Quantized Channel State Information Research Articles

Evaluation of Distributed Multi-User MIMO-OFDM With Limited Feedback

In this article, we investigate the performance of cellular networks employing remote radio units to enable distributed multi-user MIMO transmission using block-diagonalization precoding. We consider the downlink of an OFDM-based LTE compliant multi-carrier system in which the users provide channel state information (CSI) to the base station via limited capacity feedback links. With limited feedback, residual interference between the spatially multiplexed users cannot be avoided, causing an interference-limitation of the achievable downlink throughput. Efficient CSI quantization is therefore central in such systems to achieve a performance gain over single-user MIMO. Building on Grassmannian CSI quantization concepts, we propose an effective CSI feedback clustering approach in this work to exploit the correlation of the wireless channel in the frequency domain. We furthermore derive the corresponding channel quality feedback and propose a practical greedy multi-user scheduler.

Quantized Ergodic Radio Resource Allocation in Cognitive Networks With Guaranteed Quality of Service for Primary Network

In this paper, for cognitive networks, ergodic resource allocation (ERA) in the downlink of an OFDMA-based secondary network is investigated, assuming the availability of quantized channel state information (CSI) between the secondary base station and secondary users. The main objective is to maximize the average sum rate of the secondary network subject to the average total transmission power constraint and the collision probability constraint of the primary users on each subcarrier. In the proposed scheme, there is no need for the instantaneous handshaking between secondary and primary networks to provide CSI between the secondary base station and primary receivers. In fact, the secondary base station only needs the knowledge of channel distribution information. Due to the probabilistic nature of the collision probability constraint in the proposed ERA problem, it cannot be solved by conventional methods such as dual decomposition. Therefore, we propose two novel suboptimal solutions called the iterative and analytical approaches. It is also demonstrated that the solutions obtained based on the proposed approaches are very close to the optimal solution. Numerical experiments are then carried out to demonstrate the performance of the proposed methods. Numerical results show that the performance of the analytical approach is inferior to that of the iterative approach, although it exhibits significantly less computational complexity.

Robust Multiple-Antenna Cooperative Spectrum Sharing Design With Random Vector Quantization

In this paper, we propose cognitive overlay transceiver designs, where a primary transceiver pair and a secondary transceiver pair coexist in a network, and the primary user (PU) allows the secondary user (SU) to concurrently transmit its signals at the price of reducing the power of the PU's signal relayed by cooperative amplify-and-forward (AF). Since the considered transceiver design is mainly to devise the precoders both for the PU and the SU at the secondary transmitter (ST), the channel state information (CSI) has to be known at the ST. We therefore consider the limited feedback scheme with random vector quantization (RVQ), where the ST can only know the quantized channel direction information (CDI). Considering the statistics of the CSI quantization error and the linear minimum mean square error (LMMSE) receiver, we derive the closed-form MSE expressions corresponding to the PU and the SU. With the derived MSEs, we propose two robust design criteria. One criterion is to minimize the ST's power consumption under the constraint that the PU's and SU's quality-of-service (QoS; i.e., MSE) can be met. The other criterion is to minimize the SU's MSE when the PU's QoS can be controlled under a certain value and the ST satisfies the limitation of its transmission power consumption. Both the optimization problems of the proposed design criteria are not convex, and the corresponding solutions cannot be directly obtained. We then propose transfering the original optimization problems into two subproblems, where each of them is eventually formulated as a convex optimization problem, and the solutions are iteratively obtained, which is effective. Thus, the results can be obtained with the interior-point method. Simulations certify the robustness of our designs.

Interference Alignment With Partial CSI Feedback in MIMO Cellular Networks

Interference alignment (IA) is a linear precoding strategy that can achieve optimal capacity scaling at high SNR in interference networks. However, most existing IA designs require full channel state information (CSI) at the transmitters, which would lead to significant CSI signaling overhead. There are two techniques, namely CSI quantization and CSI feedback filtering, to reduce the CSI feedback overhead. In this paper, we consider IA processing with CSI feedback filtering in MIMO cellular networks. We introduce a novel metric, namely the feedback dimension, to quantify the first order CSI feedback cost associated with the CSI feedback filtering. The CSI feedback filtering poses several important challenges in IA processing. First, there is a hidden partial CSI knowledge constraint in IA precoder design which cannot be handled using conventional IA design methodology. Furthermore, existing results on the feasibility conditions of IA cannot be applied due to the partial CSI knowledge. Finally, it is very challenging to find out how much CSI feedback is actually needed to support IA processing. We shall address the above challenges and propose a new IA feasibility condition under partial CSIT knowledge in MIMO cellular networks. Based on this, we consider the CSI feedback profile design subject to the degrees of freedom requirements, and we derive closed-form trade-off results between the CSI feedback cost and IA performance in MIMO cellular networks.

