Quantized Channel State Information Research Articles

Optimized One-Way Relaying Strategy With Outdated CSI Quantization for Spatial Multiplexing

This correspondence considers a MIMO relay downlink system using precoding and limited feedback. Since the conventional precoding matrices are directly obtained by treating the quantized channel state information (CSI) feedback as real CSI, we propose an optimized relay precoding strategy by taking both effects of channel quantization error and feedback delay into account. Conditioned on the outdated CSI quantization available at the relay station, the relay precoding is optimized via minimizing an expected mean-square error (MSE) criterion over CSI mismatches. By using Karush-Kuhn-Tucker (KKT) conditions, a closed-form solution to the relay design is achieved with comparable computational complexity relative to the conventional approach. Numerical results verify the effectiveness of the proposed scheme.

On Hybrid ARQ and Quantized CSI Feedback Schemes in Quasi-Static Fading Channels

Recently, substantial attention has been paid to increase the achievable rates of wireless networks using different kinds of limited channel quality information feedback. Hybrid automatic repeat request (ARQ) and quantized channel state information (CSI) feedback are two well-known approaches applied by experts to provide the limited channel quality information at the transmitter. Considering quasi-static fading channels, this paper aims to provide some comparisons between the performance of these methods from different points of view. The paper first investigates the power- and outage-limited performance of hybrid ARQ and quantized CSI schemes under short- and long-term power constraints. Then, 1) the feedback signaling load, 2) robustness and 3) the complexity of these schemes are compared under short-term transmission power constraint. Both INcremental Redundancy (INR) and Repetition Time Diversity (RTD) approaches are considered for hybrid ARQ feedback. Finally, approximate low-complexity solutions are presented for power allocation in the INR ARQ-based scheme under long-term transmission power constraint. Analytical and numerical results demonstrate the equivalency or the superiority of these approaches in different circumstances.

Adaptive Discrete Rate and Power Transmission for Spectrum Sharing Systems

In this paper we develop a framework for optimizing the performance of the secondary link in terms of the average spectral efficiency assuming quantized channel state information (CSI) of the secondary and the secondary-to-primary interference channels available at the secondary transmitter. We consider the problem under the constraints of maximum average interference power levels at the primary receiver. We develop a sub-optimal computationally efficient iterative algorithm for finding the optimal CSI quantizers as well as the discrete power and rate employed at the cognitive transmitter for each quantized CSI level so as to maximize the average spectral efficiency. We show via analysis and simulations that the proposed algorithm converges for Rayleigh fading channels. Our numerical results give the number of bits required to sufficiently represent the CSI to achieve almost the maximum average spectral efficiency attained using full knowledge of the CSI.

On the Performance of Time-Orthogonal Incremental Relaying Based on Demodulate-and-Forward With Distributed Channel Access

This paper considers demodulate-and-forward (DmF)-based incremental relaying (IR) in a distributed setting, where each relay locally makes the decision on cooperation to eliminate network-wide coordination. Unlike traditional IR schemes that use destination feedback merely to activate relays for cooperation, the considered schemes include quantized channel state information (CSI) in destination feedback to facilitate local relay decision. Moreover, two timer-based backoff schemes are employed as the distributed relay selection method. Important performance metrics, including outage probability and average duration to complete a transmission cycle, are derived in closed form for flat Rayleigh fading channels. Comparisons with the well-known distributed relaying schemes are conducted. Numerical results demonstrate that DmF-based IR with quantized feedback serves as a promising solution for low-complexity power-limited wireless networks.

R bits user selection switch feedback for zero forcing MU-MIMO based on low rate codebook

Channel feedback for multi-user (MU)-multiple-input multiple-output (MIMO) has been widely studied and some results have been got with random vector quantization scheme. However, while the low rate fixed codebook feedbacks are adopted, the performance of zero forcing (ZF) MU-MIMO will decrease as the unpredictable inter-user interference is introduced because of quantized channel state information (CSI). To decrease inter-user interference in low rate fixed codebook feedback, an enhanced user selection switch (USS) feedback scheme for ZF MU-MIMO is proposed in this article. In USS feedback, the extra USS information is added after quantized CSI and received signal-to-noise ratio feedback. The USS information indicates inter-user interference and it can be used in user selection procedure to avoid large inter-user interference. Simulation results show that the proposed USS feedback scheme is efficient to solve the problems of unpredictable inter-user interference in conventional feedback scheme with low rate codebook in ZF MU-MIMO.

