Antenna selection for spatial multiplexing systems with linearreceivers

Future cellular systems will employ spatial multiplexing with multiple antennas at both the transmitter and receiver to take advantage of large capacity gains. In such systems it will be desirable to select a subset of available transmit antennas for link initialization, maintenance or handoff. We present a criterion for selecting the optimal antenna subset when linear, coherent receivers are used over a slowly varying channel. We propose use of the post-processing SNRs (signal to noise ratios) of the multiplexed streams whereby the antenna subset that induces the largest minimum SNR is chosen. Simulations demonstrate that our selection algorithm also provides diversity advantage thus making linear receivers useful over fading channels     

Adaptive transmit antenna selection with pragmatic space-time trellis codes

We consider the problem of selecting a subset of transmit antennas in MIMO systems to minimize error probability when only partial channel information is available at the transmitter. An upper bound for error probability of space-time coded transmit antenna selection scheme conditioned on the channel state information is presented. Based on the performance analysis, a criterion of selecting a subset of available transmit antennas to minimize the upper bound on the PEP is proposed. In contrast to other transmit antenna selection schemes for uncoded transmission or with a fixed number of antennas within the selection subset in the literature, the proposed scheme can adaptively select both a variable number of transmit antennas and their corresponding space-time codes for transmission. Furthermore, we present pragmatic space-time trellis coding schemes for slow Rayleigh fading channels. The principal advantage of the schemes is that a single encoder and decoder can be used for systems with a variable number of transmit antennas. The performance of the pragmatic space-time codes with adaptive antenna selection and the effect of the imperfect channel estimation on performance are evaluated by simulations. It is shown that the adaptive selection offers considerable antenna selection gain relative to the antenna selection system with a fixed number of antennas within the selection subset     

Analysis of Transmit Antenna Selection/Maximal-Ratio Combining in Rayleigh Fading Channels

In this paper, we investigate a multiple-input-multiple-output (MIMO) scheme combining transmit antenna selection and receiver maximal-ratio combining (the TAS/MRC scheme). In this scheme, a single transmit antenna, which maximizes the total received signal power at the receiver, is selected for uncoded transmission. The closed-form outage probability of the system with transmit antenna selection is presented. The bit error rate (BER) of the TAS/MRC scheme is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels. The BER analysis demonstrates that the TAS/MRC scheme can achieve a full diversity order at high signal-to-noise ratios (SNRs), as if all the transmit antennas were used. The average SNR gain of the TAS/MRC is quantified and compared with those of uncoded receiver MRC and space-time block codes (STBCs). The analytical results are verified by simulation. It is shown that the TAS/MRC scheme outperforms some more complex space-time codes of the same spectral efficiency. The cost of the improved performance is a low-rate feedback channel. We also show that channel estimation errors based on pilot symbols have no impact on the diversity order over quasi-static fading channels.     

Space-time codes for high data rate wireless communication:performance criterion and code construction

We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2-3 dB of the outage capacity for these channels using only 64 state encoders     

Performance Analysis of OSTBC Transmission in Amplify-and-Forward Cooperative Relay Networks

A performance analysis is presented for amplify-and-forward (AF) cooperative relay networks employing transmit antenna diversity with orthogonal space-time block codes (OSTBCs), where multiple antennas are equipped at the transmitter. We develop a symbol-error-rate (SER) and outage performance analysis for OSTBC transmissions with and without cooperative diversity over flat Rayleigh fading channels. We first derive exact probability density functions (pdf's) and cumulative distribution functions (cdf's) for the system SNR without direct transmission with an arbitrary number of transmit antennas and then present the exact closed-form SER and outage probability expressions. Next, we derive the moment-generating function (MGF) for the overall system SNR with direct transmission and present the exact SER and outage probability with joint transmit antenna diversity and cooperative diversity. The theoretical analysis is validated by simulations, which indicate an exact match between them. The results also show how the transmit antenna diversity and the cooperative diversity affect the overall system performance.      

Performance Analysis of Quantized Beamforming MIMO Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using single-stream transmit beamforming and receive combining. A MIMO beamforming system with feedback using a codebook based quantization of the beamforming vector allows practical implementation of such a strategy in a single-user scenario. The performance of this system in uncorrelated Rayleigh flat fading channels is studied from the point-of-view of signal-to-noise ratio (SNR) and outage probability. In this paper, lower bounds are derived on the expected SNR loss and the outage probability of systems that have a single receive antenna or two transmit antennas. For arbitrary transmit and receive antennas, approximations for the SNR loss and outage are derived. In particular, the SNR loss in a quantized MIMO beamforming system is characterized as a function of the number of quantization bits and the number of transmit and receive antennas. The analytical expressions are proved to be tight with asymptotically large feedback rate. Simulations show that the bounds and approximations are tight even at low feedback rates, thereby providing a benchmark for feedback system design     