Achievable Rate Analysis and Feedback Design for Multiuser MIMO Relay with Imperfect CSI

This paper investigates a multiuser MIMO relay downlink system with imperfect channel estimation and limited feedback. We analyze the achievable rate loss due to channel state information (CSI) mismatch arising from both channel estimation and quantization feedback. We first derive an upper bound to characterize the effect of imperfect CSI, and then present a limited feedback strategy for both the two-hop channels in the relay system. This newly presented feedback strategy reveals the relationship among the CSI quantization levels, the transmit power, and the pilots for channel estimation. An optimized pilot design at the base station and the relay is also presented by applying the derived bounds for the two-hop system.

Channel quantization for block diagonalization with limited feedback in multiuser MIMO downlink channels

Block diagonalization (BD) has been proposed as a simple and effective technique in multiuser multiple-input multiple-output (MU-MIMO) broadcast channels. However, when channel state information (CSI) knowledge is limited at the transmitter, the performance of the BD may be degraded because inter-user interference cannot be completely eliminated. In this paper, we propose an efficient CSI quantization technique for BD preceded systems with limited feedback where users supported by a base station are selected by dynamic scheduling. First, we express the received signal-to-interference-plus-noise ratio (SINR) when multiple data streams are transmitted to the user, and derive a lower bound expression of the expected received SINR at each user. Then, based on this measure, each user determines its quantized CSI feedback information which maximizes the derived expected SINR, which comprises both the channel direction and the amplitude information. From simulations, we confirm that the proposed SINR-based channel quantization scheme achieves a significant sum rate gain over the conventional method in practical MU-MIMO systems.

Wireless Energy and Information Transfer Tradeoff for Limited-Feedback Multiantenna Systems With Energy Beamforming

In this paper, we consider a multi-antenna system where the receiver should harvest energy from the transmitter by wireless energy transfer to support its wireless information transmission. In order to maximize the harvesting energy, we propose to perform adaptive energy beamforming according to the instantaneous channel state information (CSI). To help the transmitter to obtain the CSI for energy beamforming, we further propose a win-win CSI quantization feedback strategy, so as to improve the efficiencies of both power and information transmission. The focus of this paper is on the tradeoff of wireless energy and information transfer by adjusting the transfer duration with a total duration constraint. Through revealing the relationship between transmit power, transfer duration and feedback amount, we derive two wireless energy and information transfer tradeoff schemes by maximizing an upper bound and an approximate lower bound of the average information transmission rate, respectively. Moreover, the impact of imperfect CSI at the receiver is investigated and the corresponding wireless energy and information transfer tradeoff scheme is also given. Finally, numerical results validate the effectiveness of the proposed schemes.

Continuous Power Allocation Strategies for Sensing-Based Multiband Spectrum Sharing

We propose continuous power allocation strategies for secondary users (SUs) based on sensing the primary user (PU) channels in a multiband cognitive radio (CR) network. Unlike the conventional sensing-based spectrum sharing, where there are two transmit power levels corresponding to whether the PU is sensed present or not, in the proposed strategy, the power levels are continuous functions of the sensing statistics, and optimized with respect to the achievable rate of the SU. The continuous power allocation function is parameterized by some channel parameters of the PU and SU, and we treat the cases of perfect and quantized channel state information (CSI) separately, where the former provides an upper bound on the achievable rate with full channel information; and the latter constitutes an efficient practical power allocation method for the SU with statistic/partial channel information. The power control process consists of two phases: in the first phase, the SU listens to the multiple bands licensed to the PU and obtains the sensing statistics, e.g., the received signal energies on these bands; in the second phase, the SU adjusts its transmit power levels on these bands based on the sensing results. Optimal power allocation schemes are derived to maximize the achievable rate at the SU under several possible combinations of the peak/average transmit power constraints at the SU and the peak/average interference power constraints at the PU. Simulation results demonstrate that the proposed strategies can significantly improve the achievable throughput of the SU compared to the conventional methods.