CSI Feedback in Correlated Slow-Fading Channels

This letter studies the effect of quantized channel state information (CSI) feedback on the average rate of correlated channels. Demonstrating the general rate optimization problem, the results are obtained for both delayed and delay-free feedback conditions under different short- and long-term power allocation strategies. We also evaluate the effect of adaptive CSI quantization on the channel average rate. Analytical and numerical results show that exploiting the channel memory not only increases the forward channel data transmission efficiency but also can lead to dramatic feedback rate reduction.

Optimizing Orthogonal Multiple Access Based on Quantized Channel State Information

The performance of systems where multiple users communicate over wireless fading links benefits from channel-adaptive allocation of the available resources. Different from most existing approaches that allocate resources based on perfect channel state information, this work optimizes channel scheduling along with per user rate and power loadings over orthogonal fading channels, when both terminals and scheduler rely on quantized channel state information. Channel-adaptive policies are designed to optimize an average transmit-performance criterion subject to average quality of service requirements. While the resultant optimal policy per fading realization shows that the individual rate and power loadings can be obtained separately for each user, the optimal scheduling is slightly more complicated. Specifically, per fading realization each channel is allocated either to a single (winner) user, or to a small group of winner users whose fraction of shared resources is found by solving a linear program. This bimodal scheduling is also the optimal one when the channels are deterministic. A single scheduling scheme combining both alternatives (modes) becomes possible by smoothing the original disjoint scheme. The smooth scheduling is asymptotically optimal and incurs reduced computational complexity. Different alternatives to obtain the Lagrange multipliers required to implement the channel-adaptive policies are proposed, including stochastic iterations that are provably convergent and do not require knowledge of the channel distribution.

Grassmannian Subspace Prediction for Precoded Spatial Multiplexing MIMO With Delayed Feedback

In unitary precoded multi-antenna systems with delayed feedback, the quantized channel state information (CSI) may become outdated before its actual use at the transmitter. In this letter, by exploiting the geometric properties of the Grassmannian manifold, we invoke the use of Grassmannian subspace predictive coding (GSPC) to overcome this problem. Under the framework of GSPC, a novel limited feedback strategy is proposed which consists of a two-stage optimization process at the receiver. The first stage quantizes the estimated CSI by accounting for the feedback delay; while the second stage optimizes the prediction on the Grassmannian manifold.

Outage Analysis of Distributed Scheme on Opportunistic Relaying with Limited CSI

In this letter, we propose a distributed scheme on opportunistic amplify-and-forward (AF) relaying to minimize the system outage probability with low feedback overhead. Only the subset of relays report the calculated outage probability information to the source based on the outage probability threshold with the limited channel state information (CSI). We present the approximate expressions for the system outage probability under two scenarios, the statistical CSI and the statistical quantized CSI of the relay-destination links, respectively. Numerical results indicate that the derived analytic results are reasonable and the outage performance is better for the statistical quantized CSI case with acceptable feedback cost.

Resource allocation for maximizing outage throughput in OFDMA systems with finite-rate feedback

Abstract Previous works on orthogonal frequency division multiple access (OFDMA) systems with quantized channel state information (CSI) were mainly based on suboptimal quantization methods. In this paper, we consider the performance limit of OFDMA systems with quantized CSI over independent Rayleigh fading channels using the rate-distortion theory. First, we establish a lower bound on the capacity of the feedback channel and build the test channel that achieves this lower bound. Then, with the derived test channel, we characterize the system performance with the outage throughput and formulate the outage throughput maximization problem with quantized channel state information (CSI). To solve this problem in low complexity, we develop a suboptimal algorithm that performs resource allocation in two steps: subcarrier allocation and power allocation. Using this approach, we can numerically evaluate the outage throughput in terms of feedback rate. Numerical results show that this suboptimal algorithm can provide a near optimal performance (with a performance loss of less than 5%) and the outage throughput with a limited feedback rate can be close to that with perfect CSI.

Diversity-Multiplexing Trade-off in Adaptive Two-Way Relaying

Resource allocation for symmetric half-duplex bidirectional relaying networks is considered. Various decode-and-forward (DF) based relaying strategies that efficiently exploit quantized channel state information (CSI) at the transmitters (CSIT) are investigated. Adapting the number of channel uses for each relaying phase and allocating transmit power based on limited CSIT is shown to result in a significant improvement in the diversity-multiplexing trade-off (DMT). Without a direct link between the sources, power control is instrumental to efficiently exploit CSI feedback from sources to relay, resulting in superior performance that matches corresponding upper bounds in certain cases. With direct links between the sources, it is shown that DF two-way relaying does not suffer from a diversity loss when the multiplexing gain is high, a significant improvement over the dynamic DF protocol for one-way relaying. The best DMT is achieved when each source broadcasts partial CSI to the other nodes in the network, allowing them to adapt their transmit powers.