最大比发射/选择接收技术的性能研究

为了提高系统性能并降低接收端(移动台)的硬件复杂度,提出一种新的MIMO传输技术。即在发射端(基站)按最大比发射(MRT,maximal-ratio transmit)技术,接收端则基于信噪比最大的原则仅选择一根接收天线来处理信号,记作MRT/RAS(maximal-ratio transmit/receiver antenna selection)。根据随机矩阵和排序统计的最新理论,推导出瑞利衰落信道下MRT/RAS系统的中断概率、误码率(BER)等性能指标的确切表达式。仿真结果表明MRT/RAS系统可以取得很好的阵列增益及满分集增益。相同频谱条件下,性能超过某些复杂的空时编码系统。而且在准静态衰落信道下,信道估计错误对取得的分集阶数并没有影响。仿真试验也证明了分析结果的正确性。     

Transmit antenna selection for decision feedback detection in MIMO fading channels

In this paper, we investigate a transmit antenna selection (TAS) approach for the decision-feedback detector (DFD) over Rayleigh fading channels. In particular, for a multipleinput multiple-output (MIMO) channel with M transmit and N (N ⩾ M) receive antennas, we derive a lower bound on the outage probability for the TAS approach. The selected transmit antennas are those that maximize the post-processing signalto- noise ratio (SNR) at the receiver end. It is shown that the proposed TAS approach achieves a performance close to optimal selection based on exhaustive search, introduced in the literature, but at a lower complexity. Simulation results are presented to validate and demonstrate the performance gain of the proposed TAS approach.     

Outage probability of multi-hop MIMO relaying with transmit antenna selection and ideal relay gain over rayleigh fading channels

We present a study on the outage probability of multi-hop wireless communication systems with multiple-input multiple-output (MIMO) link based on the transmit antenna selection and the maximal-ratio combining (MRC) at the receiver. A nonregenerative system (NS) is investigated with an ideal amplifying gain. MIMO channels are assumed in uncorrelated Rayleigh fading.We derive a moment generating function (MGF) of the reciprocal of the end-to-end signal-to-noise ratio (SNR) and obtain a closed-form approximation on the outage probability through the numerical inversion of a Laplace transform. Numerical results show that the presented outage is exactly matched with the outage probability when assuming the ideal relay gain. For more practical gains, the result is shown to be a lowerbound that gets tight at high average SNR as well as for a small number of hops and/or of antennas. We also compare the outage probabilities of nonregenerative MIMO relaying with a regenerative counterpart for multiple hops.     

Spatial Modulation

Spatial modulation (SM) is a recently developed transmission technique that uses multiple antennas. The basic idea is to map a block of information bits to two information carrying units: 1) a symbol that was chosen from a constellation diagram and 2) a unique transmit antenna number that was chosen from a set of transmit antennas. The use of the transmit antenna number as an information-bearing unit increases the overall spectral efficiency by the base-two logarithm of the number of transmit antennas. At the receiver, a maximum receive ratio combining algorithm is used to retrieve the transmitted block of information bits. Here, we apply SM to orthogonal frequency division multiplexing (OFDM) transmission. We develop an analytical approach for symbol error ratio (SER) analysis of the SM algorithm in independent identically distributed (i.i.d.) Rayleigh channels. The analytical and simulation results closely match. The performance and the receiver complexity of the SM-OFDM technique are compared to those of the vertical Bell Labs layered space-time (V-BLAST-OFDM) and Alamouti-OFDM algorithms. V-BLAST uses minimum mean square error (MMSE) detection with ordered successive interference cancellation. The combined effect of spatial correlation, mutual antenna coupling, and Rician fading on both coded and uncoded systems are presented. It is shown that, for the same spectral efficiency, SM results in a reduction of around 90% in receiver complexity as compared to V-BLAST and nearly the same receiver complexity as Alamouti. In addition, we show that SM achieves better performance in all studied channel conditions, as compared with other techniques. It is also shown to efficiently work for any configuration of transmit and receive antennas, even for the case of fewer receive antennas than transmit antennas.     

