Feedback Link Research Articles

Interference Channels With Rate-Limited Feedback

We consider the two-user interference channel with rate-limited feedback. Related prior works focus on the case where feedback links have infinite capacity, while no research has been done for the rate-limited feedback problem. Several new challenges arise due to the capacity limitations of the feedback links, both in deriving inner bounds and outer bounds. We study this problem under three different interference models: the El Gamal-Costa deterministic model, the linear deterministic model, and the Gaussian model. For the first two models, we develop an achievable scheme that employs three techniques: Han-Kobayashi message splitting, quantize-and-binning, and decode-and-forward. We also derive new outer bounds for all three models and we show the optimality of our scheme under the linear deterministic model. In the Gaussian case, we propose a transmission strategy that incorporates lattice codes, inspired by the ideas developed in the first two models. For symmetric channel gains, we prove that the gap between the achievable sum rate of the proposed scheme and our new outer bounds is bounded by a constant number of bits, independent of the channel gains.

Event-based control with communication delays and packet losses

Event-based control aims at reducing the information exchange over the communication network in feedback-control systems. This article extends a state-feedback approach to event-based control to cope with communication delays and packet losses in the feedback link. The main result is a bound for the maximum tolerable communication delay, which guarantees that the event-based state-feedback loop is stable in the sense that its state remains in a bounded surrounding of the state of a continuous-time state-feedback loop. This result is extended to communication links with additional packet losses. Simulation studies and experimental results illustrate the performance of the event-based control loop.

Robust PID Control of Mobile Satellite Dish Network within Nigeria

locking a load to a desired position as quickly and precisely as possible using Proportional-Integral-Derivative controller can be a major problem even in direct control depending on the amount of delay involved. This is because the formulated corrective action is based on the past output and not the current output being corrected. Hence, the effectiveness of formulated control action is determined largely by the amount of delay between the feedback link and the time of delivery of the control action to the load's actuator. The large and variable time delays incurred by remotely controlling network of satellite dishes mounted on moving vehicles in Nigeria with land area of 923,677 km 2 further makes the control problem daunting. Therefore, the principal objective of this research is to develop a robust PID controller with satisfactory real-time optimal control performance of satellite dish network mounted on mobile vehicles spread all over Nigeria.

Mechano-geometric generative rules of morphogenesis

The ideographical approach aimed at detecting specific causative relationships within the process of development prevails in modern embryology. The present work considers the possibilities of using the nomothetic approach aimed at putting forward nonspecific general laws based on the general scientific theory of self-organization and can be formulated in morphomechanical terms based on feedback links between passive and active mechanical stress. The perspectives of this approach and the involvement of genetic factors in the regulation of feedback links are discussed.

Feedback Communication with Reduced Delay over Noisy Time-Dispersive Channels

Using a framework that lies at the intersection of communications, estimation and control, this work considers feedback communication over noisy Gaussian feedforward as well as unconstrained feedback Time Dispersive Channels (TDCs), and presents a linear scheme that reduces transmission delay for a fixed encoder dimension. The approach is based on Liu and Elia's feedback scheme, that is generalized in this paper to accommodate a noisy TDC in the feedback link, showing the usefulness of the technique despite the noisy feedback. This technique also mitigates the inherent numerical instability problem in Liu and Elia's original system, and does not require the solution of a non-convex optimization problem to find the optimal encoder/decoder for a given pair of feedforward and feedback channels. These advantages are achieved at the expense of an increase in transmission power, that becomes small when the SNR increases. Computer simulation results show that the new scheme reduces significantly the transmission delay, while still providing rates at high SNR that are close to those achieved by an optimal linear encoder. These features make the new coding scheme attractive for practical applications.

Combining Training and Quantized Feedback in Multiantenna Reciprocal Channels

The communication between a multiple-antenna transmitter and multiple receivers (users) with either a single or multiple-antenna each can be significantly enhanced by providing the channel state information at the transmitter (CSIT) of the users, as this allows for scheduling, beamforming and multiuser multiplexing gains. The traditional view on how to enable CSIT has been as follows: In time-division duplexed (TDD) systems, uplink (UL) and downlink (DL) channel reciprocity allows the use of a training sequence in the UL direction, which is exploited to obtain an UL channel estimate. This estimate is in turn recycled in the next downlink transmission. In frequency-division duplexed (FDD) systems, which lack the UL and DL reciprocity, the CSIT is provided via the use of a dedicated feedback link of limited capacity between the receivers and the transmitter. In this paper, we focus on TDD systems and put their classical approach in question. We show that the traditional TDD setup above fails to fully exploit the channel reciprocity in its true sense. In fact, we show that the system can benefit from a combined CSIT acquisition strategy mixing the use of limited feedback and that of a training sequence. This combining gives rise to a very interesting joint estimation and detection problem for which we propose two iterative algorithms. An outage rate based framework is also developed which gives the resource split between training and feedback. We demonstrate the potential of this hybrid combining in terms of the improved CSIT quality under a global training and feedback resource constraint.

