Diversity Multiplexing Tradeoff in MIMO Frequency Selective Channels with Partial CSIT

In this letter, we derive the optimal diversity- multiplexing tradeoff for a frequency selective MIMO channel with resolution-constrained channel feedback. The additional degree of freedom provided by the channel multipaths is succinctly captured in the tradeoff characterization. For instance, in a L-path SISO channel, with K-level feedback, the maximum diversity increase is exponential in K.     

Diversity and Multiplexing Tradeoff of Spatial Multiplexing MIMO Systems With CSI

Following the seminal work of Zheng and Tse, this paper investigates the fundamental diversity and multiplexing tradeoff of multiple-input-multiple-output (MIMO) systems in which knowledge of the channel state at both sides of the link is employed to transmit independent data streams through the channel eigenmodes. First, the fundamental diversity and multiplexing tradeoff of each of the individual substreams is obtained and this result is then used to derive a tradeoff optimal scheme for rate allocation along channel eigenmodes. The tradeoff of spatial multiplexing is finally compared to the fundamental tradeoff of the MIMO channel and to the one of both space only codes and V-BLAST which do not require channel state information (CSI) at the transmit side.     

Diversity and Multiplexing Tradeoff in General Fading Channels

The optimal tradeoff between diversity gain and multiplexing gain for multiple-inputmultiple-output (MIMO) channels has been studied recently under the independent and identically distributed (i.i.d.) Rayleigh-fading assumption. In this correspondence, this result is extended and the optimal tradeoff performance is derived for generalized fading channel conditions, including different fading types, nonidentical fading distributions, spatial correlation, and nonzero channel means. Our results include many known models as special cases and shed light on the effects of different channel parameters on the optimal tradeoff performance     

MIMO系统中分集增益和空间复用增益的折衷关系

论文导出了分集增益与空间复用增益间的最佳折衷关系式。该关系式为阶梯递减右连续函数,阶梯数等于接收天线数目。分集增益的取值与分组长度有关,只有当分组长度不小于发射天线数目时才能获得满分集增益。折衷关系表明,采用合适的空时编码可以同时获得分集增益和空间复用增益,但是两种增益不能同时达到最大。由最佳折衷关系可以推测一定空间复用增益时可得到的最大分集增益,以及一定分集增益时能获得的最大空间复用增益。     

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     

Diversity–Multiplexing Tradeoff of Asynchronous Cooperative Diversity in Wireless Networks

Synchronization of relay nodes is an important and critical issue in exploiting cooperative diversity in wireless networks. In this paper, two asynchronous cooperative diversity schemes are proposed, namely, distributed delay diversity and asynchronous space-time coded cooperative diversity schemes. In terms of the overall diversity-multiplexing (DM) tradeoff function, we show that the proposed independent coding based distributed delay diversity and asynchronous space-time coded cooperative diversity schemes achieve the same performance as the synchronous space-time coded approach which requires an accurate symbol-level timing synchronization to ensure signals arriving at the destination from different relay nodes are perfectly synchronized. This demonstrates diversity order is maintained even at the presence of asynchronism between relay node. Moreover, when all relay nodes succeed in decoding the source information, the asynchronous space-time coded approach is capable of achieving better DM tradeoff than synchronous schemes and performs equivalently to transmitting information through a parallel fading channel as far as the DM tradeoff is concerned. Our results suggest the benefits of fully exploiting the space-time degrees of freedom in multiple antenna systems by employing asynchronous space-time codes even in a frequency-flat-fading channel. In addition, it is shown asynchronous space-time coded systems are able to achieve higher mutual information than synchronous space-time coded systems for any finite signal-to-noise ratio (SNR) when properly selected baseband waveforms are employed.     

