Universal space-time coding

A universal framework is developed for constructing full-rate and full-diversity coherent space-time codes for systems with arbitrary numbers of transmit and receive antennas. The proposed framework combines space-time layering concepts with algebraic component codes optimized for single-input-single-output (SISO) channels. Each component code is assigned to a "thread" in the space-time matrix, allowing it thus full access to the channel spatial diversity in the absence of the other threads. Diophantine approximation theory is then used in order to make the different threads "transparent" to each other. Within this framework, a special class of signals which uses algebraic number-theoretic constellations as component codes is thoroughly investigated. The lattice structure of the proposed number-theoretic codes along with their minimal delay allow for polynomial complexity maximum-likelihood (ML) decoding using algorithms from lattice theory. Combining the design framework with the Cayley transform allows to construct full diversity differential and noncoherent space-time codes. The proposed framework subsumes many of the existing codes in the literature, extends naturally to time-selective and frequency-selective channels, and allows for more flexibility in the tradeoff between power efficiency, bandwidth efficiency, and receiver complexity. Simulation results that demonstrate the significant gains offered by the proposed codes are presented in certain representative scenarios.     

A unified construction of space-time codes with optimal rate-diversity tradeoff

The problem of constructing space-time (ST) block codes over a fixed, desired signal constellation is considered. In this situation, there is a tradeoff between the transmission rate as measured in constellation symbols per channel use and the transmit diversity gain achieved by the code. The transmit diversity is a measure of the rate of polynomial decay of pairwise error probability of the code with increase in the signal-to-noise ratio (SNR). In the setting of a quasi-static channel model, let n/sub t/ denote the number of transmit antennas and T the block interval. For any n/sub t/ /spl les/ T, a unified construction of (n/sub t/ /spl times/ T) ST codes is provided here, for a class of signal constellations that includes the familiar pulse-amplitude (PAM), quadrature-amplitude (QAM), and 2/sup K/-ary phase-shift-keying (PSK) modulations as special cases. The construction is optimal as measured by the rate-diversity tradeoff and can achieve any given integer point on the rate-diversity tradeoff curve. An estimate of the coding gain realized is given. Other results presented here include i) an extension of the optimal unified construction to the multiple fading block case, ii) a version of the optimal unified construction in which the underlying binary block codes are replaced by trellis codes, iii) the providing of a linear dispersion form for the underlying binary block codes, iv) a Gray-mapped version of the unified construction, and v) a generalization of construction of the -ary case corresponding to constellations of size /sup K/. Items ii) and iii) are aimed at simplifying the decoding of this class of ST codes.     

Khatri-Rao space-time codes

Space-time (ST) coding techniques exploit the spatial diversity afforded by multiple transmit and receive antennas to achieve reliable transmission in scattering-rich environments. ST block codes are capable of realizing full diversity and spatial coding gains at relatively low rates; ST trellis codes can achieve better rate-diversity tradeoffs at the cost of high complexity. On the other hand, V-BLAST supports high rates but has no built-in spatial coding and does not work well with fewer receive than transmit antennas. We propose a novel linear block coding scheme based on the Khatri-Rao matrix product. The proposed scheme offers flexibility for achieving full-rate or full-diversity, or a desired rate-diversity tradeoff, and it can handle any transmit/receive antenna configuration or signal constellation. The proposed codes are shown to have numerous desirable properties, including guaranteed unique linear decodability, built-in blind channel identifiability, and efficient near-maximum likelihood decoding.     

Distributed Space-Time Codes Using Constellation Rotation

Rate and diversity impose a fundamental tradeoff in wireless communication. We propose a novel distributed space-time coding (DSTC) scheme based on constellation rotation (DSTC-CR) for Amplify-and-Forward relay networks. The proposed code can achieve full-diversity or full-rate, and also offers a flexibility for a desired rate-diversity tradeoff. This code can work well with arbitrary signal constellation and any number of relays and achieve minimal-delay. Through analysis of pairwise error probability, coding design criteria, Chernoff bound, decoding strategies and optimal power allocation are provided. Simulation results show that DSTC-CR scheme outperforms diagonal DSTC (DDSTC) and distributed linear dispersion (DLD) code at high power. From the comparison with DDSTC, the DSTC-CR scheme can achieve the same information rate using a lower modulation order.     