Event-triggered PI control subject to actuator saturation

Event-triggered control aims at reducing the communication load over the feedback link in networked control systems by adapting the information exchange to the current needs. This paper firstly extends a common approach to event-triggered control by incorporating a PI controller and by showing the setpoint-tracking properties of the extended scheme. Second, it investigates the consequences of actuator saturation on the behavior of the event-triggered PI-control loop. Simulations show that the effect of actuator saturation depends on the selection of the event threshold which might even destabilize the closed-loop system due to integrator windup. Finally, anti-windup techniques are discussed to overcome this problem.

Designing of integrated system-dynamics models for an oil company

This paper presents a new approach to designing integrated simulation models for large corporations. This approach is based on the use of system-dynamics methods for implementing models of segments of the vertically integrated company taking into account the available direct and feedback links. All models have been designed with the help of power simulation tool - Powersim Studio. In addition, the designed simulation system has been integrated with created genetic algorithm and the corporate data warehouse.

Performance measures over slowly fading multiple-input multiple-output channels using quantised and erroneous feedback

In this study, a conceptual transmission scheme that adjusts rate and power of codewords which are sent over a slowly fading channel, when quantised and possibly erroneous channel state information (CSI) is available at the transmitter, is designed. Here, the goal is to maximise data throughput or the expected data rate using a two-way training protocol and temporal power control at the transmitter. The common models used in analysis either assume perfect CSI at the receiver or noiseless state feedback links. However, in practical systems, neither is the channel estimate known perfectly at the receiver nor is the feedback link perfect. Analytical expressions for the relationship between the average power and data transmission rate are obtained for various scenarios. The average spectral efficiency is analysed under various fading channels to evaluate the system performance. Here, the focus is on the average channel conditions to improve the system throughput.

Stability analysis of interconnected event-based control loops

In event-based control the feedback link within a control loop is only closed when an event indicates the need for information exchange among the sensors, controller and actuators to maintain a required loop performance. The event-based control loop is a hybrid dynamical system, which is characterized by a sequence of continuous state flows and discontinuous state jumps at the event times. This paper analyzes the stability of interconnected decentralized event-based control loops where events are triggered asynchronously. A stability criterion is derived using the comparison principle. It is shown that conditions that are sufficient to prove the stability of the continuous control system imply ultimate boundedness of the event-based state-feedback loop. The conservatism of the proposed stability test is evaluated for a thermofluid process.

Vision for a digital future

The greatest opportunities and challenges for medical journals today involve how we keep pace with technology and, in particular, with the changes in digital publishing. Leading publishers are those using new technologies—such as devices and social media—to deliver the information people want and need for medical research or medical care. Pertinent content and timely delivery combine to help achieve better outcomes for patients. Rather than simply reporting research results, journals are poised to change the way medical professionals practice. At the Neurology ® editorial retreat in March 2011, themed “Reimagining the Journal,” ideas emerged regarding publication of journals in the future; we determined that Neurology would be a leader among specialty journals in finding ways to improve and enhance the reading experience for our readers. We have already achieved several goals set at the retreat and are planning other initiatives. We are transitioning to different ways of enhancing the content, packaging, and distribution of Neurology . Neurology content is already on an app for the iPad, which many readers have described as the superior way to browse and read the journal. Web access is optimized for viewing on mobile phones, whatever the operating system. Our new journal, Neurology: Clinical Practice , will appear in print, online, and in an app for the iPad. Our correspondence section has morphed into an online interactive discussion forum, dubbed Writ e Click, with feedback links incorporated into our online and iPad versions. QR codes in the print journal link our print and digital formats; these codes link to additional data or features, such as video or audio files, or to supplemental …

Stochastic Control of Event-Driven Feedback in Multiantenna Interference Channels