On the Diversity–Multiplexing Tradeoff in Multiple-Relay Network

This paper studies the setup of a multiple-relay network in which $K$ half-duplex multiple-antenna relays assist in the transmission between either one or several multiple-antenna transmitter(s) and a multiple-antenna receiver. Each two nodes are assumed to be either connected through a quasi-static Rayleigh-fading channel, or disconnected. We propose a new scheme, which we call random sequential (RS), based on the amplify-and-forward relaying. We prove that for general multiple-antenna multiple-relay networks, the proposed scheme achieves the maximum diversity gain. Furthermore, we derive diversity–multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple-access multiple-relay $(K > 1)$ networks (without direct link between the transmitter(s) and the receiver), the proposed RS scheme achieves the optimum DMT. However, for the case of multiple-access single-relay setup, we show that the RS scheme reduces to the naive amplify-and-forward (AF) relaying and is not optimum in terms of DMT, while the dynamic decode-and-forward (DF) scheme is shown to be optimum for this scenario.      

On the Diversity Order of Spatial Multiplexing Systems With Transmit Antenna Selection: A Geometrical Approach

In recent years, the remarkable ability of multiple-input-multiple-output (MIMO) wireless communication systems to provide spatial diversity or multiplexing gains has been clearly demonstrated. For MIMO diversity schemes, it is well known that antenna selection methods that optimize the postprocessing signal-to-noise ratio (SNR) can preserve the diversity order of the original full-size MIMO system. On the other hand, the diversity order achieved by antenna selection in spatial multiplexing systems, especially those exploiting practical coding and decoding schemes, has not thus far been rigorously analyzed. In this paper, a geometrical framework is proposed to theoretically analyze the diversity order achieved by transmit antenna selection for separately encoded spatial multiplexing systems with linear and decision-feedback receivers. When two antennas are selected from the transmitter, the exact achievable diversity order is rigorously derived, which previously only appears as conjectures based on numerical results in the literature. If more than two antennas are selected, we give lower and upper bounds on the achievable diversity order. Furthermore, the same geometrical approach is used to evaluate the diversity-multiplexing tradeoff in spatial multiplexing systems with transmit antenna selection     

Bi-directional UWB MIMO Antenna for Superior Spatial Diversity,and/or Multiplexing MIMO Performance

In this paper, a two-element UWB MIMO antenna with bi-directional radiation pattern is designed for superior UWB MIMO performance. The designed antenna adopts asymmetric coplanar waveguide ground feeding. The proposed antenna ECC is lower than the ECC of its omni-directional peer antenna. Simulated and measured ECC is lower than 0.016 over the entire ultra-wide bandwidth (3.1–10.6 GHz). The isolation between elements of the designed antenna is 20–25 dB exceeding the average in recently published works. The designed antenna has a diversity gain of almost 10 dB and average multiplexing efficiency of 85% over the entire ultra-wide bandwidth. The antenna preserves radiation efficiency higher than 0.96 and gain 3 dB. The diversity performance of the proposed UWB MIMO antenna is proven through real rich-multipath indoor environment measurements. Stationarity of the elected channel is evaluated through 100 successive measurements separated by a 3-min period for 5 h long. The measured spatial correlation coefficients are much lower than 0.5 in different scenarios.     

Asymptotic Analysis of SDMA Systems with Near-Orthogonal User Scheduling (NEOUS) under Imperfect CSIT

In this paper, we focus on the asymptotic cross layer analysis of multi-antenna systems with transmit MMSE (Tx- MMSE) beamforming, near orthogonal scheduling and outdated CSIT. To capture the effect of the potential packet outage, we introduce the average system goodput, which measures the average b/s/Hz delivered to the mobiles successfully, as the system performance objective. We derive closed-form expressions for the optimal power and rate allocations as well as a low complexity near orthogonal user scheduling (NEOUS) algorithm to solve the cross-layer optimization problem.We derive the asymptotic order of growth in system goodput for general CSIT error variance σ₂ and found that for sufficiently large n_T (number of antennas at the base station) and K (number of users) where K = g?1(n_T ) for some strictly increasing function g(x) = o(x), the the system goodput grows in the order of nT log[(1-σ₂ ) logK] when σ₂ < 1. This is the same order of growth as the optimal order of growth in broadcast channels with perfect CSIT and hence, the NEOUS is order-optimal. On the other hand, we need exponentially larger K to compensate for the penalty in multiuser diversity gain due to CSIT errors.     