Power Allocation in Spectrum Sharing Cognitive Radio Networks with Quantized Channel Information

We consider a wideband spectrum sharing system where a secondary user can access a number of orthogonal frequency bands each licensed to a distinct primary user. We address the problem of optimum secondary transmit power allocation for its ergodic capacity maximization subject to an average sum (across the bands) transmit power constraint and individual average interference constraints on the primary users. The major contribution of our work lies in considering quantized channel state information (CSI) (for the vector channel space consisting of all secondary-to-secondary and secondary-to-primary channels) at the secondary transmitter as opposed to the prevalent assumption of full CSI in most existing work. It is assumed that a central entity called a cognitive radio network manager has access to the full CSI information from the secondary and primary receivers and designs (offline) an optimal power codebook based on the statistical information (channel distributions) of the channels and feeds back the index of the codebook to the secondary transmitter for every channel realization in real-time, via a delay-free noiseless limited feedback channel. A modified Generalized Lloyds-type algorithm (GLA) is designed for deriving the optimal power codebook, which is proved to be globally convergent and empirically consistent. An approximate quantized power allocation (AQPA) algorithm is presented, that performs very close to its GLA based counterpart for large number of feedback bits and is significantly faster. We also present an extension of the modified GLA based quantized power codebook design algorithm for the case when the feedback channel is noisy. Numerical studies illustrate that with only 3-4 bits of feedback per band, the modified GLA based algorithms provide secondary ergodic capacity very close to that achieved by full CSI and with only as little as 4 bits of feedback per band, AQPA provides a comparable performance, thus making it an attractive choice for practical implementation.

Distributed Adaptation of Quantized Feedback for Downlink Network MIMO Systems

This paper focuses on quantized channel state information (CSI) feedback for downlink network MIMO systems. Specifically, we propose to quantize and feedback the CSI of a subset of BSs, namely the feedback set. Our analysis reveals the tradeoff between better interference mitigation with large feedback set and high CSI quantization precision with small feedback set. Given the number of feedback bits and instantaneous/long-term channel conditions, each user optimizes its feedback set distributively according to the expected SINR derived from our analysis. Simulation results show that the proposed feedback adaptation scheme provides substantial performance gain over non-adaptive schemes, and is able to effectively exploit the benefits of network MIMO under various feedback bit budgets.

Downlink Throughput Maximization for OFDMA Systems With Feedback Channel Capacity Constraints

In this correspondence, we study the downlink throughput maximization for orthogonal frequency-division multiple-access (OFDMA) systems in the presence of feedback channel capacity constraints. We establish an information-theoretic lower bound on the capacity of feedback channel and build the corresponding test channel that achieves this lower bound. Based on the derived test channel, we formulate two optimization problems that maximize the downlink throughput with quantized channel state information (CSI): i) one problem where throughput is defined with the ergodic throughput and ii) the other problem with the outage throughput, from which we can see the performance limit for given limit feedback channels. We solve the throughput maximization problem through an iterative approach, which achieves the optimal ergodic throughput and the near-optimal outage throughput. Numerical results show that the downlink throughput with a limited feedback of CSI can be close to that with perfect CSI by exploiting correlation properties of downlink CSI for quantization.

Channel Capacity Bounds in the Presence of Quantized Channel State Information

The goal of this paper is to investigate the effect of channel side information on increasing the achievable rates of continuous power-limited non-Gaussian channels. We focus on the case where (1) there is imperfect channel quality information available to the transmitter and the receiver and (2) while the channel gain is continuously varying, there are few cross-region changes, and the noise characteristics remain in each detection region for a long time. The results are presented for two scenarios, namely, reliable and unreliable region detection. Considering short- and long-term power constraints, the capacity bounds are found for log-normal and two different Nakagami-based channel distributions, and for both Max-Lloyd and equal probability quantization approaches. Then, the optimal gain partitioning approach, maximizing the achievable rates, is determined. Finally, general equations for the channel capacity bounds and optimal channel partitioning in the case of unreliable region detection are presented. Interestingly, the results show that, for high SNR's, it is possible to determine a power-independent optimal gain partitioning approach maximizing the capacity lower bound which, in both scenarios, is identical for both short- and long-term power constraints.