Fairness, power allocation, and CSI quantization in block fading multiuser systems

This paper studies the fairness, power allocation, and channel state information (CSI) quantization in multiuser systems utilizing multiple feedback bits per user. For a given set of schedulers, we obtain the system throughput with different power allocation strategies and any combination of different fading distributions. Moreover, the system performance under user different outage probability constraints is investigated. Assuming homogenous users, as a special case, the throughput is determined for fixed and random request networks. Considering nonidentical fading channels between the transmitter and receivers, the throughput is found under the K-significant average feedback bit allocation technique, and two suboptimal fairness schemes are investigated which satisfy different quality-of-service requirements. The results show that using optimal power allocation, the first quantization region (QR) of each user is the only QR for which no power may be allocated. The system outage probability vanishes as the number of users goes to infinity. Users hard outage probability constraints can be satisfied at the cost of one more QR in the channel quantizer. Finally, the proposed fairness schemes are more flexible than the standard proportional fair (PF) scheduling in dealing with the throughput-fairness tradeoff. However, their superiority over PF scheduling depends on the fairness constraint.

On Coordinated Multi-point Transmission with Partial Channel State Information Via Delayed Feedback

Coordinated multi-point transmission (CoMP) is considered as a strategic approach to handle inter-cell interference, hence increasing spectral efficiency in interference-limited cellular networks. This paper studies a CoMP downlink transmission with delayed and quantized channel state information feedback through a capacity-limited uplink channel. The delay effects and quantization error as well as large scale path loss potentially degrade entire network performance. Under this consideration, we first characterize the system performance in terms of achievable rate for two typical CoMP techniques, namely joint processing (JP) and coordinated beamforming (CBF), in a multi-cell network. Accurate closed-form expressions are derived for evaluating the CoMP performance. Based on the derived results, an adaptive transmission strategy of switching between JP and CBF is proposed to maximize the system throughput and the operating regions of the two schemes are provided under different system setup parameters. Simulation verifies that the superiority of JP or CBF depends on system parameters including feedback delay, codebook size as well as CoMP user locations.

Structured and Sparse Limited Feedback Codebooks for Multiuser MIMO

A key component of multiuser MIMO using zero-forcing precoding is the feedback of quantized channel state information to the base station. A problem arises when each user has a common codebook as the quantized channels can form a singular matrix that results in a reduced sum-rate. In this paper, we propose two new structured constructions to generate different codebooks at each user via transformations of a base codebook. The first construction is based on the Householder transform, which is used to construct a different codebook at each user for most types of base codebooks, with no storage in addition to the base codebook. A feature of our first construction is that the transformed codebook using the Fourier base codebook has a search complexity reduction of up to 50% compared to the standard approach, although only one additional unique codebook can be constructed with this type of base codebook. To construct multiple different codebooks using the Fourier base codebook, we propose a second construction that is based on the representation theory of groups. We show that both our constructions significantly reduce storage requirements compared with the intuitive but impractical random construction, while obtaining the same sum-rate performance. In particular, we only require elements generated directly from the base codebook or from finite fields, instead of random complex numbers.

Limited Feedback-Based Multi-Antenna Relay Broadcast Channels with Block Diagonalization

The relay technology is effective in extending radio coverage and improving the performance of cell edge users. In multi-antenna relay channels, good knowledge of the channel state information (CSI) at the transmitter is important to achieve multiplexing gains of the multiple-input multiple-output technique. In this paper, we study the multi-antenna relay downlink channel with limited feedback CSI from both two-hop links. Data streams from the base station (BS) are first transmitted to a relay station (RS) with singular value decomposition-based precoding and receiver pulse shaping at the BS and RS, respectively. The block diagonalization precoding is then applied at the RS to forward the received signals to the remote multi-antenna users. We derive an upper bound for the system throughput loss due to CSI quantization error, and then propose a feedback quality control strategy to maintain a bounded rate loss relative to the perfect CSI case. It reveals that the feedback size B_1 from the RS to BS needs to scale in proportion to both transmit power at the BS and RS while the feedback size B_2 from each user to the RS only needs to scale linearly with the transmit power at the RS.

