Transmitter Channel State Information Research Articles

Robust beamforming in the MISO downlink with quadratic channel estimation and optimal training

Estimation of the channel state information (CSI) in quadratic form (i.e., quadratic channel estimation) in the downlink can be performed at the base station by using the relayed signals from the mobile users, which facilitates optimization with transmitter CSI. In this letter, the condition for the optimal training sequence for quadratic channel estimation in a multiuser multiple-input single-output (MISO) antenna system in the downlink is first obtained. The mean-square-error (MSE) in the CSI estimate is then analyzed. Based on the quadratic CSI estimates, a robust beamforming optimization algorithm to minimize the base station power while achieving individual users' quality-of-service (QoS) constraints, measured by the MSE in data reception, is proposed.

Hybrid Digital-Analog Relaying for Cooperative Transmission Over Slow Fading Channels

Hybrid digital-analog coding schemes have been proposed in source-channel coding to increase the robustness toward channel mismatch, in the absence of transmitter channel state information (CSIT). Recognizing that the same kind of robustness is needed at the relay in a three-node relay network, we propose several novel relaying protocols based on hybrid digital-analog transmission. We compare the performance of the new schemes with traditional digital-only (decode-and-forward or compress-and-forward) or analog-only (amplify-and-forward) relaying, as well as to performance bounds corresponding to genie-aided compress-and-forward relaying. Our new protocols achieve significant gains in terms of achievable expected rates, and they are able to close in on the performance bounds. In particular, we conclude that the best overall performance is obtained by an adaptive combination of decode-and-forward and hybrid digital-analog relaying.

Maximizing the Average Spectral Efficiency of Dual-Branch MIMO Systems With Discrete-Rate Adaptation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The capacity of multiple-input–multiple-output (MIMO) systems with perfect transmitter and receiver channel state information (CSI) can be attained by decoupling the MIMO channel into a set of independent subchannels and distributing the power among these subchannels in accordance with the <emphasis emphasistype="boldital"> water-filling</emphasis> solution. Implementation of this scheme on a time-varying channel, however, requires continuous-rate adaptation and is not feasible in any such practical system. In this paper, we show how to maximize the average spectral efficiency (ASE) of dual-branch MIMO systems (either two transmit or two receive antennas) with perfect transmitter and receiver CSI when using a fixed number of codes (discrete-rate adaptation). This maximum ASE is compared with the system's ergodic capacity and with the maximum ASE that can be attained if the available power is distributed among the different subchannels in accordance with the water-filling solution although only discrete-rate adaptation is possible. We assume that capacity-achieving codes for additive white Gaussian noise (AWGN) channels are available and that the power available to the transmitter to transmit the <formula formulatype="inline"><tex>$i$</tex></formula>th symbol frame is fixed and independent of the frame index <formula formulatype="inline"><tex>$i$</tex></formula>. </para>

Finite-SNR Analysis and Optimization of Decode-and-Forward Relaying Over Slow-Fading Channels

We provide analytical results on the finite signal-to-noise ratio (SNR) outage performance of packet-based decode-and-forward relaying over a quasi-static fading channel, with different types of transmitter channel state information (CSI). At the relay, we consider repetition coding (RC) and parallel coding (PC). At the destination, we consider receivers based on selection combining (SC), code combining (CC), and maximum-ratio combining (MRC) (the latter only for the case of RC at the relay). Based on available CSI, we optimize the number of channel uses consumed by the source and by the relay for each packet. In doing so, we consider three different protocols that make use of different combinations of long-term CSI, 1-bit CSI, and complete CSI, respectively, at the source node. Several interesting observations emerge. For example, we show that for high SNRs, SC and CC provide the same outage probabilities when the source has perfect CSI.

Method for efficient representation of the information on the weighting coefficients of a transmitting beamformer in wireless digital communication systems with multielement adaptive antennas

We consider the problem of transmission of channel state information for a transmitting beamformer in digital communication systems with adaptive transmitting and receiving antennas. It is shown that using the unitary property of the weighting matrices of the transmitting beamformer, we can significantly reduce the amount of transmitted information with the help of the well-known Givens decomposition. We propose a method for determining the optimal bit allocation for quantization of the complex weighting coefficients of the transmitting beamformer. Results of mathematical simulation of a wireless digital communication system with multielement adaptive antenna arrays are shown for a multipath Rayleigh channel.

