Limited Feedback for Multicell Zero-Forcing Coordinated Beamforming in Time-Varying Channels

Haksoo Kim,Heejung Yu,Lee, Yong H. IEEE 2015 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY Vol.64 No.6

<P>We consider limited feedback for zero-forcing-based coordinated beamforming over time-varying channels. Most previous work on limited feedback focuses on the feedback rate of the channel state information (CSI), while assuming that feedback occurs for every channel use. This feedback update policy, however, may not be optimal for time-varying channels. To take channel variations into account, we propose a scheme that adjusts both the feedback rate and the feedback update period, depending on channel statistics. We derive an upper bound of the expected rate loss caused by the limited feedback. Based on this bound, we formulate an optimization problem minimizing the residual interference power and derive closed-form solutions for the feedback rate and the feedback update period while fixing one of the parameters and optimizing the other. Using the closed-form expressions, we propose an algorithm that iteratively updates the parameters. Simulation results demonstrate that the proposed limited feedback scheme can outperform the conventional scheme, which feeds back the CSI at every channel use.</P>

제한된 피드백 정보를 사용하는 공간 다중화를 위한 부 공간 방식 기반 Precoding 기법

문철,서정태,Mun Cheol,Seo Jeong-Tae 한국통신학회 2005 韓國通信學會論文誌 Vol.30 No.10A

본 논문에서는 제한된 피드백 정보를 사용하는 공간 다중화 기법에 사용될 수 있는 부 공간 방식 기반 preceding 기법을 제안한다. 제안된 preceding 기법은 수신기에서 다수의 공통 기저 집합(common basis sets)으로 부터 용량을 최대로 하는 기저들을 선택하고, 선택된 기저들은 feedback 정보를 통해 송신기에 전달되곤 송신기에서는 선택된 기저들로 이루처진 preceding 행렬을 구성한다. 선택된 기저들은 해당 기저들이 속한 기저 집합의 index에 대한 feedback 정보와 선택된 기저 집합에서 각 기저들의 선택 여부에 대한 feedback 정보를 통해 송신기로 feedback된다. 선택된 기저 집합 index는 송수신기가 약속한 공통 기저 집합 중에서 해당 MIMP 채널의 부 공간의 좌표(coordinate)에 가장 적합한 좌표를 나타내고, 해당 좌표에서 상당한 양의 에너지를 포함하는 기저들을 선택함으로써 적은 feedback 정보량으로 MIMO 채널을 묘사한다. 시뮬레이션을 통해 제안된 부 공간 방식 기반 preceding 기법이 적은 feedback 정보량을 사용하면서 폐루프 MIMO 용량 (closed-loop MIMO capacity)에 근접하는 용량을 제공함을 보인다. In this paper, for spatial multiplexing with limited feedback, we propose subspace method based preceding in which the active bases are selected at the receiver from a finite number of basis sets Down at both receiving and transmitting ends, conveyed to the transmitter using limited feedback, and assembled into a preceding matrix at the transmitter. The selected bases are conveyed to the transmitter using feedback information on both the index of the selected basis set, which defines the most appropriate set of coordinates for describing a multiple-input multiple-output (MIMO) channel, and the principal bases maximizing the capacity in the selected basis set. We show that the proposed subspace method based preceding provides a capacity similar to that of the closed-loop MIMO even with limited feedback.