Cross Layer Design of Downlink Multi-Antenna OFDMA Systems with Imperfect CSIT for Slow Fading Channels

In most existing works, perfect knowledge of channel state information at the transmitter (CSIT) is assumed to realize the potential benefit of cross-layer scheduling and spatial multiplexing gains of MIMO/OFDMA systems. However, perfect knowledge of CSIT is not easy to achieve in practice due to estimation noise or delay in feedback. In this paper, we shall focus on the cross-layer design of downlink multi-antenna OFDMA systems with imperfect CSIT for slow fading channels. We shall show that our proposed cross-layer scheduler can exploit the multiuser diversity and spatial multiplexing gain even in the presence of moderate CSIT error.     

On the BER Performance of Hierarchical M-QAM Constellations With Diversity and Imperfect Channel Estimation

The analytical bit error rate of hierarchical quadrature amplitude modulation formats, which include uniform and nonuniform constellations, over flat Rayleigh fading environments is studied in this paper. The analysis takes into account the effect of imperfect channel estimation and considers diversity reception with both independent identically and nonidentically distributed channels, employing maximal ratio combining.     

Robust Optimal Cross-Layer Designs for TDD-OFDMA Systems with Imperfect CSIT and Unknown Interference: State-Space Approach Based on 1-bit ACK/NAK Feedbacks

Cross-layer designs for OFDMA systems have been shown to offer significant gains of spectral efficiency by exploiting the multiuser diversity over the temporal and frequency domains. In this paper, we shall propose a robust optimal cross-layer design for downlink TDD-OFDMA systems with imperfect channel state information at the base station (CSIT) and unknown interference in slow fading channels. Exploiting the ACK/NAK (1-bit) feedbacks from the mobiles, the proposed cross-layer design does not require knowledge of the CSIT error statistics or interference statistics. To take into account of the potential packet error due to the imperfect CSIT and unknown interference, we define average system goodput (which measures the average b/s/Hz successfully delivered to the mobile) as our optimization objective. We formulate the cross-layer design as a state-space control problem. The optimal power, optimal rate and optimal user allocations are determined as the output equations from the system states based on dynamic programming approach. Simulation results illustrate that the performance of the proposed closed-loop cross-layer design is very robust with respect to imperfect CSIT, unknown interference, model mismatch as well as channel variations due to Doppler.     

Array Gain and Diversity Order of Multiuser MISO Antenna Systems

In considering generalized zero-forcing, this paper derives the optimal linear signal processing solution for the multiuser multiple-input single-output (MISO) broadcast fading channels where a single base station is communicating simultaneously to many mobile stations in the same frequency and time slot. We then investigate the array gain, defined as the average of the squared channel response, and the diversity order, defined as the inverse of the normalized variance of the squared channel response, of the optimized system. It is concluded that each user in the multiuser MISO system behaves like a single-user system with (n _T  − M + 1)-th order receiver diversity if there are M simultaneous users and n _T antennas are employed at the base station.

Impact of Spatial Correlation on the Finite-SNR Diversity-Multiplexing Tradeoff

The impact of spatial correlation on the performance limits of multielement antenna (MEA) channels is analyzed in terms of the diversity-multiplexing tradeoff (DMT) at finite signal-to-noise ratio (SNR) values. A lower bound on the outage probability is first derived. Using this bound accurate finite-SNR estimate of the DMT is then derived. This estimate allows to gain insight on the impact of spatial correlation on the DMT at finite SNR. As expected, the DMT is severely degraded as the spatial correlation increases. Moreover, using asymptotic analysis, we show that our framework encompasses well-known results concerning the asymptotic behavior of the DMT.     