Spatial interference avoidance is a simple and effective way of mitigating interference in multi-antenna wireless networks. The deployment of this technique requires channel-state information (CSI) feedback from each receiver to all interferers, resulting in substantial network overhead. To address this issue, this paper proposes the method of distributive control that intelligently allocates CSI bits over multiple feedback links and adapts feedback to channel dynamics. For symmetric channel distributions, it is optimal for each receiver to equally allocate the average sum-feedback rate for different feedback links, thereby decoupling their control. Using the criterion of minimum sum-interference power, the optimal feedback-control policy is shown using stochastic-optimization theory to exhibit opportunism. Specifically, a specific feedback link is turned on only when the corresponding transmit-CSI error is significant or interference-channel gain large, and the optimal number of feedback bits increases with this gain. For high mobility and considering the sphere-cap-quantized-CSI model, the optimal feedback-control policy is shown to perform water-filling in time, where the number of feedback bits increases logarithmically with the corresponding interference-channel gain. Furthermore, we consider asymmetric channel distributions with heterogeneous path losses and high mobility, and prove the existence of a unique optimal policy for jointly controlling multiple feedback links. Given the sphere-cap-quantized-CSI model, this policy is shown to perform water-filling over feedback links. Finally, simulation demonstrates that feedback-control yields significant throughput gains compared with the conventional differential-feedback method.

Effect of Feedback Delay on the Performance of Cooperative Networks with Relay Selection

In this paper, we analyze the effect of feedback delay and channel estimation errors on the performance of a decode-and-forward (DF) cooperative transmission scenario with relay selection. In our relay selection scheme, only one relay with the best relay-to-destination (R → D) channel quality is selected among the set of relays that decode the source information correctly. Specifically, the destination terminal first estimates the channel state information (CSI) of all active R → D links and then sends the index of the best relay to the relay terminals via a delayed feedback link. Due to the time varying nature of the fading channels, selection is performed based on the old version of the channel estimate. Closed-form expressions for the outage probability, average capacity and average symbol error rate (ASER) are derived. Through asymptotic diversity order analysis, we show that the presence of feedback delay reduces the asymptotic diversity order to one, while the effect of channel estimation errors reduces it to zero. Finally, simulation results are presented to corroborate the analytical results.

Average capacity performance of opportunistic relay selection with outdated CSI

The authors investigate the effect of feedback delay on the average capacity of a decode-and-forward cooperative network with relay selection. In particular, a multi-relay cooperative scenario is considered, where the best relay is selected from a subset of relays that are able to decode the source information correctly. In this selection scenario, the authors assume that the destination terminal estimates the relay-to-destination ( R→D ) channel-state-information perfectly and sends the index of the best relay to the relay terminals via a delayed feedback link. The authors investigate the performance of the considered scenario in terms of average capacity. Simulation results are presented to corroborate the analytical results.

Joint power control and beamforming codebook design for MISO channels under the outage criterion

This paper investigates the joint design of power control and beamforming codebooks for limited-feedback multiple-input single-output (MISO) wireless systems. The problem is formulated as the minimization of the outage probability subject to the transmit power constraint and cardinality constraints on the beamforming and power codebooks. We show that the two codebooks need to be designed jointly in this setup, and provide a numerical method for the joint optimization. For independent and identically distributed (i.i.d.) Rayleigh channel, we also propose a low-complexity approach of fixing a uniform beamforming codebook and optimizing the power codebook for that particular beamformer, and show that it performs very close to the optimum. Further, this paper investigates the optimal tradeoffs between beamforming and power codebook sizes. We show that as the outage probability decreases, optimal joint design should use more feedback bits for power control and fewer feedback bits for beamforming. The jointly optimized beamforming and power control modules combine the power gain of beamforming and diversity gain of power control, which enable it to approach the performance of the system with perfect channel state information as the feedback link capacity increases—something that is not possible with either beamforming or power control alone.

Multiuser MIMO downlink transmission with BEM-based limited feedback over doubly selective channels

This article studies the problem of limited feedback design for heterogeneous multiuser (MU) transmissions over time- and frequency-selective (doubly selective) multiple-input multiple-output downlink channels. Under a doubly selective propagation condition, a basis expansion model (BEM) is deployed as a fitting parametric model for capturing the time-variation of the MU downlink channels and for reducing the number of the channel parameters. The resulting dimension reduction in the time-variant channel representation, in turn, translates into a reduced feedback load of channel state information (CSI) to the base station (BS). To produce limited feedback information, vector quantization of the BEM coefficients is performed at mobile terminals under the assumption that perfect BEM coefficient estimation has been established by existing algorithms. Then, the output indices of the quantized BEM coefficient vectors are sent to the BS via error-free, zero-latency feedback links. To assess the feasibility of using the BEM-based limited feedback design in a MU network with an arbitrary number of active users, the resultant sum-rate performance of the network is provided by employing the block-diagonalization precoding and greedy scheduling techniques at the BS. The relevant numerical results show that the BEM-based limited feedback scheme is able to significantly alleviate the detrimental effect of outdated CSI feedback which likely occurs as using the conventional block-fading assumption in MU transmissions over (fast) time-varying channels.

