Rate-limited Feedback Research Articles

Distributed Machine-Learning for Early HARQ Feedback Prediction in Cloud RANs

In this work, we propose novel HARQ prediction schemes for Cloud RANs (C-RANs) that use feedback over a rate-limited feedback channel (2 - 6 bits) from the Remote Radio Heads (RRHs) to predict at the User Equipment (UE) the decoding outcome at the BaseBand Unit (BBU) ahead of actual decoding. In particular, we propose a Dual Autoencoding 2-Stage Gaussian Mixture Model (DA2SGMM) that is trained in an end-to-end fashion over the whole C-RAN setup. Using realistic link-level simulations in the sub-THz band at 100 GHz, we show that the novel DA2SGMM HARQ prediction scheme clearly outperforms all other adapted and state-of-the-art schemes. The DA2SGMM shows a superior performance in terms of blockage detection as well as HARQ prediction in the no-blockage and single-blockage cases. In particular, the DA2SGMM with 4~bit feedback achieves a more than 200 % higher throughput in average compared to its best alternative. Compared to regular HARQ, the DA2SGMM reduces the maximum transmission latency by more than 72.4 %, while maintaining more than 75 % of the throughput in the no-blockage scenario. In the single-blockage scenario, DA2SGMM significantly increases the throughput for most of the evaluated Signal-to-Noise-Ratios (SNRs) compared to regular HARQ.

Multiple Access Wiretap Channel With Partial Rate-Limited Feedback

Multiple Access Wiretap Channel With Partial Rate-Limited Feedback

Deep Learning for Distributed Channel Feedback and Multiuser Precoding in FDD Massive MIMO

This paper shows that deep neural network (DNN) can be used for efficient and distributed channel estimation, quantization, feedback, and downlink multiuser precoding for a frequency-division duplex massive multiple-input multiple-output system in which a base station (BS) serves multiple mobile users, but with rate-limited feedback from the users to the BS. A key observation is that the multiuser channel estimation and feedback problem can be thought of as a distributed source coding problem. In contrast to the traditional approach where the channel state information (CSI) is estimated and quantized at each user independently, this paper shows that a joint design of pilots and a new DNN architecture, which maps the received pilots directly into feedback bits at the user side then maps the feedback bits from all the users directly into the precoding matrix at the BS, can significantly improve the overall performance. This paper further proposes robust design strategies with respect to channel parameters and also a generalizable DNN architecture for varying number of users and number of feedback bits. Numerical results show that the DNN-based approach with short pilot sequences and very limited feedback overhead can already approach the performance of conventional linear precoding schemes with full CSI.

On Optimizing Feedback-Rate Allocation for Downlink MIMO-NOMA With Quantized CSIT

We consider multiple-input multiple output (MIMO) non-orthogonal multiple access (NOMA) downlink channels with zeroforcing beamforming transmission. The base station has multiple transmit antennas while all mobile devices have single receive antenna. With a limited feedback rate, channel direction information (CDI) needs to be quantized and fed back from mobile users to a base station. Thus, the accuracy of the quantized channel state information at the transmitter (CSIT) will depend on the feedback rate. To increase spectral efficiency, 2 active users in some clusters share the same beamforming vector and thus, will interfere fully with each other. Given a total-feedback rate, we analyze the feedback allocation for clusters with single active user and 2 active users. The objective is to either minimize the maximum outage probability or maximize the minimum rate among all active users in a cell. We show that the proposed feedback allocation is close to the optimum. Some numerical examples show that the resulting rate performance with the proposed feedback allocation is increased by 100% over that with the uniform feedback allocation.