Feedback Subsampling in Temporally-Correlated Slowly-Fading Channels using Quantized CSI

This paper studies the problem of feedback subsampling in temporally-correlated wireless networks utilizing quantized channel state information (CSI). Under both peak and average power constraints, the system data transmission efficiency is studied in two scenarios. First, we focus on the case where the codewords span one fading block. In the second scenario, the throughput is determined for piecewise slowly-fading channels where the codewords are so long that a finite number of correlated gain realizations are experienced during each codeword transmission. Considering different temporal correlation conditions in both scenarios, substantial throughput increment is observed with feedback rates well below 1 bit per slot.

Single-user MIMO versus multi-user MIMO in distributed antenna systems with limited feedback

This article investigates the performance of cellular networks employing distributed antennas in addition to the central antennas of the base station. Distributed antennas are likely to be implemented using remote radio units, which is enabled by a low latency and high bandwidth dedicated link to the base station. This facilitates coherent transmission from potentially all available antennas at the same time. Such distributed antenna system (DAS) is an effective way to deal with path loss and large-scale fading in cellular systems. DAS can apply precoding across multiple transmission points to implement single-user MIMO (SU-MIMO) and multi-user MIMO (MU-MIMO) transmission. The throughput performance of various SU-MIMO and MU-MIMO transmission strategies is investigated in this article, employing a Long-Term evolution (LTE) standard compliant simulation framework. The previously theoretically established cell-capacity improvement of MU-MIMO in comparison to SU-MIMO in DASs is confirmed under the practical constraints imposed by the LTE standard, even under the assumption of imperfect channel state information (CSI) at the base station. Because practical systems will use quantized feedback, the performance of different CSI feedback algorithms for DASs is investigated. It is shown that significant gains in the CSI quantization accuracy and in the throughput of especially MU-MIMO systems can be achieved with relatively simple quantization codebook constructions that exploit the available temporal correlation and channel gain differences.

Quantized CSI-Based Tomlinson-Harashima Precoding in Multiuser MIMO Systems

This paper considers the implementation of Tomlinson-Harashima (TH) precoding for multiuser MIMO systems based on quantized channel state information (CSI) at the transmitter side. Compared with the results in [1], our scheme applies to more general system setting where the number of users in the system can be less than or equal to the number of transmit antennas. We also study the achievable average sum rate of the proposed quantized CSI-based TH precoding scheme. The expressions of the upper bounds on both the average sum rate of the systems with quantized CSI and the mean loss in average sum rate due to CSI quantization are derived. We also present some numerical results. The results show that the nonlinear TH precoding can achieve much better performance than that of linear zero-forcing precoding for both perfect CSI and quantized CSI cases. In addition, our derived upper bound on the mean rate loss for TH precoding converges to the true rate loss faster than that of zero-forcing precoding obtained in [2] as the number of feedback bits becomes large. Both the analytical and numerical results show that nonlinear precoding suffers from imperfect CSI more than linear precoding does.

Robust Multi-Antenna Multi-User Precoding Based on Generalized Multi-Unitary Decomposition With Partial CSI Feedback

In this paper, we present a novel matrix decomposition method, called generalized multi-unitary decomposition (GMUD), and use it to achieve robust multi-antenna multi-user multiple-input-multiple-output (MIMO) precoding with limited and partial channel information feedback. GMUD transforms complex matrix {H} into H = P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">θ</sub> , <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">θ,r</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sup> , where R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> is a lower triangular matrix, and P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">θ, r</sub> and Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">θ, r</sub> are unitary matrices. A unique feature of GMUD is that it gives multiple solutions of the unitary matrices P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">θ, r</sub> and Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">θ, r</sub> based on two parameters, namely the direction parameter θ and magnitude parameter r. This property enables the GMUD precoder to steer the precoding vectors of different users to jointly optimize their performance. Compared with regularized-inverse precoding (an existing multi-user MIMO precoding technique that we have extended to handle multiple receive antennas), the advantages of GMUD precoding are that it requires only partial channel state information (CSI) from the users, and its performance is robust to CSI quantization.

Quantization and Bit Allocation for Channel State Feedback in Relay-Assisted Wireless Networks

This paper investigates quantization of channel state information (CSI) and bit allocation across wireless links in a multi-source, single-relay cooperative cellular network. Our goal is to minimize the loss in performance, measured as the achievable sum rate, due to limited-rate quantization of CSI. We develop both a channel quantization scheme and allocation of limited feedback bits to the various wireless links. We assume that the quantized CSI is reported to a central node responsible for optimal resource allocation. We first derive tight lower and upper bounds on the difference in rates between the perfect CSI and quantized CSI scenarios. These bounds are then used to derive an effective quantizer for arbitrary channel distributions. Next, we use these bounds to optimize the allocation of bits across the links subject to a budget on total available quantization bits. In particular, we show that the optimal bit allocation algorithm allocates more bits to those links in the network that contribute the most to the sum-rate. Finally, the paper investigates the choice of the central node; we show that this choice plays a significant role in CSI bits required to achieve a target performance level.