Downlink Opportunistic Scheduling with Low-Rate Channel State Feedback: Error Rate Analysis and Optimization of the Feedback Parameters

In this paper, the downlink opportunistic scheduling approach is studied in a multiuser environment with single-antenna transmitter and users. Exact bit error rate (BER) expressions are derived under the assumptions of full and quantized channel state information (CSI) at the transmitter. These expressions are then used to optimize the channel state feedback parameters. Moreover, asymptotic BERs are investigated in the limiting cases of a high signal-to-noise ratio (SNR) and a large number of users K. It is shown that both under the full and quantized CSI assumptions, the achieved BER is proportional to SNR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-K</sup> and K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-SNR</sup> in these two asymptotic cases, respectively. This means that the diversity order is equal to K, whereas the multiuser diversity gain is equal to SNR. In the case when the CSI feedback is quantized, the impact of feedback errors on the achieved BER is studied. It is shown that the opportunistic scheduling can greatly improve the BER performance even if the feedback is quite low-rate and erroneous.

MIMO Relaying Broadcast Channels With Linear Precoding and Quantized Channel State Information Feedback

Multi-antenna relaying has emerged as a promising technology to enhance the system performance in cellular networks. However, when precoding techniques are utilized to obtain multi-antenna gains, the system generally requires channel state information (CSI) at the transmitters. We consider a linear precoding scheme in a MIMO relaying broadcast channel with quantized CSI feedback from both two-hop links. With this scheme, each remote user feeds back its quantized CSI to the relay, and the relay sends back the quantized precoding information to the base station (BS). An upper bound on the rate loss due to quantized channel knowledge is first characterized. Then, in order to maintain the rate loss within a predetermined gap for growing SNRs, a strategy of scaling quantization quality of both two-hop links is proposed. It is revealed that the numbers of feedback bits of both links should scale linearly with the transmit power at the relay, while only the bit number of feedback from the relay to the BS needs to grow with the increasing transmit power at the BS. Numerical results are provided to verify the proposed strategy for feedback quality control.

Capacity bounds of transmit beamforming over MISO time-varying channels with imperfect feedback

In wireless multiple input single output (MISO) systems, transmit beamforming using feedback of quantized channel state information (CSI) can provide both diversity gain and array gain with simple implementation. Most of previous researches include several ideal assumptions, such as block-fading channels, perfect CSI at the receiver, or error-free and zero-delay feedback link. This paper investigates a more realistic Jakes’ time-varying MISO Rayleigh fading channel with CSI estimation error and feedback delay, derives the upper and lower bounds on the ergodic capacity, and obtains the optimal frame length according to the capacity lower bound given the normalized feedback bits. The numerical and simulation results show that the derived upper and lower bounds on the capacity is quite close, increasing channel estimation error or Doppler spread will reduce the capacity bounds, and the optimal frame length can maximize the capacity lower bound.

Capacity Limits and Performance Analysis of Cognitive Radio With Imperfect Channel Knowledge

Cognitive radio (CR) design aims to increase spectrum utilization by allowing the secondary users (SUs) to coexist with the primary users (PUs), as long as the interference caused by the SUs to each PU is properly regulated. At the SU, channel-state information (CSI) between its transmitter and the PU receiver is used to calculate the maximum allowable SU transmit power to limit the interference. We assume that this CSI is imperfect, which is an important scenario for CR systems. In addition to a peak received interference power constraint, an upper limit to the SU transmit power constraint is also considered. We derive a closed-form expression for the mean SU capacity under this scenario. Due to imperfect CSI, the SU cannot always satisfy the peak received interference power constraint at the PU and has to back off its transmit power. The resulting capacity loss for the SU is quantified using the cumulative-distribution function of the interference at the PU. Additionally, we investigate the impact of CSI quantization. To investigate the SU error performance, a closed-form average bit-error-rate (BER) expression was also derived. Our results are confirmed through comparison with simulations.

Multi-Mode Transmission for the MIMO Broadcast Channel with Imperfect Channel State Information

This paper proposes an adaptive multi-mode transmission strategy to improve the spectral efficiency achieved in the multiple-input multiple-output (MIMO) broadcast channel with delayed and quantized channel state information. The adaptive strategy adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual inter-user interference. Accurate closed-form approximations are derived for the achievable rates for different modes, which help identify the active mode that maximizes the average sum throughput for given feedback delay and channel quantization error. The proposed transmission strategy can be easily combined with round-robin scheduling to serve a large number of users. As instantaneous channel information is not exploited, the proposed algorithm cannot provide multiuser diversity gain, but it is still able to provide throughput gain over single-user MIMO at moderate signal-to-noise ratio. In addition, it has a light feedback overhead and only requires feedback of instantaneous channel state information from a small number of users. In the system with a feedback load constraint, it is shown that the proposed algorithm provides performance close to that achieved by opportunistic scheduling with instantaneous feedback from a large number of users.