On the Two-User MISO Interference Channel With Single-User Decoding: Impact of Imperfect CSIT and Channel Dimension Reduction

This paper examines the Rayleigh fading multiple-input single-output interference channel with single-user decoding and limited channel state information (CSI) feedback. Its contribution is twofold. First, the achievable rate-region with imperfect CSI at the transmitters due to channel quantization errors is analyzed for the two-user case. An analytically tractable inner bound on that region is derived, which provides insights into the problem. Similarly to the case of perfect CSI at the transmitters, it can be shown that beamforming constitutes an optimal strategy for achieving the boundary points of the inner bound. Second, we present a novel CSI feedback scheme that reduces the cross-link CSI feedback overhead, and enhances throughput for any rate-limited feedback scheme. This feedback reduction is crucial when control channels for sharing information between transmitters and unintended receivers are rate limited. A distinguishing feature of the proposed scheme is that feedback is taken into account already at the channel estimation stage. While maintaining a high array gain in the direct channel towards the intended user, the scheme induces an effective low-dimensional cross-link channel, which can be quantized more accurately than the full-dimensional channel. This eventually leads to enhanced performance while maintaining a low CSI feedback overhead. Finally, the proposed feedback scheme is extended to the case of $N>2$ users and shown to provide a significant reduction in CSI feedback overhead in a practically oriented setting.

Joint Channel Resources Allocation and Beamforming in Energy Harvesting Systems

We study a multiple-input single-output energy harvesting (EH) system, where the receiver is capable of harvesting energy from an energy source with a deterministic energy profile. Assuming the practical assumptions of imperfect channel state information (CSI) and limited-rate feedback channel, the minimum mean square error and the random vector quantized (RVQ) schemes are resorted to implement the CSI estimation and feedback, respectively. Considering the characteristic of the EH system, a power and time allocation strategy is proposed for the CSI training and feedback to maximize an upper bound of the downlink data rate. Using the optimization theory, the optimal resources allocation and the RVQ beamforming vector are obtained together with the optimal subset of training antennas. Numerical results verify the tightness of the upper bound and significant advantages of the proposed scheme over other approaches.

Limited Rate Feedback for Two-User MISO Gaussian Interference Channel With and Without Secrecy

We study a two-user multiple-input single-output Gaussian interference channel with limited rate feedback and transmitter cooperation. Each receiver quantizes the channel state information of the direct and cross channels, and sends the codebook indices back to the transmitters through two sum-rate-limited feedback channels. The quantization errors reduce the beamforming gain from the direct transmitter, and cause interference leakage from the cross transmitter. Under an assumption of high signal-to-noise ratio, we first approximate the average transmission rate of each link, and use the sum rate to find the optimal transmit power and corresponding feedback bit allocation. We show that the maximum sum throughput is achieved using full transmit power, and the achievable sum rate under limited feedback is bounded above by a constant. We then extend the results to the case where secrecy is desired. In contrast to the first problem, increasing the transmit power beyond a certain point decreases the secrecy performance. Additionally, we analyze the asymptotic behavior of the solutions when the total feedback bandwidth and the number of transmit antennas grow large. We derive all results in closed form. Simulations validate the theoretical analysis and demonstrate the significant performance gains that result from the use of optimal transmit power control and intelligent feedback bit allocation.

Achievable Rates for Discrete Memoryless Multicast Networks With and Without Feedback

Discrete memoryless multicast network (DM-MN) is considered in this paper. We analyze the lower bounds of noisy network coding (NNC) and distributed decode-forward (DDF) for DM-MN, and show that both NNC and DDF ignore the channel output observed at the transmitter. Motivated by this observation, new coding schemes are proposed to improve NNC and DDF by exploiting the transmitter’s observation and applying hybrid relaying strategies. We first study a special case when the transmitter’s observation is rate-limited feedback signals, and propose a scheme that strictly improves NNC when feedback rates are sufficiently large. For the relay channel with perfect relay-transmitter feedback, our achievable rate reduces to Gabbai and Bross’s rate, which is strictly larger than NNC, DDF, and all known lower bounds on the achievable rates proposed for the setup without feedback. In our scheme, both relays and receivers compress their received signals like NNC, and the relays decode independent “common” and “private” parts of the source message. The generated compression indices are sent to the transmitter through feedback, from which the transmitter reconstructs the receivers’ and relays’ inputs and can thus cooperate with the receivers and relays. We then extend our idea to DM-MN without feedback. For this case, although the transmitter observes channel output, both NNC and DDF simply ignore it, while our new scheme has the transmitter utilize its channel output to decode a set of relays’ and receivers’ compression indices, which achieves some cooperation levels between the transmitter and the receivers and relays. An enhanced relay channel is introduced to show that our scheme strictly outperforms NNC and DDF.

