An analytical comparison of partial power-feedback designs for MIMO block fading channels

It has been shown that with perfect feedback (CSIT), the optimal multiple input/multiple output (MIMO) transmission strategy is a cascade of channel encoder banks, power control matrix, and eigen-beamforming matrix. However, the feedback capacity requirement for perfect CSIT is 2n/sub T//spl times/n/sub R/, which is not scalable with respect to n/sub T/ or n/sub R/. In this letter, we shall compare the performance of two levels of partial power-feedback strategies, namely, the scalar symmetric feedback and the vector feedback, for MIMO block fading channels. Unlike quasi-static fading, variable rate encoding is not needed for block fading channels to achieve the optimal channel capacity.     

Capacity achieving high rate space-time block codes

It is well known, that the Alamouti scheme is the only space-time code from orthogonal design achieving the capacity of multiple-input multiple-output (MIMO) wireless communication system with n/sub T/=2 transmit antennas and n/sub R/=1 receive antenna. In this work, we propose the n-times stacked Alamouti scheme for n/sub T/=2n transmit antennas and show that this scheme achieves the capacity in the case of n/sub R/=1 receive antenna. For the more general case of more than one receive antenna, we show that if the number of transmit antennas is higher than the number of receive antennas we achieve a high portion of the capacity with this scheme.     

Sum capacity of MIMO Gaussian broadcast channels with channel energy constraints

The motivation of this paper is to find the class of channels that provides the best sum capacity of a MIMO Gaussian broadcast channel with both transmit power and channel energy constraints when N/sub t//spl ges/KN/sub r/, where N/sub t/, N/sub r/, and K denote the number of transmit antennas, the number of receive antennas, and the number of users in the system, respectively. The best sum capacity is achieved when the user channels are mutually orthogonal to each other. For each individual user, equal energy is distributed to all non-zero spatial eigenmodes. Further, we optimize the number of non-zero eigenmodes for all users and the optimal power distribution among users. Although, we only study the case of N/sub t//spl ges/KN/sub r/ in this paper, we conjecture that similar results still hold for N/sub t/相似文献   

Transmitter optimization and performance gain for multiple-input single-output systems with finite-rate direction feedback

Consider finite-rate channel-direction feedback in a system with multiple transmit but single receive antennas. We investigate how the transmitter should be optimized for symbol error rate with finite-rate feedback, and how the symbol error rate and outage probability improve as a function of the number of feedback bits. It is found that when the number of feedback directions is equal to or larger than the number of transmit antennas, transmit beamforming is optimal. Otherwise, the antennas should be divided into two groups, where antenna selection is used in the first group to choose the strongest channel, and equal power allocation is used in the second group. At high signal to noise ratio (SNR), the optimal power allocation between these two antenna groups is proportional to the number of antennas in each group. Based on high SNR analysis, we quantify the power gain of each feedback bit. It is shown that the incremental gain increases initially and diminishes when the number of feedback bits surpasses the logarithm (base 2) of the number of transmit antennas.     

Design Guidelines for Training-Based MIMO Systems With Feedback

In this paper, we study the optimal training and data transmission strategies for block fading multiple-input multiple-output (MIMO) systems with feedback. We consider both the channel gain feedback (CGF) system and the channel covariance feedback (CCF) system. Using an accurate capacity lower bound as a figure of merit that takes channel estimation errors into account, we investigate the optimization problems on the temporal power allocation to training and data transmission as well as the training length. For CGF systems without feedback delay, we prove that the optimal solutions coincide with those for nonfeedback systems. Moreover, we show that these solutions stay nearly optimal even in the presence of feedback delay. This finding is important for practical MIMO training design. For CCF systems, the optimal training length can be less than the number of transmit antennas, which is verified through numerical analysis. Taking this fact into account, we propose a simple yet near optimal transmission strategy for CCF systems, and derive the optimal temporal power allocation over pilot and data transmission.     

