Small Number Of Feedback Bits Research Articles

Limited Feedback Channel Estimation in Massive MIMO With Non-Uniform Directional Dictionaries

Channel state information (CSI) at the base station (BS) is crucial to achieve beamforming and multiplexing gains in multiple-input multiple-output (MIMO) systems. State-of-the-art limited feedback schemes require feedback overhead that scales linearly with the number of BS antennas, which is prohibitive for 5G massive MIMO. This paper proposes novel limited feedback algorithms that lift this burden by exploiting the inherent sparsity in double-directional MIMO channel representation using overcomplete dictionaries. These dictionaries are associated with angle of arrival and angle of departure that specifically account for antenna directivity patterns at both ends of the link. The proposed algorithms achieve satisfactory channel estimation accuracy using a small number of feedback bits, even when the number of transmit antennas at the BS is large-making them ideal for 5G massive MIMO. Judicious simulations reveal that they outperform a number of popular feedback schemes and underscore the importance of using angle dictionaries matching the given antenna directivity patterns, as opposed to uniform dictionaries. The proposed algorithms are lightweight in terms of computation, especially on the user equipment side, making them ideal for actual deployment in 5G systems.

Rate Adaptation for Cooperative HARQ

We analyze the average throughput and the outage probability for relay-based incremental redundancy HARQ transmission over block fading channel. We focus on the effects of having an error-free multi-bit feedback channel instead of the single-bit ACK/NACK feedback used in conventional HARQ. This multi-bit feedback message provides the cooperating nodes with outdated channel state information (CSI) so that they can adapt their transmission rate. We discuss a network with M relay nodes and assume adaptive transmission rate for all the cooperating nodes. We describe the adaptation problem as a Markov Decision Process (MDP) and employ the Dynamic Programming (DP) for optimization. The numerical results obtained in the case of one relay transmission, indicate that significant throughput gains can be obtained when compared to non-adaptive, i.e, fixed-rate HARQ. Moreover, we study the performance limits of the system model by finding an upper bound of the throughput for the cooperative HARQ channel which is applicable to both adaptive and non-adaptive models. Finally, we analyze the discretization issues and conclude that only a small number of feedback bits is required by the adaptive system to outperform the conventional single-bit HARQ.

Enabling Code Diversity for Mobile Radio Channels using Long-Range Fading Prediction

Code diversity integrates space-time coding with beamforming by using a small number of feedback bits to select from a family of space-time codes. Different codes lead to different induced channels at the receiver, where Channel State Information (CSI) is used to instruct the transmitter how to choose the code. Feedback can be combined with sub-optimal low complexity decoding of the component codes to match Maximum-Likelihood (ML) decoding performance of any individual code in the family. It can also be combined with ML decoding of the component codes to improve performance beyond ML decoding performance of any individual code. Prior analysis of code diversity did not take into account the effect of the mobile speed and the delay in the feedback channel. This paper demonstrates the practicality of code diversity in space-time coded systems by showing that performance gains based on instantaneous feedback are largely preserved when long-range prediction of time-varying correlated fading channels is employed to compensate for the effect of the feedback delay. To maintain prediction accuracy for realistic SNR, noise reduction that employs oversampled pilots is used prior to fading prediction. We also propose a robust low pilot rate method that utilizes interleaving to improve the spectral efficiency. Simulations are presented for two channel models: the conventional Jakes model and a realistic physical channel model where the parameters associated with the reflectors vary in time and the arrival rays have different strengths and asymmetric arrival angles.

Bit Allocation and Statistical Precoding for Correlated MIMO Channels With Limited Feedback

In this paper, we jointly consider statistical precoding and feedback of bit allocation (BA) for multiple-input-multiple-ouput (MIMO) systems over correlated channels. The proposed system will be termed a BA system. We assume that the statistics of the channel is known to the transmitter and a reverse link of very low rate is available so that the receiver can send back the quantized BA. Based on the statistics of the channel, we derive the statistical precoder so that bounds of the error rate averaged over the random correlated channel are minimized. Due to statistical precoding, the distribution of the BA is highly nonuniform. Treating BA as a vector signal, we quantize it using vector quantization (VQ), which is known to be particularly useful for quantizing signals with nonuniform distributions. As the distribution of BA is taken into consideration in the codebook design, a good tradeoff between performance and feedback rate can be achieved. Simulations show that the combination of statistical precoding and VQ-based quantization for BA leads to good performance with a small number of feedback bits.

Novel limited feedback scheme under the MIMO broadcast system

By deducing the distribution of the normalized channel covariance matrix, a novel limited feedback scheme is proposed under multiple users (MU) multiple-input multiple-output (MIMO) broadcast channel (BC) system. The proposed scheme has advantages in three aspects. First, it has no constraints on the number of users or antennas. Second, each user's feedback bits are independent of the number of receiving antennas. Third, the proposed scheme avoids the storage of large-size codebook on the transceivers. Simulation results show that the performance of the proposed scheme is close to the perfect channel state information (CSI) case and it just needs a small number of feedback bits.