공간 다중화를 위한 부 공간 방식 Precoding 기법

문철,정챵규,박동희,곽윤식 한국정보통신학회 2005 한국정보통신학회논문지 Vol.9 No.7

In this paper, for spatial multiplexing with limited feedback, we propose subspace based precoding in which the active bases are selected at the receiver from a finite number of basis sets known at both receiving and transmitting ends, conveyed to the transmitter using limited feedback, and assembled into a precoding matrix at the transmitter. The selected bases are conveyed to the transmitter using feedback information on both the index of a basis set, which indicates the most appropriate set of coordinates for describing a MIMO channel, and the active bases having the significant amounts of energy in the selected basis set. We show that the proposed subspace based precoding provides capacity similar to that of the closed-loop MIMO even with limited feedback. 본 논문에서는 제한된 피드백 정보를 사용하는 공간 다중화 기법에 사용될 수 있는 부 공간 방식 기반 precoding 기법을 제안한다. 제안된 precoding 기법은 수신기에서 다수의 공통 기저 집합(common basis sets)으로부터 용량을 최대로 하는 기저들을 선택하고, 선택된 기저들은 feedback 정보를 통해 송신기에 전달되고, 송신기에서는 선택된 기저들로 이루어진 precoding 행렬을 구성한다. 선택된 기저들은 해당 기저들이 속한 기저 집합의 index에 대한 feedback 정보와 선택된 기저 집합에서 각 기저들의 선택 여부에 대한 feedback 정보를 통해 송신기로 feedback된다. 선택된 기저 집합 index는 송수신기가 약속한 공통 기저 집합 중에서 해당 MIMO 채널의 부 공간의 좌표(coordinate)에 가장 적합한 좌표를 나타내고, 해당 좌표에서 상당한 양의 에너지를 포함하는 기저들을 선택함으로써 적은 feedback 정보량으로 MIMO 채널을 묘사한다. 시뮬레이션을 통해 제안된 부 공간 방식 기반 precoding 기법이 적은 feedback 정보량을 사용하면서 폐루프 MIMO 용량 (closed-loop MIMO capacity)에 근접하는 용량을 제공함을 보인다.

Deep learning driven beam selection for orthogonal beamforming with limited feedback

Jinho Choi,Moldir Yerzhanova,Jihong Park,Yun Hee Kim 한국통신학회 2022 ICT Express Vol.8 No.3

This letter studies deep learning methods for beam selection in multiuser beamforming with limited feedback. We construct a set of orthogonal random beams and allocate the beams to users to maximize the sum rate, based on limited feedback regarding the channel power on the orthogonal beams. We formulate the beam allocation problem as a classification or a regression task using a deep neural network (DNN). The results demonstrate that the DNN-based methods achieve higher sum rates than a conventional limited feedback solution in the low signal-to-noise ratio regime under Rician fading, thanks to their robustness to noisy limited feedback.

Subspace Method Based Precoding for MIMO Spatial Multiplexing

문철,정창규,박동희,곽윤식,Mun Cheol,Jung Chang-Kyoo,Park DongHee,Kwak Yoonsik The Korea Institute of Information and Commucation 2005 한국정보통신학회논문지 Vol.9 No.6

In this paper, for spatial multiplexing with limited feedback, we propose subspace based precoding in which the active bases are selected at the receiver from a finite number of basis sets known at both receiving and transmitting ends, conveyed to the transmitter using limited feedback, and assembled into a preceding matrix at the transmitter. The selected bases are conveyed to the transmitter using feedback information on both the index of a basis set, which indicates the most appropriate set of coordinates for describing a MIMO channel, and the active bases having the significant amounts of energy in the selected basis set. We show that the proposed subspace based precoding provides capacity similar to that of the closed-loop MIMO even with limited feedback. 본 논문에서는 제한된 피드백 정보를 사용하는 공간 다중화 기법에 사용될 수 있는 부 공간 방식 기반 preceding 기법을 제안한다. 제안된 preceding 기법은 수신기에서 다수의 공통 기저 집합(common basis sets)으로부터 용량을 최대로 하는 기저들을 선택하고, 선택된 기저들은 feedback 정보를 통해 송신기에 전달되고, 송신기에서는 선택된 기저들로 이루어진 precoding 행렬을 구성한다. 선택된 기저들은 해당 기저들이 속한 기저 집합의 index에 대한 feedback 정의와 선택된 기저 집합에서 각 기저들의 선택 여부에 대한 feedback 정보를 통해 송신기로 feedback된다. 선택된 기저 집합 index는 송수신기가 약속한 공통 기저 집합중에서 해당 MIMO 채널의 부 공간의 좌표(coordinate)에 가장 적합한 좌표를 나타내고, 해당 좌표에서 상당한 양의 에너지를 포함하는 기저들을 선택함으로써 적은 feedback 정보량으로 MIMO 채널을 묘사하다. 시뮬레이션을 통해 제안된 부 공간 방식 기반 precoding 기법이 적은 feedback 정보량을 사용하면서 폐루프 MIMO 용량 (closed-loop MIMO capacity)에 근접하는 용량을 제공함을 보인다.