Explicit Space–Time Codes Achieving the Diversity–Multiplexing Gain Tradeoff

A recent result of Zheng and Tse states that over a quasi-static channel, there exists a fundamental tradeoff, referred to as the diversity-multiplexing gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space-time (ST) code. This tradeoff is precisely known in the case of independent and identically distributed (i.i.d.) Rayleigh fading, for Tgesn_t+n_r-1 where T is the number of time slots over which coding takes place and n_t,n_r are the number of transmit and receive antennas, respectively. For Tt+n_r-1, only upper and lower bounds on the D-MG tradeoff are available. In this paper, we present a complete solution to the problem of explicitly constructing D-MG optimal ST codes, i.e., codes that achieve the D-MG tradeoff for any number of receive antennas. We do this by showing that for the square minimum-delay case when T=n_t=n, cyclic-division-algebra (CDA)-based ST codes having the nonvanishing determinant property are D-MG optimal. While constructions of such codes were previously known for restricted values of n, we provide here a construction for such codes that is valid for all n. For the rectangular, T>n_t case, we present two general techniques for building D-MG-optimal rectangular ST codes from their square counterparts. A byproduct of our results establishes that the D-MG tradeoff for all Tgesn_t is the same as that previously known to hold for Tgesn_t+n _r-1     

Diversity-multiplexing tradeoff in multiple-access channels

In a point-to-point wireless fading channel, multiple transmit and receive antennas can be used to improve the reliability of reception (diversity gain) or increase the rate of communication for a fixed reliability level (multiplexing gain). In a multiple-access situation, multiple receive antennas can also be used to spatially separate signals from different users (multiple-access gain). Recent work has characterized the fundamental tradeoff between diversity and multiplexing gains in the point-to-point scenario. In this paper, we extend the results to a multiple-access fading channel. Our results characterize the fundamental tradeoff between the three types of gain and provide insights on the capabilities of multiple antennas in a network context.     

On Space–Time Trellis Codes Achieving Optimal Diversity Multiplexing Tradeoff

Multiple antennas can be used for increasing the amount of diversity (diversity gain) or increasing the data rate (the number of degrees of freedom or spatial multiplexing gain) in wireless communication. As quantified by Zheng and Tse, given a multiple-input-multiple-output (MIMO) channel, both gains can, in fact, be simultaneously obtained, but there is a fundamental tradeoff (called the Diversity-Multiplexing Gain (DM-G) tradeoff) between how much of each type of gain, any coding scheme can extract. Space-time codes (STCs) can be employed to make use of these advantages offered by multiple antennas. Space-Time Trellis Codes (STTCs) are known to have better bit error rate performance than Space-Time Block Codes (STBCs), but with a penalty in decoding complexity. Also, for STTCs, the frame length is assumed to be finite and hence zeros are forced towards the end of the frame (called the trailing zeros), inducing rate loss. In this correspondence, we derive an upper bound on the DM-G tradeoff of full-rate STTCs with nonvanishing determinant (NVD). Also, we show that the full-rate STTCs with NVD are optimal under the DM-G tradeoff for any number of transmit and receive antennas, neglecting the rate loss due to trailing zeros. Next, we give an explicit generalized full-rate STTC construction for any number of states of the trellis, which achieves the optimal DM-G tradeoff for any number of transmit and receive antennas, neglecting the rate loss due to trailing zeros     

On Space–Time Coding With Pulse Position and Amplitude Modulations for Time-Hopping Ultra-Wideband Systems

In this work, we propose novel families of space-time (ST) block codes that can be associated with impulse radio ultra-wideband (IR-UWB) communication systems. The carrier-less nature of this nonconventional totally real transmission technique necessitates the construction of new suitable coding schemes. In fact, the last generation of complex-valued ST codes (namely, the perfect codes) cannot be associated with IR-UWB systems where the phase reconstitution at the receiver side is practically infeasible. On the other hand, while the perfect codes were considered mainly with quadrature amplitude modulation (QAM) and hexagonal (HEX) constellations, IR-UWB systems are often associated with pulse-position modulation (PPM) and hybrid PPM-PAM (pulse-amplitude modulation) constellations. In this paper, instead of adopting the classical approach of constructing ST codes over infinite fields or for the perfect codes), we study the possibility of constructing modulation-specific codes that are exclusive to PPM and PPM-PAM. The proposed full-rate codes are totally real, information lossless, and have a uniform average energy per transmit antenna. They permit to achieve a full diversity order with any number of transmit antennas. In some situations, the proposed schemes have an optimal nonvanishing coding gain and satisfy all the construction constraints of the perfect codes in addition to the constraint of being totally real. Simulations performed over realistic indoor UWB channels showed that the proposed schemes outperform the best known codes constructed from cyclic division algebras.     

