approximately universality criterion by Tavildar and Viswanath is translated into language of lattice theory and some conjectures are given.
Partial interference cancellation (PIC) group decoding proposed by Guo and Xia is an attractive low-complexity alternative to the optimal processing for multiple-input multiple-output (MIMO) wireless communications. It can well deal with the tradeoff among rate, diversity and complexity of space-time block codes (STBC). In this paper, a systematic design of full-diversity STBC with low-complexity PIC group decoding is proposed. The proposed code design is featured as a group-orthogonal STBC by replacing every element of an Alamouti code matrix with an elementary matrix composed of multiple dia…
Recently, Guo and Xia introduced low complexity decoders called Partial Interference Cancellation (PIC) and PIC with Successive Interference Cancellation (PIC-SIC), which include the Zero Forcing (ZF) and ZF-SIC receivers as special cases, for point-to-point MIMO channels. In this paper, we show that PIC and PIC-SIC decoders are capable of achieving the full cooperative diversity available in wireless relay networks. We give sufficient conditions for a Distributed Space-Time Block Code (DSTBC) to achieve full diversity with PIC and PIC-SIC decoders and construct a new class of DSTBCs with low …
We consider the sequential transmission of a stream of messages over a block-fading multi-input-multi-output (MIMO) channel. A new message arrives at the beginning of each coherence block, and the decoder is required to output each message sequentially, after a delay of $T$ coherence blocks. In the special case when $T=1$, the setup reduces to the quasi-static fading channel. We establish the optimal diversity-multiplexing tradeoff (DMT) in the high signal-to-noise-ratio (SNR) regime, and show that it equals $T$ times the DMT of the quasi-static channel. The converse is based on utilizing the …
We consider slow fading relay channels with a single multi-antenna source-destination terminal pair. The source signal arrives at the destination via N hops through N-1 layers of relays. We analyze the diversity of such channels with fixed network size at high SNR. In the clustered case where the relays within the same layer can have full cooperation, the cooperative decode-and-forward (DF) scheme is shown to be optimal in terms of the diversity-multiplexing tradeoff (DMT). The upper bound on the DMT, the cut-set bound, is attained. In the non-clustered case, we show that the naive amplify-and…
In this article, the first general constructions of fast-decodable, more specifically (conditionally) $g$-group decodable, space-time block codes for the Nonorthogonal Amplify and Forward (NAF) Multiple-Input Multiple-Output (MIMO) relay channel under the half-duplex constraint are proposed. In this scenario, the source and the intermediate relays used for data amplification are allowed to employ multiple antennas for data transmission and reception. The worst-case decoding complexity of the obtained codes is reduced by up to $75%$. In addition to being fast-decodable, the proposed codes achie…
We consider large MIMO systems, where by `{\em large}' we mean number of transmit and receive antennas of the order of tens to hundreds. Such large MIMO systems will be of immense interest because of the very high spectral efficiencies possible in such systems. We present a low-complexity detector which achieves uncoded near-exponential diversity performance for hundreds of antennas (i.e., achieves near SISO AWGN performance in a large MIMO fading environment) with an average per-bit complexity of just $O(N_tN_r)$, where $N_t$ and $N_r$ denote the number of transmit and receive antennas, respe…
Constellation Constrained (CC) capacity regions of a two-user SISO Gaussian Multiple Access Channel (GMAC) with finite complex input alphabets and continuous output are computed in this paper. When both the users employ the same code alphabet, it is well known that an appropriate rotation between the alphabets provides unique decodability to the receiver. For such a set-up, a metric is proposed to compute the angle(s) of rotation between the alphabets such that the CC capacity region is maximally enlarged. Subsequently, code pairs based on Trellis Coded Modulation (TCM) are designed for the tw…
In this paper a MIMO quasi static block fading channel with finite N-ary delay-free, noise-free feedback is considered. The transmitter uses a set of N Space-Time Block Codes (STBCs), one corresponding to each of the N possible feedback values, to encode and transmit information. The feedback function used at the receiver and the N component STBCs used at the transmitter together constitute a Finite Feedback Scheme (FFS). Although a number of FFSs are available in the literature that provably achieve full-diversity, there is no known universal criterion to determine whether a given arbitrary F…