Bit Allocation and Pairing Methods for Multi-User Distributed Antenna Systems With Limited Feedback

Hoon Lee,Eunsung Park,Haewook Park,Inkyu Lee Institute of Electrical and Electronics Engineers 2014 IEEE Transactions on Communications Vol. No.

<P>In this paper, we study bit allocation and pairing methods based on distributed zero forcing beamforming for downlink multi-user distributed antenna (DA) systems with limited feedback. Before assigning the feedback bit for each DA port, we need to solve the pairing issue that determines the set of DA ports to support a user. To this end, we first analyze an upper bound of a mean rate loss between perfect channel state information systems and limited feedback systems. Since minimizing the obtained bound is a joint optimization problem with respect to the pairing and the bit allocation, it is difficult to identify a solution analytically. Instead, we propose a two-step algorithm that derives the pairing based on the bound of the rate loss and then obtain the non-iterative bit allocation method independently. To further improve the performance, an enhanced feedback bit allocation algorithm is also proposed by applying an iterative optimization technique. In addition, we investigate a scaling law of limited feedback systems to maintain a constant rate loss as signal-to-noise ratio increases. From simulation results, we confirm that the proposed algorithms offer about 135% performance gains over a conventional scheme for five DA port systems and verify that our analysis is well matched with the numerical results.</P>

On Achievable Multiplexing Gain of BD in MIMO Broadcast Channels With Limited Feedback

Moonsik Min,Yo-Seb Jeon,Gi-Hong Im IEEE 2016 IEEE Transactions on Wireless Communications Vol.15 No.2

<P>To maintain a specific degree of multiplexing gain with limited feedback in multiple-input/multiple-output broadcast channels, the number of feedback bits has been increased linearly with the signal-to-noise ratio (SNR) measured in decibel, and conditions for the slope of this increase have been derived in previous studies. However, previous studies mostly focused on the chordal distance (ChD) for channel quantization, although it is not an optimally designed distance measure. Thus, the possibility exists that the same degree of multiplexing gain can be obtained by using fewer feedback bits than the existing method requires. In this paper, we propose an optimal distance measure that can maximize the multiplexing gain achieved by limited-feedback-based block diagonalization over broadcast channels. Then, we provide a sufficient condition for the number of feedback bits to achieve a specific degree of multiplexing gain with the proposed method. The sufficient number of feedback bits is given by a linear function of the SNR (decibel) as in previous studies, but the slope of the linear increase can be much less than that obtained in previous studies. As a consequence, the proposed method achieves higher multiplexing gain and corresponding throughput than the existing methods with the same number of feedback bits.</P>

Opportunistic Feedback With a Reservation Channel in a Wireless TDD System

Jae-Woo So,Cioffi, J.M. IEEE 2009 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY Vol.58 No.3

<P>A random-access-based feedback protocol with a reservation-based (RB) channel is proposed for multiuser diversity in a wireless time-division-duplex system. The feedback channels consist of one RB channel and several contention-based (CB) channels. The users randomly access the CB channels if their channel states exceed a threshold, and a base station (BS) schedules a user who reports the highest signal-to-noise ratio from multiple users that successfully provide feedback. If there is no successful feedback in the CB channels, the BS uses the feedback information that a designated user reports through the RB channel. The proposed feedback protocol achieves an almost ideal sum-rate capacity with a fixed number of feedback channels regardless of the number of users.</P>

Capacity Maximizing Adaptive Subcarrier Selection in OFDM with Limited Feedback

문철,정창규,박동희,곽윤식,Mun Cheol,Jung Chang-Kyoo,Park DongHee,Kwak Yoonsik The Korea Institute of Information and Commucation 2005 한국정보통신학회논문지 Vol.9 No.5