Impact of Spatial Fading Correlation and Keyhole on the Capacity of MIMO Systems with Transmitter and Receiver CSI

This paper investigates the impact of spatial fading correlation and keyhole (pinhole) condition on the capacity of multiple-input multiple-output (MIMO) channels when instantaneous channel state information (CSI) is available at the transmitter and receiver sides. A separable correlation model is considered, whereby spatial fading correlation is accounted for at either or at both sides of the collocated MIMO wireless channel. Two extreme scenarios of a double scattering environment are analyzed: (i) an extremely rich scattering environment corresponding to a conventional semi-correlated Rayleigh fading channel and (ii) a double-correlated rank-deficient keyhole channel with a single degree of freedom. In the case of semi-correlated Rayleigh fading, the capacity expressions are derived for two types of correlation structures among the transmitting or the receiving antennas, namely, a constant correlation model and an arbitrary correlation model, the latter being induced by a full-rank Hermitian covariance matrix with non-repeating distinct eigenvalues. On the other hand, the capacity expressions pertaining to the double-correlated keyhole channel are derived given arbitrary Hermitian covariance matrices at the transmitter and the receiver. For all channel types and correlation structures, closed-form expressions for the capacity of the eigen-mode optimal power and rate adaptation policy as well as for the sub-optimal eigen-mode channel inversion and its truncated variant are derived. Monte Carlo simulations are also carried out thereby upholding our theoretical analysis.

Quantized Principal Component Selection Precoding for Spatial Multiplexing with Limited Feedback

In this paper, for spatial multiplexing with limited feedback, a quantized principal component selection (QPCS) precoding scheme is proposed that achieves comparable capacity to the closed-loop multiple-input multiple-output (MIMO) and furthermore adapts to various fading channel conditions without any additional feedback bits and transmit channel state information (CSI). We propose a systematic design method for a codebook consisting of a finite number of unitary matrices based on a maximizing minimum distance criterion in the one- dimensional angular domain and show that the method outperforms the Grassmannian subspace packing method in various fading channel conditions. The proposed QPCS precoding scheme allows for adjustment of the precoding matrix based on limited feedback information on the principal vectors approximating a MIMO channel in the angular domain according to various channel conditions. Furthermore, for practical implementation of the QPCS precoding scheme, we propose a structured precoder optimization procedure and show that the proposed procedure induces a negligible capacity loss compared with the exhaustive precoder optimization, even with considerably reduced complexity.

Capacity of MIMO Rician fading channels with transmitter and receiver channel state information

This paper investigates the capacity of multiple- input multiple-output (MIMO) wireless communication systems when instantaneous channel state information (CSI) is available at both the transmitter and the receiver in a line-of-sight Rician fading environment. Specifically, an infinite series representation for the ergodic capacity of MIMO channels subject to uncorrected Rician fading (URiF) is derived, assuming both transmitter and receiver CSI. The ergodic capacity and its associated outage probability are expressed as a function of a cutoff value capturing the optimal power allocation scheme. Moreover, an equation for evaluating the cutoff value using standard numerical search techniques is derived, along with closed-form expressions for the capacity of the URiF MIMO channel when the so-called eigen-mode channel inversion technique and its truncated variant are implemented. We then provide numerical results showing the effects of Ricianness on the capacity of the eigen-mode optimal power and rate adaptation, and the sub-optimal channel inversion techniques and compare the achievable spectral efficiencies with and without channel knowledge at the transmitter thereby highlighting the capacity gains enabled by channel side information in a Rician fading environment.

Achievable Rates with Imperfect Transmitter Side Information Using a Broadcast Transmission Strategy

rdquoWe investigate the performance of the broadcast approach for various fading distributions, which correspond to different models of partial transmit channel state information (CSI). The first model considered is the quantized limited feedback. In this model, the receiver can send as feedback only a finite number of bits describing the fading gain. We derive the optimal power allocation for the broadcast approach for the quantized feedback model. For a Rayleigh fading channel, numerical results here show that if the feedback word can be longer than one bit, the broadcasting gain becomes negligible, due to diminished channel uncertainty. The second partial transmit CSI model is a stochastic Gaussian model with mean and variance information, which is commonly used for modeling the channel estimation error. In a single-input single-output (SISO) channel, this model also corresponds to the Ricean fading distribution, for which we derive maximal achievable broadcasting rates. We further consider a multiple-input single-output (MISO) channel, and derive the optimal power allocation strategy in a broadcast approach. Numerical results here show that uniform power allocation is preferable over beamforming power allocation in the region where broadcasting gain over single level coding is non-negligible.

Capacity-Approaching Multiple Coding for MIMO Rayleigh Fading Systems With Transmit Channel State Information

We study transmit power adaptation and capacity-approaching coding/decoding in multiple-input-multiple-output (MIMO) Rayleigh fading channels under the assumption that perfect channel state information (CSI) is known at both the transmitter and the receiver. The capacity in MIMO systems with transmitter CSI can be achieved via two schemes: 1) a multiple-coding scheme with temporal and spatial water filling and 2) a single-coding scheme with temporal and spatial water filling. The former requires an infinite number of different codes, and the latter one requires interblock coding and, therefore, a very long code. We propose three simple but powerful methods for transforming the MIMO fading channel into a set of additive white Gaussian noise channels to which standard codes for the Gaussian channel can then be applied. We show through a number of examples that these methods can closely approach channel capacity. As a by-product, the closed-form expressions of the marginal probability density function of the ordered and unordered eigenvalues of Wishart matrices are derived.