Power Allocation for Secondary Outage Minimization in Spectrum Sharing Networks with Limited Feedback

We address an optimal transmit power allocation problem that minimizes the outage probability of a secondary user (SU) who is allowed to coexist with a primary user (PU) in a narrowband spectrum sharing cognitive radio network, under a long term average transmit power constraint at the secondary transmitter (SU-TX) and an average interference power constraint at the primary receiver (PU-RX), with quantized channel state information (CSI) (including both the channels from SU-TX to SU-RX, denoted as g <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and the channel from SU-TX to PU-RX, denoted as g <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ) at the SU-TX. The optimal quantization regions in the vector channel space is shown to have a "stepwise" structure. With this structure, the above outage minimization problem can be explicitly formulated and solved by employing the Karush-Kuhn-Tucker (KKT) necessary optimality conditions to obtain a locally optimal quantized power codebook. A low-complexity near-optimal quantized power allocation algorithm is derived for the case of large number of feedback bits. More interestingly, we show that as the number of partition regions approaches infinity, the length of interval between any two adjacent quantization thresholds on the g <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> axis is asymptotically equal when the average interference power constraint is active. Similarly, we show that when the average interference power constraint is inactive, the ratio between any two adjacent quantization thresholds on the g <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> axis becomes asymptotically identical. Using these results, an explicit expression for the asymptotic SU outage probability at high rate quantization (as the number of feedback bits goes to infinity) is also provided, and is shown to approximate the optimal outage behavior extremely well for large number of bits of feedback via numerical simulations. Analysis on the extension to multiple secondary users case (cognitive multiple-access network) is also discussed. Numerical results illustrate that with only a few bits of feedback, the derived algorithms provide secondary outage performance very close to that with full CSI at the SU-TX.

Stability and Delay of Zero-Forcing SDMA With Limited Feedback

This paper addresses the stability and queueing delay of space-division multiple access (SDMA) systems with bursty traffic, where zero-forcing beamforming enables simultaneous transmissions to multiple mobiles. Computing beamforming vectors relies on quantized channel state information (CSI) feedback (limited feedback) from mobiles. Define the stability region for SDMA as the set of multiuser packet-arrival rates for which the steady-state queue lengths are finite. Given perfect feedback of channel-direction information (CDI) and equal power allocation over scheduled queues, the stability region is proved to be a convex polytope having the derived vertices. A similar result is obtained for the case with perfect feedback of CDI and channel-quality information (CQI), where CQI allows scheduling and power control for enlarging the stability region. For any set of arrival rates in the stability region, multiuser queues are shown to be stabilized by the joint queue-and-beamforming control policy that maximizes the departure-rate-weighted sum of queue lengths. The stability region for limited feedback is found to be the perfect-CSI region multiplied by one minus a small factor. The required number of feedback bits per mobile is proved to scale logarithmically with the inverse of the above factor as well as linearly with the number of transmit antennas minus one. The effect of limited feedback on queueing delay is also quantified. CDI quantization errors are shown to multiply average queueing delay by a factor <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> >; 1. For given <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> → 1, the number of feedback bits per mobile is proved to be <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (-log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (1-1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> )) .

Adaptive bit allocation scheme in multi-cell cooperative block diagonalization systems with delayed and limited feedback

In multi-cell cooperative multi-input multi-output (MIMO) systems, base station (BS) can exchange and utilize channel state information (CSI) of adjacent cell users to manage co-channel interference. Users quantize the CSIs of desired channel and interference channels using finite-rate feedback links, then BS can generate cooperative block diagonalization (BD) precoding matrices using the obtained quantized CSI at transmitter to supress co-channel interference. In this paper, a novel adaptive bit allocation scheme is proposed to minimize the rate loss due to imperfect CSI. We derive the closed-form expression of rate loss caused by both channel delay and limited feedback. Based on the derived rate loss expression, the proposed scheme can adaptively allocate more bits to quantize the better channels with smaller delays and fewer bits to worse channels with larger delays. Simulation results show that the proposed scheme yields higher performance than other allocation schemes.