본 논문은 제한적인 피드백을 이용하는 OFDM 시스템에서 용량 극대화를 위한 효율적인 적응 부 반송파 선택 방식을 제안한다. 제안하는 방식에서는 데이터 전송에 사용될 부 반송파들과 각 부 반송파에 적용될 변조 및 코딩 방식들이 수신기에서 결정되고, 제한적인 피드백을 통해 송신기로 전달된다. 본 연구에서는 채널 환경에 따라 적절한 수의 높은 신호 대 잡음 비를 갖는 부 반송파들을 선택함으로써 용량이 극대화됨을 이론적으로 유도한다. 또한, 낮은 복잡도로 최적의 부 반송파 집합을 선택하기 위한 정렬 방식을 사용하는 적응 부 반송파 선택 알고리즘을 제안한다. 시뮬레이션 결과는 제안된 적응 부 반송파 선택 방식이 제한된 feedback 정보량만으로 water-filling 방식에 의한 부 반송파 선택 방식이나 water-filling 전력 할당에 의한 용량보다 높은 용량을 제공함을 보여준다. We propose an efficient adaptive subcarrier selection scheme, in which the active subcarriers and their modulation and coding schemes (MCSs) are selected at the receiver, and subsequently conveyed to the transmitter using limited feedback We theoretically show that capacity maximization can be achieved by selecting subcarriers with highest signal-to-noise ratios (SNRs) and adapting the number of active subcarriers according to channel environments. Furthermore, an ordering based adaptive subcarrier selection algorithm is proposed to select the optimal active subcarriers with low complexity. Numerical results show that the proposed adaptive subcarrier selection scheme provides higher capacity than that obtained by water-filling approaches, even with limited feedback.

제한된 피드백 정보를 이용하는 이중 공간 다중화 시스템의 Preceding 기법

이명원,문철,육종관,Lee, Myoung-Won,Mun, Cheol,Yook, Jong-Gwan 한국전자파학회 2006 한국전자파학회논문지 Vol.17 No.12

본 논문에서는 제한된 피드백 정보를 사용하는 공간 다중화 시스템을 위한 preceding 기법을 제안하였다. 제안하는 precoding 기법은 unitary 행렬로 구성된 precoder 코드북내에서 preceding 행렬의 선택 정보를 송신단에 전달하는 장구간 피드백과 선택된 unitary 행렬의 열 벡터 중 전송체 사용될 열 벡터 정보를 송신단에 전달하는 단구간 피드백을 이용한다. 또한, zero-forcing 수신기를 사용하는 $2{\times}2$ MIMO 시스템에 대해 평균 throughput을 최대화하는 precoder 코드북을 디자인하였다. 모의 실험 결과에 따르면 제안된 기법은 몇 비트의 장구간 피드백 정보를 추가함으로써 평균 SNR이 20 dB인 환경에서 멀티모드 안테나 선택 기술이나 멀티모드 기저 선택 기술에 비해 throughput 성능이 각각 11.2 %, 5.1 % 증가한다. In this paper, for spatial multiplexing with limited feedback, a precoding scheme is proposed based on the joint use of minimal instantaneous feedback and long-term feedback of a small number of bits, wherein the long-term feedback is used to convey a selected preceding matrix within a precodercodebook consisting of a number of unitary matrices, and the active column vectors of the selected unitary matrix are conveyed to the transmitter using instantaneous feedback. Focusing on the case of dual multi-input multi-output(MIMO) systems, precoder codebook design for maximizing the average throughput of a spatial multiplexing system with a zero-forcing(ZF) receiver is proposed. It is shown that the proposed scheme provides a considerable throughput enhancement over multi-mode antenna selection and multi-mode basis selection only with the additional long-yterm feedback of a small number of bits. For example, the throughput increases by 11.5 % than antenna selection and 5.1% than basis selection, respectively, when SNR=20 dB.