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     

Optimizing the joint transmit and receive MMSE design using mode selection

To approach the potential multiple-input multiple-output (MIMO) capacity while optimizing the system bit-error rate (BER) performance, the joint transmit and receive minimum mean squared error (joint Tx/Rx MMSE) design has been proposed. It is the optimal linear scheme for spatial multiplexing MIMO systems, assuming a fixed number of spatial streams p as well as fixed modulation and coding across these spatial streams. However, the number of spatial streams has been arbitrarily chosen and fixed, which may lead to an inefficient power allocation strategy and a poor BER performance. In this paper, we relax the constraint of fixed number of streams p and optimize this value for the current channel realization, under the constraints of fixed average total transmit power P/sub T/ and fixed rate R, what we refer to as mode selection . Based on the observation of the existence of a dominant optimal number of streams value for the considered Rayleigh flat-fading MIMO channel model, we further propose an "average" mode selection that avoids the per-channel adaptation through using the latter dominant value for all channel realizations. Finally, we exhibit the significant BER improvement provided by our mode selection over the conventional joint Tx/Rx MMSE design. Such significant improvement is due to the better exploitation of the MIMO spatial diversity and the more efficient power allocation enabled by our mode selection.     

Optimal constellation labeling for iteratively decoded bit-interleaved space-time coded Modulation

We consider the design of iteratively decoded bit-interleaved space-time coded modulation (BI-STCM) over fast Rayleigh-fading channels with N/sub t/ transmit and N/sub r/ receive antennas. We propose the design criterion to achieve the largest asymptotic coding gain inherited in the constellation labeling. In particular, for orthogonal space-time block codes, the labeling design criterion reduces to maximizing the (-N/sub t/N/sub r/)th power mean of the complete set of squared Euclidean distances associated with all "error-free feedback" events in the constellation. Based on this power mean criterion, we show that the labeling optimization problem falls into the category of quadratic assignment problems for constellations of any shape and with an arbitrary number of transmit and receive antennas. For a set of practical values of N/sub t/ and N/sub r/, we present optimal labeling maps for 8-PSK, 16-QAM, and 64-QAM constellations.     

The Downlink Capacity of Single-User SA-MIMO System

In this paper, a novel multiple antenna system framework, which combines smart antennas (SA) with multiple-input-multiple-output (MIMO) at the transmitter, is proposed. The downlink capacity of the single-user SA-MIMO wireless systems is investigated. The joint optimization problem corresponding to the capacity is deduced. After that, upper bounds of the capacity are given in general case and in the case of equal power allocation, respectively. Furthermore, in the case of equal power allocation and the same direction of departure from one transmit smart antenna to all antenna arrays at the receiver the closed-form expression of the capacity is obtained. Some numerical results are given to show that smart antennas can bring significant capacity gain for the MIMO systems due to the smart antennas gain, without additional spatial degrees of freedom, especially at high SNR with strong correlation among the MIMO channel links or at low SNR.     

On the Capacity and Design of Limited Feedback Multiuser MIMO Uplinks

The theory of multiple-input–multiple-output (MIMO) technology has been well developed to increase fading channel capacity over single-input–single-output (SISO) systems. This capacity gain can often be leveraged by utilizing channel state information at the transmitter and the receiver. Users make use of this channel state information for transmit signal adaptation. In this correspondence, we derive the capacity region for the MIMO multiple access channel (MIMO MAC) when partial channel state information is available at the transmitters, where we assume a synchronous MIMO multiuser uplink. The partial channel state information feedback has a cardinality constraint and is fed back from the basestation to the users using a limited rate feedback channel. Using this feedback information, we propose a finite codebook design method to maximize the sum rate. In this correspondence, the codebook is a set of transmit signal covariance matrices. We also derive the capacity region and codebook design methods in the case that the covariance matrix is rank one (i.e., beamforming). This is motivated by the fact that beamforming is optimal in certain conditions. The simulation results show that when the number of feedback bits increases, the capacity also increases. Even with a small number of feedback bits, the performance of the proposed system is close to an optimal solution with the full feedback.      