Bit error rate minimising pilot symbol arrangement in closed-loop orthogonal frequency division multiplexing systems

The use of a feedback link in wireless orthogonal frequency division multiplexing (OFDM) systems is analysed. Although open-loop scenarios have been rigorously investigated in the literature, closed-loop scenarios, in which there is a feedback link from a strong to a weak user, have not been thoroughly studied. The study mainly focus on the recently proposed dynamic pilot symbol arrangement strategy. It was shown in a recent paper that for coherent OFDM transmission, this strategy is capable of delivering substantial gains in the performance. Pilot symbols are used to sample channel behaviour so that data symbols can be decoded correctly. However, these pilots do not need to be arranged so as to estimate the channel in the best possible way. In this work, the authors propose a pilot symbol arrangement strategy that minimises the bit error rate, we analyse the solution in detail and propose a low complexity search that maintains most of the quality of an exhaustive search. This low complexity search makes the pilot symbol method viable for medium to large-scale OFDM systems. The authors also analyse the use of a Wiener filter for channel estimation combined with the dynamic pilot symbol strategy and show that it delivers good gains in comparison to a simple maximum likelihood channel estimate.

Minimum Energy to Send $k$ Bits Through the Gaussian Channel With and Without Feedback

The minimum achievable energy per bit over memoryless Gaussian channels has been previously addressed in the limit when the number of information bits goes to infinity, in which case it is known that the availability of noiseless feedback does not lower the minimum energy per bit, which is -1.59 dB below the noise level. This paper analyzes the behavior of the minimum energy per bit for memoryless Gaussian channels as a function of k, the number of information bits. It is demonstrated that in this nonasymptotic regime, noiseless feedback leads to significantly better energy efficiency. In particular, without feedback achieving energy per bit of -1.57 dB requires coding over at least k=106 information bits, while we construct a feedback scheme that transmits a single information bit with energy -1.59 dB and zero error. We also show that unless k is very small, approaching the minimal energy per bit does not require using the feedback link except to signal that transmission should stop.

Feedback in the Non-Asymptotic Regime

Without feedback, the backoff from capacity due to non-asymptotic blocklength can be quite substantial for blocklengths and error probabilities of interest in many practical applications. In this paper, novel achievability bounds are used to demonstrate that in the non-asymptotic regime, the maximal achievable rate improves dramatically thanks to variable-length coding and feedback. For example, for the binary symmetric channel with capacity 1/2 the blocklength required to achieve 90% of the capacity is smaller than 200, compared to at least 3100 for the best fixed-blocklength code (even with noiseless feedback). Virtually all the advantages of noiseless feedback are shown to be achievable, even if the feedback link is used only to send a single signal informing the encoder to terminate the transmission (stop-feedback). It is demonstrated that the non-asymptotic behavior of the fundamental limit depends crucially on the particular model chosen for the “end-of-packet” control signal. Fixed-blocklength codes and related questions concerning communicating with a guaranteed delay are discussed, in which situation feedback is demonstrated to be almost useless even non-asymptotically.

On the achievable rates of multiple antenna broadcast channels with feedback-link capacity constraint

In this paper, we study a MIMO fading broadcast channel where each receiver has perfect channel state information while the channel state information at the transmitter is acquired by explicit channel feedback from each receiver through capacity-constrained feedback links. Two feedback schemes are considered, i.e., the analog and digital feedback. We analyze the achievable ergodic rates of zero-forcing dirty-paper coding (ZF-DPC), which is a nonlinear precoding scheme inherently superior to linear ZF beamforming. Closed-form lower and upper bounds on the achievable ergodic rates of ZF-DPC with Gaussian inputs and uniform power allocation are derived. Based on the closed-form rate bounds, sufficient and necessary conditions on the feedback channels to ensure nonzero and full downlink multiplexing gain are obtained. Specifically, for analog feedback in both AWGN and Rayleigh fading feedback channels, it is sufficient and necessary to scale the average feedback link SNR linearly with the downlink SNR in order to achieve the full multiplexing gain. While for the random vector quantization-based digital feedback with angle distortion measure in an error-free feedback link, it is sufficient and necessary to scale the number of feedback bits B per user as where M is the number of transmit antennas and is the average downlink SNR.