On Optimizing Feedback Interval for Temporally Correlated MIMO Channels With Transmit Beamforming and Finite-Rate Feedback

A receiver with perfect channel state information (CSI) in a point-to-point multiple-input multiple-output (MIMO) channel can compute the transmit beamforming vector that maximizes the transmission rate. For frequency-division duplex, a transmitter is not able to estimate CSI directly and has to obtain a quantized transmit beamforming vector from the receiver via a rate-limited feedback channel. We assume that time evolution of MIMO channels is modeled as a Gauss-Markov process parameterized by a temporal-correlation coefficient. Since feedback rate is usually low, we assume rank-one transmit beamforming or transmission with single data stream. For given feedback rate, we analyze the optimal feedback interval that maximizes the average received power of the systems with two transmit or two receive antennas. For other system sizes, the optimal feedback interval is approximated by maximizing the rate difference in a large system limit. Numerical results show that the large system approximation can predict the optimal interval for finite-size system quite accurately. Numerical results also show that quantizing transmit beamforming with the optimal feedback interval gives larger rate than the existing Kalman-filter scheme does by as much as 10% and than feeding back for every block does by 44% when the number of feedback bits is small.

On the Symmetric $K$ -User Interference Channels With Limited Feedback

In this paper, we develop achievability schemes for symmetric $K$-user interference channels with a rate-limited feedback from each receiver to the corresponding transmitter. We study this problem under two different channel models: the linear deterministic model, and the Gaussian model. For the deterministic model, the proposed scheme achieves a symmetric rate that is the minimum of the symmetric capacity with infinite feedback, and the sum of the symmetric capacity without feedback and the symmetric amount of feedback. For the Gaussian interference channel, we use lattice codes to propose a transmission strategy that incorporates the techniques of Han-Kobayashi message splitting, interference decoding, and decode and forward. This strategy achieves a symmetric rate which is within a constant number of bits to the minimum of the symmetric capacity with infinite feedback, and the sum of the symmetric capacity without feedback and the amount of symmetric feedback. This constant is obtained as a function of the number of users, $K$. The symmetric achievable rate is used to characterize the achievable generalized degrees of freedom which exhibits a gradual increase from no feedback to perfect feedback in the presence of feedback links with limited capacity.

Limited Rate Feedback in a MIMO Wiretap Channel With a Cooperative Jammer

We study strategies for enhanced secrecy using cooperative jamming in secure communication systems with limited rate feedback. A Gaussian multiple-input multiple-output (MIMO) wiretap channel with a jamming helper is considered. The transmitter and helper both require channel state information (CSI), which is quantized at the receiver and fed back through two sum-rate-limited feedback channels. The quantization errors result in reduced beamforming gain from the transmitter, as well as interference leakage from the helper. First, under the assumption that the eavesdropper's CSI is completely unknown, we derive a lower bound on the average main channel rate and find the feedback bit allocation that maximizes the jamming power under a constraint on the bound. For the case where statistical CSI for the eavesdropper's channel is available, we derive a lower bound on the average secrecy rate, and we optimize the bound to find a suitable bit allocation and the transmit powers allocated to the transmitter and helper. For the case where the transmitter and helper have the same number of antennas, we obtain a closed-form solution for the optimal bit allocation. Simulations verify the theoretical analysis and demonstrate the significant performance gain that results with intelligent feedback bit allocation and power control.