Channel Access Scheme for MIMO-Enabled Ad Hoc Networks with Adaptive Diversity/Multiplexing Gains

Transmission power control (TPC) is used in wireless networks to improve channel reuse and/or reduce energy consumption. It has been often applied to single-input single-output (SISO) systems, where each node is equipped with a single antenna. Multi-input multi-output (MIMO) systems can improve the throughput or the signal-to-noise ratio (SNR) by providing multiplexing or diversity gains, respectively. In this paper, we incorporate a power-controlled MAC protocol for a wireless network with two antennas per node. Our protocol, coined CMAC, combines different types of MIMO gains, allowing for dynamic switching between diversity and multiplexing modes so as to maximize a utility function that depends on both energy consumption and throughput. CMAC adapts the “antenna mode,” the transmission power, and the modulation order on a per-packet basis. By “antenna mode” we mean one of five possible transmit/receive antenna configurations: 1 × 1 (SISO), 2 × 1 (MISO-D), 1 × 2 (SIMO-D), 2 × 2 (MIMO-D), and 2 × 2 (MIMO-M). The second, third, and fourth configurations offer a diversity gain, whereas the last configuration offers a multiplexing gain. By using control packets to bound the transmission power of potentially interfering terminals, CMAC allows for multiple interference-limited transmissions to take place in the vicinity of a receiving terminal. We study via simulations the performance of CMAC in ad hoc topologies. Our results indicate that relative to non-adaptive protocols, CMAC achieves a significant improvement in both the overall energy consumption and the throughput.

On the sum-rate scaling law of downlink MU-MIMO decomposition transmission with fixed quality imperfect CSIT

In recent years, downlink multi-user multiple-input multiple-output (MU-MIMO) transmission techniques have attracted much attention because of their potential to significantly increase system capacity compared to single-user (SU) transmission. Unfortunately, accurate channel state information at the transmitter (CSIT) is crucial for these techniques to efficiently separate multiple users in the space domain so as to realize their capacity gain. In practice however accurate CSIT is difficult to obtain. In this letter we investigate the impact of imperfect CSIT on the system performance in terms of sum-rate scaling law for systems employing MU-MIMO decomposition scheme for downlink transmission. In particular, we derive the sum-rate scaling factors for various system configurations and find that imperfect CSIT has different effects on different categories of system configurations. Simulation results demonstrate the accuracy of our analysis.     

Tradeoff Analysis of Performance and Complexity on GSECps Diversity Combining Scheme

Generalized switch and examine combining (GSEC) was recently proposed as a low-complexity diversity combining scheme for diversity-rich environment. In this paper, we present and analyze a modified version of GSEC scheme, termed as GSEC with post-examine selection (GSECps). The GSECps scheme operates in the same way as GSEC when channel conditions are favorable and becomes equivalent to the generalized selection combining (GSC) scheme otherwise. We show, through a thorough and accurate tradeoff analysis of performance versus complexity, that GSECps can deliver a better performance-complexity tradeoff than both GSEC and GSC schemes.     

小斜视角下稀疏空域SIMO雷达运动目标成像方法

针对小斜视角下单发多收(SIMO)雷达对空运动目标单次快拍成像时天线数目较多的问题,提出了一种稀疏空域SIMO雷达运动目标成像方法。首先详细分析了小斜视角下SIMO雷达单次快拍成像原理,其次结合压缩感知理论具体阐述了小斜视角下稀疏空域SIMO雷达运动目标成像方法。该方法不仅能够对运动目标实现单次快拍成像,避免了非合作运动目标强加速、大转角等引起的运动补偿难题,同时又能够大幅减少接收天线单元数,便于工程实现。最后利用仿真实验验证了文中方法的有效性和可行性。