Adaptive Power Allocation for Multihop Regenerative Relaying With Limited Feedback

A multihop regenerative relay system is considered. We explore adaptive power allocation (PA) under a total power constraint to minimize the system error probability when the perfect channel state information (CSI) is known at the transmitters. We propose adaptive PA schemes with limited feedback when the transmitters have no perfect knowledge of CSI. Simulation results demonstrate the good performance of the proposed PA scheme with perfect CSI. When no perfect CSI is available at the transmitters, the proposed PA schemes with a small number of feedback bits are able to achieve very close performance to the adaptive PA with perfect CSI.

Adaptive Modulation Based on Finite-Rate Feedback in Broadcast Channels

In a single-input single-output (SISO) downlink with multiple users, to obtain the multiuser diversity gain, the full channel state information (CSI) of all users is required for selecting the desired user and transmission mode. However, feedback channels are often capable of carrying only a limited number of bits. With such rate limited feedback links, we intend to maximize the average throughput of each user by designing transmit power levels, signal constellations and feedback thresholds jointly. Both un-coded adaptive M-ary quadrature amplitude modulation (MQAM) and adaptive trellis-coded modulation (TCM) are investigated. A nested iterative algorithm is proposed to obtain a finite number of transmission modes and thresholds. Optimization in the heterogeneous network is also considered. Simulation results demonstrate a small number of feedback bits make the throughput approach to that with perfect CSI. As the number of users increases, the multiuser diversity gain is achieved and the average feedback load of each user is reduced.

On the Capacity and Design of Limited Feedback Multiuser MIMO Uplinks

The theory of multiple-input-multiple-output (MIMO) technology has been well developed to increase fading channel capacity over single-input-single-output (SISO) systems. This capacity gain can often be leveraged by utilizing channel state information at the transmitter and the receiver. Users make use of this channel state information for transmit signal adaptation. In this correspondence, we derive the capacity region for the MIMO multiple access channel (MIMO MAC) when partial channel state information is available at the transmitters, where we assume a synchronous MIMO multiuser uplink. The partial channel state information feedback has a cardinality constraint and is fed back from the basestation to the users using a limited rate feedback channel. Using this feedback information, we propose a finite codebook design method to maximize the sum rate. In this correspondence, the codebook is a set of transmit signal covariance matrices. We also derive the capacity region and codebook design methods in the case that the covariance matrix is rank one (i.e., beam- forming). This is motivated by the fact that beamforming is optimal in certain conditions. The simulation results show that when the number of feedback bits increases, the capacity also increases. Even with a small number of feedback bits, the performance of the proposed system is close to an optimal solution with the full feedback.

Code Diversity in Multiple Antenna Wireless Communication

The standard approach to the design of individual space-time codes is based on optimizing diversity and coding gains. This geometric approach leads to remarkable examples, such as perfect space-time block codes, for which the complexity of Maximum Likelihood (ML) decoding is considerable. Code diversity is an alternative and complementary approach where a small number of feedback bits are used to select from a family of space-time codes. Different codes lead to different induced channels at the receiver, where Channel State Information (CSI) is used to instruct the transmitter how to choose the code. This method of feedback provides gains associated with beamforming while minimizing the number of feedback bits. It complements the standard approach to code design by taking advantage of different (possibly equivalent) realizations of a particular code design. Feedback can be combined with sub-optimal low complexity decoding of the component codes to match ML decoding performance of any individual code in the family. It can also be combined with ML decoding of the component codes to improve performance beyond ML decoding performance of any individual code. One method of implementing code diversity is the use of feedback to adapt the phase of a transmitted signal as shown for 4 by 4 Quasi-Orthogonal Space-Time Block Code (QOSTBC) and multi-user detection using the Alamouti code. Code diversity implemented by selecting from equivalent variants is used to improve ML decoding performance of the Golden code. This paper introduces a family of full rate circulant codes which can be linearly decoded by fourier decomposition of circulant matrices within the code diversity framework. A 3 by 3 circulant code is shown to outperform the Alamouti code at the same transmission rate.

Minimizing Transmit Power for Coherent Communications in Wireless Sensor Networks With Finite-Rate Feedback

We minimize average transmit power with finite-rate feedback for coherent communications in a wireless sensor network (WSN), where sensors communicate with a fusion center using adaptive modulation and coding over a wireless fading channel. By viewing the coherent WSN setup as a distributed space-time multiple-input single-output (MISO) system, we present optimal distributed beamforming and resource allocation strategies when the full (F-) channel state information at the transmitters (CSIT) is available through a feedback channel. We also develop optimal adaptive transmission policies and design optimal quantizers for the finite-rate feedback case where the sensors only have quantized (Q-) CSIT, or, each sensor has F-CSIT of its own link with the FC but only Q-CSIT of other sensors. Numerical results confirm that our novel finite-rate feedback-based strategies achieve near-optimal power savings based on even a small number of feedback bits.

Limited Feedback Diversity Techniques for Correlated Channels

Employing multiple antennas at the transmitter is a well-established technique for providing diversity advantage in wireless systems. Transmit beamforming relies on the assumption of current channel knowledge at the transmitter, which is unrealistic when the forward and reverse links are separated in frequency. One solution to this problem is for the receiver to send a small number of feedback bits that convey channel information to the transmitter. Feedback design techniques have been proposed over the past few years, but they were derived using the assumption of spatially uncorrelated Rayleigh fading. This correspondence addresses the design of limited feedback beamformers when the channel is correlated.