Capacity Enhancement Using MIMO Antenna Arrays in Realistic Macro-Cellular Urban Environment

In MIMO systems the antenna array configuration in the BS and MS has a large influence on the available channel capacity. In this paper, we first introduce a new Frequency Selective (FS) MIMO framework for macro-cells in a realistic urban environment. The MIMO channel is built over a previously developed directional channel model, which considers the terrain and clutter information in the cluster, line-of-sight and link loss calculations. Next, MIMO configuration characteristics are investigated in order to maximize capacity, mainly the number of antennas, inter-antenna spacing and SNR impact. Channel and capacity simulation results are presented for the city of Lisbon, Portugal, using different antenna configurations. Two power allocations schemes are considered, uniform distribution and FS spatial water-filling. The results suggest optimized MIMO configurations, considering the antenna array size limitations, specially at the MS side.     

A new family of Grassmann space-time codes for non-coherent MIMO systems

A family of space-time codes suited for noncoherent multi-input multi-output (MIMO) systems is presented. These codes use all the complex degrees of freedom of the system, i.e. M/spl times/(1-(M/T)) symbols per channel use. They are constructed as codes on the Grassmann manifold G/sub T,M/(/spl Copf/) where T is the temporal codelength and M is the number of transmit antennas.     

An Efficient CSI Feedback Scheme for MIMO-OFDM Wireless Systems

For antenna-array-based multiple-input multiple- output orthogonal-frequency-division-multiplexing (MIMO-OFDM) wireless systems, gain in channel throughput reduced through sufficient feedback of the channel state information (CSI) is significant, particularly when the number of transmit antennas is larger than the number of receive antennas. In this letter, we demonstrate that, in such scenarios, (1) the CSI of each OFDM sub-carrier can be parameterized into a short bit stream by a proposed low-complexity QR decomposition on the corresponding MIMO channel matrix, (2) the overall CSI can be reliably represented by a proposed parameter interpolation on the above bit streams of only a fraction of sub-carriers, and (3) a MIMO-OFDM system with a low-rate CSI feedback parameterized above can provide a channel throughput comparable to the channel capacity.     

High-SNR power offset in multiantenna communication

The analysis of the multiple-antenna capacity in the high-SNR regime has hitherto focused on the high-SNR slope (or maximum multiplexing gain), which quantifies the multiplicative increase as a function of the number of antennas. This traditional characterization is unable to assess the impact of prominent channel features since, for a majority of channels, the slope equals the minimum of the number of transmit and receive antennas. Furthermore, a characterization based solely on the slope captures only the scaling but it has no notion of the power required for a certain capacity. This paper advocates a more refined characterization whereby, as a function of SNR|/sub dB/, the high-SNR capacity is expanded as an affine function where the impact of channel features such as antenna correlation, unfaded components, etc., resides in the zero-order term or power offset. The power offset, for which we find insightful closed-form expressions, is shown to play a chief role for SNR levels of practical interest.     

Adaptive antennas for space-time codes in outdoor channels

Space-time codes have been introduced to improve mobile system performance in a multipath fading environment. We consider a multiple-input multiple-output (MIMO) system with m mobile antennas and n base station antennas, in which there are L multipaths at the base station at distinct angles of arrival. We show that when the channel has no intersymbol interference (ISI), then adaptive antennas in the form of beamforming, can be combined with space-time coding, to achieve a diversity gain of mL and a large signal-to-noise ratio (SNR) gain whenever n/spl ges/L. When the channel has ISI, beamforming can be used by the MIMO systems to achieve an SNR gain over a single-input multiple-output system, although both systems have the same diversity gain.     

Spatio-temporal coding for wireless communication

Multipath signal propagation has long been viewed as an impairment to reliable communication in wireless channels. This paper shows that the presence of multipath greatly improves achievable data rate if the appropriate communication structure is employed. A compact model is developed for the multiple-input multiple-output (MIMO) dispersive spatially selective wireless communication channel. The multivariate information capacity is analyzed. For high signal-to-noise ratio (SNR) conditions, the MIMO channel can exhibit a capacity slope in bits per decibel of power increase that is proportional to the minimum of the number multipath components, the number of input antennas, or the number of output antennas. This desirable result is contrasted with the lower capacity slope of the well-studied case with multiple antennas at only one side of the radio link. A spatio-temporal vector-coding (STVC) communication structure is suggested as a means for achieving MIMO channel capacity. The complexity of STVC motivates a more practical reduced-complexity discrete matrix multitone (DMMT) space-frequency coding approach. Both of these structures are shown to be asymptotically optimum. An adaptive-lattice trellis-coding technique is suggested as a method for coding across the space and frequency dimensions that exist in the DMMT channel. Experimental examples that support the theoretical results are presented     