QoS-Driven Jointly Optimal Subcarrier Pairing and Power Allocation for Decode-and-Forward OFDM Relay Systems

In this paper, we investigate the quality-of-service (QoS) driven subcarrier pairing and power allocation for two-hop decode-and-forward (DF) OFDM relay systems. By integrating the concept of effective capacity, our goal is to maximize the system throughput subject to a given delay-QoS constraint. Based on whether the destination can receive the signal transmitted by the source, we consider two scenarios, i.e. OFDM DF relay systems without diversity and OFDM DF relay systems with diversity, respectively. For OFDM DF relay systems without diversity, we demonstrate that the jointly optimal subcarrier pairing and power allocation can be implemented with two separate steps. For OFDM DF relay systems with diversity, we propose an iterative algorithm to achieve jointly optimal subcarrier pairing and power allocation. Furthermore, we find that the analytical results show different conclusions for the two types of OFDM relay systems. For OFDM relay systems without diversity, the optimal power allocation depend on not only the channel quality of subcarriers but also the delay QoS constraints, while the optimal subcarrier pairing just depends on the channel quality of subcarriers. For OFDM relay systems with diversity, both the optimal subcarrier pairing and power allocation depend on the channel quality of subcarriers and the delay QoS constraints. Simulation results show that our proposed scheme offers a superior performance over the existing schemes.     

Co-ordinate Interleaved Spatial Multiplexing with Channel State Information

Performance of spatial multiplexing multiple-input multiple-output (MIMO) wireless systems can be improved with channel state information (CSI) at both ends of the link. This paper proposes a new linear diagonal MIMO transceiver, referred to as co-ordinate interleaved spatial multiplexing (CISM). With CSI at transmitter and receiver, CISM diagonalizes the MIMO channel and interleaves the co-ordinates of the input symbols (from rotated QAM constellations) transmitted over different eigenmodes. The analytical and simulation results show that with co-ordinate interleaving across two eigenmodes, the diversity gain of the data stream transmitted over the weaker eigenmode becomes equal to that of the data transmitted on the stronger eigenmode, resulting in a significant improvement in the overall diversity. The diversity-multiplexing tradeoff (DMT) is analyzed for CISM and is shown that it achieves higher diversity gain at all positive multiplexing gains compared to existing diagonal transceivers. Over rank n MIMO channels, with input symbols from rotated n-dimensional constellations, the DMT of CISM is a straight line connecting the endpoints (0,N_tN_r) and (min{N_t,N_r}, 0), where N_t, and N_r} are the number of transmit and receive antennas, respectively.     

Reduced-Complexity Receiver Structures for Space–Time Bit-Interleaved Coded Modulation Systems

Transmission efficiency in radio channels can be considerably improved by using multiple transmit and receive antennas and employing a family of schemes called space-time (ST) coding. Both extended range and/or improved bandwidth efficiency can be achieved, compared with a radio link with a single transmit and receive antenna. Bit-interleaved coded modulation schemes give diversity gains on fading channels with higher order modulation constellations combined with conventional binary convolutional codes also for the case of a single transmit and receive antenna radio link. In this paper, we study a family of flexible bandwidth-efficient ST coding schemes which combine these two ideas in a narrowband flat-fading channel and single-carrier modems. We address receiver complexity for the case of a large number of transmit antennas and higher order modulation constellations. Especially, we focus on practical configurations, where the number of transmit antennas is greater than that of receive antennas. Simplified receivers using tentative decisions are proposed and evaluated by means of simulations. Tradeoffs between complexity reduction and performance loss are presented. We emphasize systems that are of particular interest in applications where the number of transmit antennas exceeds the number of receive antennas. A system with four transmit antennas with an eight-fold complexity reduction and a performance loss of about 1 dB is demonstrated     

On the robustness of space-time coding

Space-time (ST) coding has emerged as one of the most promising technologies for meeting the challenges imposed by the wireless channel. This technology is primarily concerned with two-dimensional (2-D) signal design for multitransmit antenna wireless systems. Despite the progress in ST coding, several important questions remain unanswered. In a practical multiuser setting, one would expect different users to experience different channel conditions. This motivates the design of robust ST codes that exhibit satisfactory performance in various environments. In this paper, we investigate the robustness of ST codes in line-of-sight and correlated Rayleigh fading channels. We develop the design criteria that govern the performance of ST codes in these environments. Our analysis demonstrates that full-diversity ST codes are essential to achieving satisfactory performance in line-of-sight channels. We further show that a simple phase randomization approach achieves significant performance gains in the line-of-sight case without affecting the performance in Rayleigh fading channels. In the correlated fading environments, we characterize the achievable diversity order based on the number of diversity degrees of freedom in the channel. This characterization supports experimental observations that suggest that the quasistatic model is not a worst-case scenario and establishes the necessary tradeoff between the transmission rate and performance robustness. Finally, we consider the design of ST codes using some prior knowledge about the channel spatio-temporal correlation function.     