Coding Schemes With Rate-Limited Feedback That Improve Over the No Feedback Capacity for a Large Class of Broadcast Channels

We propose two coding schemes for the two-receiver discrete memoryless broadcast channel (BC) with rate-limited feedback from one or both receivers. They improve over the no feedback capacity region for a large class of channels, including the class of strictly essentially less-noisy BCs that we introduce in this paper. Examples of strictly essentially less-noisy BCs are the binary symmetric BC or the binary erasure BC with unequal crossover or erasure probabilities at the two receivers. When the feedback rates are sufficiently large, our schemes recover all previously known capacity results for discrete memoryless BCs with feedback. In both our schemes, we let the receivers feedback quantization messages about their receive signals. In the first scheme, the transmitter simply relays the quantization information obtained from Receiver 1 to Receiver 2, and vice versa. This provides each receiver with a second observation of the input signal and can thus improve its decoding performance unless the BC is physically degraded. Moreover, each receiver uses its knowledge of the quantization message describing its own outputs so as to attain the same performance as if this message had not been transmitted at all. In our second scheme, the transmitter first reconstructs and processes the quantized output signals, and then sends the outcome as a common update information to both receivers. A special case of our second scheme also applies to memoryless BCs without feedback but with strictly causal state-information at the transmitter and causal state-information at the receivers. It recovers all previous achievable regions also for this setup with state-information.

Limited Rate Feedback Scheme for Resource Allocation in Secure Relay-Assisted OFDMA Networks

In this paper, we consider the problem of resource allocation for secure communications in decode-and-forward (DF) relay-assisted orthogonal frequency-division multiple access (OFDMA) networks. In our setting, users want to securely communicate to the base station (BS) with the help of a set of relay stations (RSs) in the presence of multiple eavesdroppers. We assume that all channel state information (CSI) of the legitimate links and only the channel distribution information (CDI) of the eavesdropper links are available. We formulate our problem as an optimization problem whose objective is to maximize the sum secrecy rate of the system subject to individual transmit power constraint for each user and RS. As a first work which considers limited feedback schemes for secure communications in cooperative OFDMA networks, we consider the limited-rate feedback case, where in addition to transmit power and subcarrier assignments, channel quantization should be performed and boundary regions of channels should be computed. We further consider the noisy feedback channel. We solve our problem using the dual Lagrange approach and propose an iterative algorithm whose convergence is analyzed. Using simulations, we evaluate the performance of the proposed scheme in numerous situations.

Wiretap Channel With Causal State Information and Secure Rate-Limited Feedback

In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and the legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate $R_f$ . We derive upper and lower bounds on the secrecy capacity and show that, when the channel to the eavesdropper is degraded , the bounds are tight and the secrecy capacity is completely characterized. The capacity achieving scheme is based on Wyner, Csiszar, and Korner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. The upper bound is more involved and requires a nontrivial recursive lemma extending previous results in the literature to include both state and feedback. We conclude the paper by showing that a few interesting known results can be seen as special cases of the above, as well as discussing the case where the source of local randomness at the encoder is limited.

Resource Allocation in Decode-and-Forward Cooperative Communications Networks with Limited Rate Feedback Channel

In this paper, we propose a limited rate feedback scheme for decode-and-forward (DF) relay-assisted networks. It is assumed that the cellular user is far from the base station such that the direct communication is impossible and communication is performed with the help of a DF relay. To study the limited feedback channel, two cases are proposed: Perfect channel distribution information (CDI)-quantized channel state information (CSI) and quantized CDI-quantized CSI. While in the former, the space of channel gains is quantized into a finite number of regions, in the latter case, the space of CDI parameters is also quantized. We formulate the proposed resource allocation into an optimization problem whose objective is to maximize the average achievable rate under an average transmission power constraint. To solve the proposed optimization problems, we adopt the block coordinated descent algorithm, which is based on the space of variables partitioning into finite sets, and particle swarm optimization (PSO), which is an evolutionary computation technique. To solve the optimization problem for quantized CDI-quantized CSI case, we consider an approach based on the Lloyd algorithm. We also model and study the error in the feedback channel. Finally, the impact of different system parameters on the performance of the proposed scheme is investigated through simulations.