Communication on the Grassmann manifold: a geometric approach tothe noncoherent multiple-antenna channel

We study the capacity of multiple-antenna fading channels. We focus on the scenario where the fading coefficients vary quickly; thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver. We use a noncoherent block fading model proposed by Marzetta and Hochwald (see ibid. vol.45, p.139-57, 1999). The model does not assume any channel side information at the receiver or at the transmitter, but assumes that the coefficients remain constant for a coherence interval of length T symbol periods. We compute the asymptotic capacity of this channel at high signal-to-noise ratio (SNR) in terms of the coherence time T, the number of transmit antennas M, and the number of receive antennas N. While the capacity gain of the coherent multiple antenna channel is min{M, N} bits per second per Hertz for every 3-dB increase in SNR, the corresponding gain for the noncoherent channel turns out to be M* (1 - M*/T) bits per second per Hertz, where M*=min{M, N, [T/2]}. The capacity expression has a geometric interpretation as sphere packing in the Grassmann manifold     

Degrees of freedom in some underspread MIMO fading channels

Consider a multiple-input multiple-output (MIMO) fading channel in which the fading process varies slowly over time. Assuming that neither the transmitter nor the receiver have knowledge of the fading process, do multiple transmit and receive antennas provide significant capacity improvements at high signal-to-noise ratio (SNR)? For regular fading processes, recent results show that capacity ultimately grows doubly logarithmically with the SNR independently of the number of transmit and receive antennas used. We show that for the Gauss-Markov fading process in all regimes of practical interest the use of multiple antennas provides large capacity improvements. Nonregular fading processes show completely different high-SNR behaviors due to the perfect predictability of the process from noiseless observations. We analyze the capacity of MIMO channels with nonregular fading by presenting a lower bound, which we specialize to the case of band-limited slowly varying fading processes to show that the use of multiple antennas is still highly beneficial. In both cases, regular and nonregular fading, this capacity improvement can be seen as the benefit of having multiple spatial degrees of freedom. For the Gauss-Markov fading model and all regimes of practical interest, we present a communication scheme that achieves the full number of degrees of freedom of the channel with tractable complexity. Our results for underspread Gauss-Markov and band-limited nonregular fading channels suggest that multiple antennas are useful at high SNR.     

On the Capacity of Radio Communication Systems with Diversity in a Rayleigh Fading Environment

In this paper, we study the fundamental limits on the data rate of multiple antenna systems in a Rayleigh fading environment. WithMtransmit andMreceive antennas, up toMindependent channels can be established in the same bandwidth. We study the distribution of the maximum data rate at a given error rate in the channels between up toMtransmit antennas andMreceive antennas and determine the outage probability for systems that use various signal processing techniques. We analyze the performance of the optimum linear and nonlinear receiver processor and the optimum linear transmitter/receiver processor pair, and the capacity of these channels. Results show that with optimum linear processing at the receiver, up toM/2channels can be established with approximately the same maximum data rate as a single channel. With either nonlinear processing at the receiver or optimum linear transmitter/receiver processing, up toMchannels can be established with approximately the same maximum data rate as a single channel. Results show the potential for large capacity in systems with limited bandwidth.     

MIMO Channels in the Low-SNR Regime: Communication Rate, Error Exponent, and Signal Peakiness

We consider multiple-input multiple-output (MIMO) fading channels and characterize the reliability function in the low signal-to-noise (SNR) regime as a function of the number of transmit and receive antennas. For the case when the fading matrix H has independent entries, we show that the number of transmit antennas plays a key role in reducing the peakiness in the input signal required to achieve the optimal error exponent for a given communication rate. Further, by considering a correlated channel model, we show that the maximum performance gain (in terms of the error exponent and communication rate) is achieved when the entries of the channel fading matrix are fully correlated. The results we presented in this work in the low-SNR regime can also be applied to the infinite bandwidth regime     

Antenna diversity in multiuser data networks

We consider the use of multiple antennas at the transmitter and/or the receiver to provide open-loop spatial diversity in a multiuser wireless data network. With channel quality information (CQI) available to the transmitter, and by always scheduling the transmission to the active user having the best channel conditions at the time of scheduling, another form of diversity, termed multiuser diversity, is obtained in a data system. This paper provides an analysis of the interaction between these two forms of diversity. From a network point of view, we prove that the asymptotic sum rate, in the limit of a large number of active homogeneous users and subject to the same average total transmit power, is inversely related to the number of transmit antennas for independent and identically distributed (i.i.d.) flat Rayleigh fading channels. In the case of i.i.d. flat Rician fading, the asymptotic sum rate also depends inversely on the number of transmit antennas, but directly on the number of receive antennas. Numerically, we show that the total diversity gain is also constrained by finite CQI quantization and channel fading statistics.     

Combined transmit antenna selection and detection over spatial correlated MIMO systems

In this paper a method that combines transmit antenna selection and reduced-constellation detection in spatially correlated Multi-Input Multi-Output (MIMO) fading channels is presented. To mitigate the performance degradation caused by the use of antenna selection that is based on correlation among columns, an iterative receiver scheme that uses only a subset of the constellation points close to the expected symbol value estimated in the previous iteration is proposed. The size of the subset can adapt to the maximum correlation of the sub-matrix after the simple antenna selection. Furthermore, the error rate performance of the scheme under linear Minimum Mean Square Error (MMSE) or Ordered Successive Interference Cancellation (OSIC) for the first run detection and different interleaver lengths is investigated while the transmit antenna selection is considered. The simulation results show a sig- nificant advantage both for implementation complexity and for error rate performance under a fixed data rate.     

