AoD-adaptive subspace codebook for channel feedback in FDD massive MIMO systems

Abstract

Channel feedback is essential in frequency division duplexing (FDD) massive multiple-input multipleoutput (MIMO) systems. Unfortunately, previous work on multiuser MIMO has shown that the codebook size for channel feedback should scale exponentially with the number of base station (BS) antennas, which is greatly increased in massive MIMO systems. To reduce the codebook size and feedback overhead, we propose an angle-of-departure (AoD)-adaptive subspace codebook for channel feedback in FDD massive MIMO systems. Our key insight is to leverage the observation that path AoDs vary more slowly than the path gains. Within the angle coherence time, by utilizing the constant AoD information, the proposed AoD-adaptive subspace codebook is able to quantize the channel vector in a more accurate way. We also provide performance analysis of the proposed codebook in the large-dimensional regime, where we prove that to limit the capacity degradation within an acceptable level, the required number A part of this paper was presented

Efficient downlink channel reconstruction for FDD transmission systems

“…In [2], [3], the authors utilized the slowly changing feature of the space and estimated the downlink CSI from the downlink training process. Numerical results in [4] also showed that a significant overhead reduction can be achieved via the partial support information obtained from the uplink.…”

Channel Feedback Codebook Design for Millimeter-Wave Massive MIMO Systems Relying on Lens Antenna Array

“…Next, we will discuss the quantization error, which is different from that in [6] and [9] due to the specific distribution of the equivalent channel h e k . In the rest of this paper, we can omit the subscript k without loss of generality, where h e , A, and P denote the equivalent channel, the steering matrix, and the number of dominant paths per user, respectively.…”

“…Finally, the k-th user will quantize the equivalent channel h e k based on the proposed RDSC by finding d k,F k that is closest to h e k , where the index F k is computed as is just a scalar, we follow the widely used assumption that this magnitude h e k can be fed back to the BS perfectly [6], [7], [9]. The codebook index F k can be fed back using B bits.…”

“…Proof: We firstly calculate the (i, j)-th element of UA, which is obtained as the product of the i-th row vector a(δ(i− 1)) H of U and the j-th column vector a(ψ j ) of A. In the large-dimensional regime, due to the orthogonality between a(δ(i − 1)) and a(ψ j ) (∀ψ j = δ(i − 1)) [9], UA has one nonzero element "1" in each column, whose location is different in different columns. Note that the beam selector S is designed to choose N RF rows of UA which includes non-zero elements and N RF is usually much larger than P (e.g., N RF = P K [2]).…”

“…Firstly, we exploit the recently proposed concept of angle coherence time [9], [10] defined as the period, within which the AoDs remain near-constant. During the angle coherence time, the channel vector h k = A k g k in (3) is distributed in the column space of A k ∈ C M ×P k , which is termed as the channel subspace, determined by P k ( M ) AoDs.…”