Finite-SNR Diversity–Multiplexing Tradeoff for Correlated Rayleigh and Rician MIMO Channels

A nonasymptotic framework is presented to analyze the diversity-multiplexing tradeoff of a multiple-input-multiple-output (MIMO) wireless system at finite signal-to-noise ratios (SNRs). The target data rate at each SNR is proportional to the capacity of an additive white Gaussian noise (AWGN) channel with an array gain. The proportionality constant, which can be interpreted as a finite-SNR spatial multiplexing gain, dictates the sensitivity of the rate adaptation policy to SNR. The diversity gain as a function of SNR for a fixed multiplexing gain is defined by the negative slope of the outage probability versus SNR curve on a log-log scale. The finite-SNR diversity gain provides an estimate of the additional power required to decrease the outage probability by a target amount. For general MIMO systems, lower bounds on the outage probabilities in correlated Rayleigh fading and Rician fading are used to estimate the diversity gain as a function of multiplexing gain and SNR. In addition, exact diversity gain expressions are determined for orthogonal space-time block codes (OSTBC). Spatial correlation significantly lowers the achievable diversity gain at finite SNR when compared to high-SNR asymptotic values. The presence of line-of-sight (LOS) components in Rician fading yields diversity gains higher than high-SNR asymptotic values at some SNRs and multiplexing gains while resulting in diversity gains near zero for multiplexing gains larger than unity. Furthermore, as the multiplexing gain approaches zero, the normalized limiting diversity gain, which can be interpreted in terms of the wideband slope and the high-SNR slope of spectral efficiency, exhibits slow convergence with SNR to the high-SNR asymptotic value. This finite-SNR framework for the diversity-multiplexing tradeoff is useful in MIMO system design for realistic SNRs and propagation environments     

A comparison of frequency-division systems to code-division systems in overloaded channels

In this paper, a frequency-division counterpart of joint power control and sequence design problem for code- division multiple-access (CDMA) systems is solved. Total transmit and receive power minimizations are considered for frequency- division multiplexing (FDM) and frequency-division multiple- access (FDMA) communications over overloaded channels. After the definition of channel overloading for CDMA systems is extended to the frequency-division systems, the user admissibility is characterized by a necessary and sufficient condition for the existence of the optimal solution under unequal signal-to- interference-plus-noise ratio constraints at the output of linear receivers and asymmetric data transmission rate constraints among users. The optimal signal power, bandwidth, transmit waveform, and receive waveform are derived for each user as the decision parameters of the optimization problem. It is shown that, if this solution is applied for the uplink users to minimize the total receive power, the optimal FDMA system performs the same as the optimal CDMA system. It is also shown that, if this solution is applied for the downlink users to minimize the total transmit power, the optimal FDM system always outperforms the code-division system that minimizes the extended total squared correlation. Numerical results suggest that the optimal FDM system and the optimal downlink code-division system achieve the same performance when the total transmit power is minimized.     

几种接收机在MIMO信道下的性能比较

多入多出（MIMO）无线信道具有空间复用增益和分集增益特性,因此MIMO系统和单入单出（SISO）无线系统相比能够获得更高的频谱效率。本文在不同天线组合下分析了几种MIMO空时信号处理算法的性能,仿真结果和理论分析表明：空间复用增益和分集增益不能同时获得最大,因此在设计MIMO通信系统时可根据实际情况选择天线数,即不仅考虑系统抵抗信道衰落的分集增益,还要考虑能够提供更高的数据传输速率,通过折衷考虑空间复杂增益和分集增益,从更全面的观点评估系统的性能。     