On the Design of Space–Time Trellis Codes for Transmit-Correlated Fading Channels

The analysis and design of space-time codes for correlated fading channels when the diversity gain is large enough is considered. We derive a simple form for a distance metric that characterizes the code performance in the presence of transmit correlation, and propose some design criteria to build good space-time trellis codes (STTCs) for correlated channels. For the case of two transmit antennas, we show that in strongly correlated channels, performance is governed by the constellation that results from the sum of the constellations associated with the transmit antennas. This suggests the use of new constellations to design better codes for correlated channels. The design criteria are then extended to any number of transmit antennas. Based on these criteria, we derive new STTCs for two and three transmit antennas that perform much better in correlated channels than the STTC optimized for the independent and identically distributed case. We also consider set partitioning applied to the sum constellation as a simple technique to design good codes for correlated channels. The codes derived show performance close to the codes found by an exhaustive search. Finally, we consider antenna selection as an alternative to build good codes for more than two antennas in fading-correlated scenarios     

Cutoff rate and signal design for the quasi-static Rayleigh-fadingspace-time channel

We consider the computational cutoff rate and its implications on signal design for the complex quasi-static Rayleigh flat-fading spatio-temporal channel under a peak-power constraint where neither transmitter nor receiver know the channel matrix. The cutoff rate has an integral representation which is an increasing function of the distance between pairs of complex signal matrices. When the analysis is restricted to finite-dimensional sets of signals, interesting characterizations of the optimal rate-achieving signal constellation can be obtained. For an arbitrary finite dimension, the rate-optimal constellation must admit an equalizer distribution, i.e., a positive set of signal probabilities which equalizes the average distance between signal matrices in the constellation. When the number N of receive antennas is large, the distance-optimal constellation is nearly rate-optimal. When the number of matrices in the constellation is less than the ratio of the number of time samples to the number of transmit antennas, the rate-optimal cutoff rate attaining constellation is a set of equiprobable mutually orthogonal unitary matrices. When the signal-to-noise ratio (SNR) is below a specified threshold, the matrices in the constellation are rank one and the cutoff rate is achieved by applying all transmit power to a single antenna and using orthogonal signaling. Finally, we derive recursive necessary conditions and sufficient conditions for a constellation to lie in the feasible set     

Limiting performance of block-fading channels with multipleantennas

We derive the performance limits of a radio system consisting of a transmitter with t antennas and a receiver with r antennas, a block-fading channel with additive white Gaussian noise (AWGN), delay and transmit-power constraints, and perfect channel-state information available at both the transmitter and the receiver. Because of a delay constraint, the transmission of a codeword is assumed to span a finite (and typically small) number M of independent channel realizations; therefore, the relevant performance limits are the information outage probability and the “delay-limited” (or “nonergodic”) capacity. We derive the coding scheme that minimizes the information outage probability. This scheme can be interpreted as the concatenation of an optimal code for the AWGN channel without fading to an optimal beamformer. For this optimal scheme, we evaluate minimum-outage probability and delay-limited capacity. Among other results, we prove that, for the fairly general class of regular fading channels, the asymptotic delay-limited capacity slope, expressed in bits per second per hertz (b/s/Hz) per decibel of transmit signal-to-noise ratio (SNR), is proportional to min (t,r) and independent of the number of fading blocks M. Since M is a measure of the time diversity (induced by interleaving) or of the frequency diversity of the system, this result shows that, if channel-state information is available also to the transmitter, very high rates with asymptotically small error probabilities are achievable without the need of deep interleaving or high-frequency diversity. Moreover, for a large number of antennas, delay-limited capacity approaches ergodic capacity     

On Noncoherent MIMO Channels in the Wideband Regime: Capacity and Reliability

We consider a multiple-input multiple-output (MIMO) wideband Rayleigh block-fading channel where the channel state is unknown to both the transmitter and the receiver and there is only an average power constraint on the input. We compute the capacity and analyze its dependence on coherence length, number of antennas and receive signal-to-noise ratio (SNR) per degree of freedom. We establish conditions on the coherence length and number of antennas for the noncoherent channel to have a "near-coherent" performance in the wideband regime. We also propose a signaling scheme that is near-capacity achieving in this regime. We compute the error probability for this wideband noncoherent MIMO channel and study its dependence on SNR, number of transmit and receive antennas and coherence length. We show that error probability decays inversely with coherence length and exponentially with the product of the number of transmit and receive antennas. Moreover, channel outage dominates error probability in the wideband regime. We also show that the critical as well as cutoff rates are much smaller than channel capacity in this regime