The Poisson Fading Channel

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this first paper of a two-part series, a single-user single-input single-output (SISO) shot-noise-limited Poisson channel is considered over which an information signal is transmitted by modulating the intensity of an optical beam, and individual photon arrivals are counted at the photodetector receiver. The transmitted signal, which is chosen to satisfy peak and average constraints, undergoes multiplicative fading, which occurs over coherence time intervals of fixed duration. The fade coefficient (channel state) remains constant in each coherence interval, and varies across successive such intervals in an independent and identically distributed (i.i.d.) fashion. A single-letter characterization of the capacity of this channel is obtained when the receiver is provided with perfect channel state information (CSI) while the transmitter CSI can be imperfect. The asymptotic behavior of channel capacity in the low and high peak-signal-to-shot-noise ratio (SNR) regimes is studied. </para>

Interpolation-Based Multi-Mode Precoding for MIMO-OFDM Systems with Limited Feedback

Spatial multiplexing with multi-mode precoding provides a means to achieve both high capacity and high reliability in multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems. Multi-mode precoding uses linear transmit precoding that adapts the number of spatial multiplexing data streams or modes, according to the transmit channel state information (CSI). As such, it typically requires complete knowledge of the multi-mode precoding matrices for each subcarrier at the transmitter. In practical scenarios where the CSI is acquired at the receiver and fed back to the transmitter through a low-rate feedback link, this requirement may entail a prohibitive feedback overhead. In this paper, we propose to reduce the feedback requirement by combining codebook-based precoder quantization, to efficiently quantize and represent the optimal precoder on each subcarrier, and multi-mode precoder frequency down-sampling and interpolation, to efficiently reconstruct the precoding matrices on all subcarriers based on the feedback of the indexes of the quantized precoders only on a fraction of the subcarriers. To enable this efficient interpolation-based quantized multimode precoding solution, we introduce (1) a novel precoder codebook design that lends itself to precoder interpolation, across subcarriers, followed by mode selection, (2) a new precoder interpolator and, finally, (3) a clustered mode selection approach that significantly reduces the feedback overhead related to the mode information on each subcarrier. Monte-Carlo bit-error rate (BER) performance simulations demonstrate the effectiveness of the proposed quantized multi-mode precoding solution, at reasonable feedback overhead

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

Outage Probability Based Optimal Transmission of Space Time Block Codes over Correlated Distributed Antennas

Aiming to optimally transmit space-time block codes (STBCs) over distributed antennas (DAs), this paper examines downlink transmit antenna subset selection with power allocation for STBCs in non-ergodic Rayleigh fading channels with receive antenna correlations. Closed-form outage probability is first derived, which is a function of data rate, rate of STBCs, transmit power, large-scale fading (shadowing and path loss), power allocation weights to each DA and receive antenna correlation. However, achieving the optimal power allocation solution is computationally demanding and the use of sub-optimal techniques is necessitated. Assuming feedback of eigenvalues of transmit and receive antenna correlation matrix at the transmitter and accurate channel state information (CSI) at the receiver, an antenna subset selection with sub-optimal power allocation scheme is proposed, whose performance approaches optimal. The effectiveness of this sub-optimal method has been demonstrated by numerical results.

Unquantized and uncoded channel state information feedback in multiple-antenna multiuser systems

We propose a channel state information (CSI) feedback scheme based on unquantized and uncoded (UQ-UC) transmission. We consider a system where a mobile terminal obtains the downlink CSI and feeds it back to the base station using an uplink feedback channel. If the downlink channel is an independent Rayleigh fading channel, then the CSI may be viewed as an output of a complex independent identically distributed Gaussian source. Further, if the uplink feedback channel is an additive white Gaussian noise channel, and the downlink CSI is perfectly known at the mobile terminal, it can be shown that UQ-UC CSI transmission (that incurs zero delay) is optimal in that it achieves the same minimum mean-squared error distortion as a scheme that optimally (in the Shannon sense) quantizes and encodes the CSI, while theoretically incurring infinite delay. Since the UQ-UC transmission is suboptimal on correlated wireless channels, we propose a simple linear CSI feedback receiver that can be used to improve the performance of UQ-UC transmission while still retaining the attractive zero-delay feature. We provide bounds on the performance of such UQ-UC CSI feedback and study its impact on the achievable information rates. Furthermore, we explore its application and performance in multiple-antenna multiuser wireless systems, and also propose a corresponding pilot-assisted channel-state estimation scheme