Optimal Throughput-Diversity-Delay Tradeoff in MIMO ARQ Block-Fading Channels

In this paper, we consider an automatic-repeat-request (ARQ) retransmission protocol signaling over a block-fading multiple-input–multiple-output (MIMO) channel. Unlike previous work, we allow for multiple fading blocks within each transmission (ARQ round), and we constrain the transmitter to fixed rate codes constructed over complex signal constellations. In particular, we examine the general case of average input-power-constrained constellations with a fixed signaling alphabet of finite cardinality. This scenario is a suitable model for practical wireless communications systems employing orthogonal frequency division multiplexing (OFDM) techniques over a MIMO ARQ channel. Two cases of fading dynamics are considered, namely, short-term static fading where channel fading gains change randomly for each ARQ round, and long-term static fading where channel fading gains remain constant over all ARQ rounds pertaining to a given message. As our main result, we prove that for the block-fading MIMO ARQ channel with a fixed signaling alphabet satisfying a short-term power constraint, the optimal signal-to-noise ratio (SNR) exponent is given by a modified Singleton bound, relating all the system parameters. To demonstrate the practical significance of the theoretical analysis, we present numerical results showing that practical Singleton-bound-achieving maximum distance separable codes achieve the optimal SNR exponent.      

Approximately universal codes over slow-fading channels

Performance of reliable communication over a coherent slow-fading multiple-input multiple-output (MIMO) channel at high signal-to-noise ratio (SNR) is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains. This paper studies the problem of designing codes that optimally tradeoff the diversity and multiplexing gains. The main contribution is a precise characterization of codes that are universally tradeoff-optimal, i.e., they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel. This characterization is referred to as approximate universality; the approximation is in the connection between error probability and outage capacity with diversity and multiplexing gains, respectively. The characterization of approximate universality is then used to construct new coding schemes as well as to show optimality of several schemes proposed in the space-time coding literature.     

Achieving the Optimal Diversity-Versus-Multiplexing Tradeoff for MIMO Flat Channels With QAM Space–Time Spreading and DFE Equalization

The use of multiple transmit (Tx) and receive (Rx) antennas allows to transmit multiple signal streams in parallel and hence to increase communication capacity. We have previously introduced simple convolutive linear precoding schemes that spread transmitted symbols in time and space, involving spatial spreading, delay diversity and possibly temporal spreading. In this paper we show that the use of the classical multiple-input-multiple-output (MIMO) decision feedback equalizer (DFE) (but with joint detection) for this system allows to achieve the optimal diversity-versus-multiplexing tradeoff introduced in Zheng and Tse, "Diversity and multiplexing: A fundamental tradeoff in multiple-antenna channels," IEEE Trans. Inf. Theory, May 2003, when a minimum mean squared error (MMSE) design is used. One of the major contributions of this work is the diversity analysis of a MMSE equalizer without the Gaussian approximation. Furthermore, the tradeoff is discussed for an arbitrary number of transmit and receive antennas. We also show the tradeoff obtained for a MMSE zero forcing (ZF) design. So, another originality of this paper is to show that the MIMO optimal tradeoff can be attained with a suboptimal receiver, in this case a DFE, as opposed to optimal maximum likelihood sequence estimation (MLSE)     

Capacity of Rayleigh fading channels under different adaptivetransmission and diversity-combining techniques

We study the Shannon capacity of adaptive transmission techniques in conjunction with diversity-combining. This capacity provides an upper bound on spectral efficiency using these techniques. We obtain closed-form solutions for the Rayleigh fading channel capacity under three adaptive policies: optimal power and rate adaptation, constant power with optimal rate adaptation, and channel inversion with fixed rate. Optimal power and rate adaptation yields a small increase in capacity over just rate adaptation, and this increase diminishes as the average received carrier-to-noise ratio (CNR) or the number of diversity branches increases. Channel inversion suffers the largest capacity penalty relative to the optimal technique, however, the penalty diminishes with increased diversity. Although diversity yields large capacity gains for all the techniques, the gain is most pronounced with channel inversion. For example, the capacity using channel inversion with two-branch diversity exceeds that of a single-branch system using optimal rate and power adaptation. Since channel inversion is the least complex scheme to implement, there is a tradeoff between complexity and capacity for the various adaptation methods and diversity-combining techniques     

Optimized nonuniform PSK for multiclass traffic and its application to space-time block codes

We construct nonuniform phase-shift keying (PSK) constellations that provide unequal error protection for multiclass traffic such as compressed voice and video data. Then closed-form expressions expression for the exact bit-error rate (BER) of the nonuniform PSK constellations is derived in multiple receive-antenna systems over Rayleigh fading channels. Based on this BER analysis, we optimize the nonuniform PSK constellations such that the BERs of all the bits of each class are equalized or such that the total transmission power is minimized subject to the average BER constraints. In particular, we demonstrate that even for transmitting single-class traffic, the optimized nonuniform PSK constellations can be better than the conventional uniform PSK. Finally, we extend the nonuniform PSK constellations to space-time coded communications systems with multiple transmit and multiple receive antennas.