Spatial multiplexing with transmit antenna and constellation selection for correlated MIMO fading channels

We consider spatial multiplexing systems in correlated multiple-input multiple-output (MIMO) fading channels with equal power allocated to each transmit antenna. Under this constraint, the number and subset of transmit antennas together with the transmit symbol constellations are determined assuming knowledge of the channel correlation matrices. We first consider a fixed data rate system and vary the number of transmit antennas and constellation such that the minimum margin in the signal-to-noise ratio (SNR) is maximized for linear and Vertical Bell Laboratories Layered Space-Time (V-BLAST) receivers. We also derive transmit antenna and constellation selection criteria for a successive interference cancellation receiver (SCR) with a fixed detection order and a variable number of bits transmitted on each substream. Compared with a system using all available antennas, performance results show significant gains using a subset of transmit antennas, even for independent fading channels. Finally, we select a subset of transmit antennas to maximize data rate given a minimum SNR margin. A lower bound on the maximum outage data rate is derived. The maximum outage data rate of the SCR receiver is seen to be close to the outage channel capacity.     

Joint antenna selection and link adaptation for MIMO systems

Multi-input multi-output (MIMO) systems, with multiple antennas at both the transmitter and the receiver, are anticipated to be widely employed in future wireless networks due to their predicted tremendous system capacity. To protect the transmitted data against random channel impairment, it is desirable to consider link adaptation, such as rate adaptation and power control, to improve the system performance and guarantee certain quality of service. Based on the observation that link adaptation and antenna selection problems are often coupled, we propose a joint antenna subset selection and link adaptation study for MIMO systems. After the formulation of the multidimensional joint optimization problem, the main contribution of this paper lies in the design of efficient algorithms approaching the optimal solution for both uncorrelated and correlated MIMO channels. Specifically, we propose one simplified antenna selection and link adaptation rule based on the expected optimal number of active antennas for uncorrelated MIMO with Rayleigh fading and one for correlated MIMO channels only based on the slowly varying channel correlation information. Our proposed algorithms are verified through numerical results, demonstrating significant gains over traditional MIMO signaling, while feasible for practical implementation.     

On the Information Rate of MIMO Systems With Finite Rate Channel State Feedback Using Beamforming and Power On/Off Strategy

It is well known that multiple-input multiple-output (MIMO) systems have high spectral efficiency, especially when channel state information at the transmitter (CSIT) is available. In many practical systems, it is reasonable to assume that the CSIT is obtained by a limited (i.e., finite rate) feedback and is therefore imperfect. We consider the design problem of how to use the limited feedback resource to maximize the achievable information rate. In particular, we develop a low complexity power on/off strategy with beamforming (or Grassmann precoding), and analytically characterize its performance. Given the eigenvalue decomposition of the covariance matrix of the transmitted signal, refer to the eigenvectors as beams, and to the corresponding eigenvalues as the beam's power. A power on/off strategy means that a beam is either turned on with a constant power, or turned off. We will first assume that the beams match the channel perfectly and show that the ratio between the optimal number of beams turned on and the number of antennas converges to a constant when the numbers of transmit and receive antennas approach infinity proportionally. This motivates our power on/off strategy where the number of beams turned on is independent of channel realizations but is a function of the signal-to-noise ratio (SNR). When the feedback rate is finite, beamforming cannot be perfect, and we characterize the effect of imperfect beamforming by quantization bounds on the Grassmann manifold. By combining the results for power on/off and beamforming, a good approximation to the achievable information rate is derived. Simulations show that the proposed strategy is near optimal and the performance approximation is accurate for all experimented SNRs.     

MIMO Broadcast Channels With Finite-Rate Feedback

Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The well-known zero-forcing transmission technique is considered, and simple expressions for the throughput degradation due to finite-rate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the signal-to-noise ratio (SNR) (in decibels) in order to achieve the full multiplexing gain. This is in sharp contrast to point-to-point multiple-input multiple-output (MIMO) systems, in which it is not necessary to increase the feedback rate as a function of the SNR