Robust transmit eigen beamforming based on imperfect channel state information

Transmit beamforming is a powerful technique for enhancing the performance and increasing the throughput of wireless communication systems that employ multiple antennas at the transmitter. A major drawback of most existing transmit beamforming techniques is that they require nearly perfect knowledge of the channel at the transmitter, which is typically not available in practice. Transmitter designs that address the imperfect channel state information (CSI) problem commonly use statistical models for the channel and/or mismatch between the presumed and actual transmitter CSI. Since these approaches are model based, they can suffer from mismodeling. In this paper, a more robust framework is proposed in which no statistical assumptions are made about the CSI mismatch or the channel. The goal is to design a transmitter that has the best performance under the worst-case CSI mismatch. The transmitter designed herein achieves this goal for all CSI mismatches below a certain threshold level. The proposed design combines beamforming along the eigenvectors of the (deterministic) autocorrelation of the channel matrix perceived by the transmitter and power loading across those beams. While the power-loading algorithm resembles conventional water-filling to some degree, it explicitly incorporates robustness to the CSI mismatch, and the water level can be determined in a simple systematic way.

Capacity Bounds and Power Allocation for Wireless Relay Channels

We consider three-node wireless relay channels in a Rayleigh-fading environment. Assuming transmitter channel state information (CSI), we study upper bounds and lower bounds on the outage capacity and the ergodic capacity. Our studies take into account practical constraints on the transmission/reception duplexing at the relay node and on the synchronization between the source node and the relay node. We also explore power allocation. Compared to the direct transmission and traditional multihop protocols, our results reveal that optimum relay channel signaling can significantly outperform multihop protocols, and that power allocation has a significant impact on the performance.

On Channels With Partial Channel State Information at the Transmitter

We consider an independent and identically distributed (i.i.d.) state-dependent channel with partial (rate-limited) channel state information (CSI) at the transmitter (CSIT) and full CSI at the receiver (CSIR). The CSIT comprises two parts, both subject to a rate constraint, and communicated over noiseless way-side channels. The first part is coded CSI, provided by a third party (a genie), and the second part is the output of a deterministic scalar quantizer of the state. A single-letter expression for the capacity of the channel is given. In case the CSIT comprises only the coded part, we show that the capacity previously suggested in the literature is too optimistic, and suggest a correction as part of our expression for the information capacity. For the general setting, an optimal coding scheme based upon multiplexing of several codebooks is presented. It is proved that the capacity of the channel is the same whether the quantizer's output is observed causally or noncausally by the encoder. In the rest of the correspondence, we focus on the special case where the system employs a stationary quantizer. Using a rate distortion approach we bound the alphabet's size of the auxiliary random variable (RV) of the information capacity. Next, we turn to the additive white Gaussian noise (AWGN) channel with fading, and show that the determination of the capacity region reduces to finding the optimal genie strategies and the optimal power allocation distribution along the product alphabet of the auxiliary RV and the quantizer's output alphabets. The suggested model can be applied, for example, to an orthogonal frequency-division multiplexing (OFDM) communication system. Here the fading across frequencies comprises the channel state sequence. Coded fading information is provided to the channel encoder via a way-side, rate-limited channel. In addition, since coding operation is expensive, a simpler scheme provides the channel encoder with quantized fading information, e.g., whether each coefficient is above/below a threshold.

On the Design of Adaptive Space–Time Codes

In this letter, we investigate the design of adaptive space-time codes that exploit partial transmitter channel state information (CSI). We introduce the adaptive space-time parsing paradigm as a generalization of the transmitter selection-diversity approach. We then use this new framework to construct full-diversity adaptive space-time codes for delay-limited applications with fixed-rate transmission. The proposed codes allow for reduced-complexity decoders and are robust to inaccuracies in the transmitter CSI.

On the Ergodic Capacity as a Function of the Correlation Properties in Systems With Multiple Transmit Antennas Without CSI at the Transmitter

In this letter, the impact of correlation of the transmit antennas of a multiple-input single-output (MISO) system, with no channel state information (CSI) at the transmitter and perfect CSI at the receiver is analyzed. We show that the ergodic capacity for the single-user MISO system is Schur-concave with respect to the vector with eigenvalues of the channel covariance matrix, i.e., the more correlation that exists between the transmit antennas, the less is the achievable capacity. Furthermore, the capacity loss for fully correlated transmit antennas in comparison with the uncorrelated case is derived. The results for the ergodic capacity are compared with the impact of correlation on the outage probability. The relationship between correlation properties and outage probability is more complicated than the relationship between the correlation properties and the ergodic capacity. It is shown that the outage probability is Schur-convex in the high signal-to-noise ratio (SNR) regime, and Schur-concave in the low SNR regime.