Uplink Radio Resource Allocation in AF and DF Relay-Assisted Networks With Limited Rate Feedback

In this paper, we develop quantized ergodic resource allocation in uplink orthogonal frequency-division multiple-access (OFDMA)-based relay-assisted networks in which both amplify-and-forward (AF) and decode-and-forward (DF) protocols are investigated. The main objective is to maximize the average sum rate subject to the power constraint at the users and relays. Using the dual-decomposition technique and the block-coordinate descent algorithm (BCDA), we then obtain a near-optimal solution for the proposed problems. The proposed methods significantly decrease the required feedback information, which reduce the overhead on the bandwidth and the cost. Furthermore, we investigate the impact of the noisy feedback channel on the system performance. Extensive simulation results are also presented, which indicate that DF outperforms AF in various conditions. It is also observed that by increasing the number of quantization regions, the average sum rate approaches the case in which full channel state information is available.

Outage probability analysis of multiple input multiple output ad‐hoc networks with random topology

Outage probability performance of multiple-input multiple-output (MIMO) ad-hoc network with quantised beamforming and finite rate feedback is analysed with the assumption that the nodes are uniformly distributed with random topology. In quantised beamforming, each receiver sends the label of the best beamforming vector obtained from the codebook to the transmitter through a finite rate limited feedback. The code book is shared between the desired users to prevent decoding of other user's information in a MIMO ad-hoc network. In such a practical environment, feedback links can only convey finite number of bits, from which transmit beamformer designs are investigated using either the outage probability or average signal to interference ratio as the figure of merit. In this study, a mathematical analysis for the estimation of the interference power statistics and the corresponding outage probability in MIMO wireless ad-hoc networks with random position of interference nodes is carried out. In lieu of validating the obtained simulation results, theoretical results have also been compared.

A Novel Energy Efficient Scheme With a Finite-Rate Feedback Channel

In this letter, we propose an energy efficient communication scheme with a limited feedback rate for Rayleigh fading channels. First, we employ the available feedback words to quantize the channel-to-noise ratio (CNR) range and divide it into different regions. Then, we formulate the average energy efficiency (EE) for a given number of CNR regions using a fixed power and rate in each region. After that, we propose an offline optimization algorithm to compute the energy efficient CNR thresholds of each region and the associated transmission powers that maximize the EE. Finally, we evaluate the proposed scheme through simulations, by comparing the EE performance and effective achievable capacity against the case of perfect-CSI.

Insufficiency of Linear-Feedback Schemes in Gaussian Broadcast Channels With Common Message

We consider the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(K\geq 2\) </tex-math></inline-formula> -user memoryless Gaussian broadcast channel (BC) with feedback and common message only. We show that linear-feedback schemes with a message point, in the spirit of Schalkwijk and Kailath’s scheme for point-to-point channels or Ozarow and Leung’s scheme for BCs with private messages, are strictly suboptimal for this setup. Even with perfect feedback, the largest rate achieved by these schemes is strictly smaller than capacity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(C\) </tex-math></inline-formula> (which is the same with and without feedback). In the extreme case where the number of receivers <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(K\to \infty \) </tex-math></inline-formula> , the largest rate achieved by linear-feedback schemes with a message point tends to 0. To contrast this negative result, we describe a scheme for rate-limited feedback that uses the feedback in an intermittent way, i.e., the receivers send feedback signals only in few channel uses. This scheme achieves all rates <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(R\) </tex-math></inline-formula> up to capacity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(C\) </tex-math></inline-formula> with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(L\) </tex-math></inline-formula> th order exponential decay of the probability of error if the feedback rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(R_{\text {fb}}\) </tex-math></inline-formula> is at least <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\((L-1)R\) </tex-math></inline-formula> for some positive integer <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">\(L\) </tex-math></inline-formula> .

Stiefel Manifold and TCQ based on Unit Memory Coding for MIMO System

The Multi Input and Multi Output (MIMO) systems have been analyzed with a number of quantization techniques. In this short communication, few problems like performance and accuracy are investigated through a quantization technique based on Stiefel Manifold (SM). In order to improve these problems, suitable Trellis Coded Quantization (TCQ) based on Unit Memory (UM) coding is studied and applied to SM of MIMO components as a novel approach. Anticipated results are the bit error performance which is an overall improvement of feedback connected between transmitter and receiver of MIMO. As a conclusion, this research not only reduces the quantization problems on SM but also improve the performance and accuracy of limited-rate feedback used in MIMO system.