Design of reduced complexity feedback precoding for MIMO‐OFDM

Abstract

Beamforming technique is applied to significantly increase the performance of a MIMO system, if the channel information (CI) of the communication system is available at the transmitter. For the transmitter to obtain the entire CI, however, a considerable reverse-link bandwidth is required. To save the bandwidth, a limited-rate closed-loop system, therefore, uses a predetermined codebook which is derived from the CI. The codebook consists of a finite number of precoders out of which the index of the best one is transmitted from the receiver to the transmitter using only a few bits saving substantial bandwidth. However, the amount of bits that need to be fed back can still be significantly large for MIMO-OFDM systems when the precoding matrix index (PMI) for each subcarrier should be transmitted. Such per-subcarrier precoding scheme has high feedback overhead and also incurs huge computational cost to determine the best PMI for each subcarrier. We, therefore, propose a per-band precoding scheme that precodes a band (group) of subcarriers by only one precoder. More importantly, we develop, for the proposed per-band scheme, reduced-complexity precoding selection methods that lead to the design of efficient receivers. The effectiveness of the proposed scheme is investigated through computer simulations. 143When a MIMO transmitter obtains a channel information (CI), the performance of the communication system can be further enhanced [4][5][6]. The availability of the CI enables the transmitter to precode the data and beamform the transmitted signal in such a way that the signal eigen modes match to those of the channel modes [7]. Applying precoding decomposes the signal into orthogonal spatial eigen modes and it effectively decouples the channel into parallel subchannels that transmit independent signals. Such decoupling of the channel provides the ability to adapt the allocation of power to the eigen modes of the signal according to the strength of their corresponding channel modes [8,9]. Therefore, it is well known that precoding, or beamforming, along with an optimal power allocation scheme, water-filling, enables a MIMO system to achieve maximum capacity [10,11].In cellular time-division-duplex systems, the transmitter may be able to derive the forward CI, using the principle of reciprocity, from the estimates of the reverse channel. In cellular frequencydivision duplex systems, however, because reciprocity does not apply, the forward CI cannot be derived from the estimates of the reverse channel. An alternative approach would be to send back CI from receiver to transmitter over an additional reverse channel [12]. Feeding back the entire CI to the transmitter, however, would require a high-rate reverse channel which demands considerable additional transmission resource. Reducing the amount of feedback overhead has been a subject of a lot of research work, and, therefore, several methods have been proposed in the literature [13,14].A limited-feedback closed-loop MIMO system employs a codebook to represent the CI tha...

Achievable rates of SVD‐based codebooks for zero‐forcing and Tomlinson‐Harashima precoding schemes with limited feedback MU‐MIMO system

“…The main parameters utilized to generate the numerical results are given in Table I. The achievable sum-rate for TH and ZF precodings by using SVD codebooks is compared by varying the feedback bits in steps from 10,12,14,16,18, and 20 bits for each user is shown in Figure 4. The achievable sum-rate results clearly show that TH precoding outperforms the ZF precoding by using SVD codebooks because of the ability SVD codebooks to more precisely improve the channel.…”

“…Thereby motivated by these problems, in this paper, we pose some questions such as: what kind of codebooks are required instead of existing codebooks [5][6][7][8][9][10][11][12][13][14] to precisely improve the channel at the Tx side? What will be the closed-form solution of the achievable rates for the proposed codebooks to efficiently apply precoding schemes?…”

“…In literature, to reduce the quantization error by improving the quantization accuracy, the Grassmannian or line packing‐based codebooks , predictive vector quantization (VQ)‐based codebooks , channel statistics‐based codebooks , limited feedback burden‐based precoding , subspace quantization‐based combining , ZF and codebook‐based beamforming , codebook design for beamforming analysis , and random VQ based codebook design schemes have been suggested to increase the quantization precision. In spite of the ability of these procedures to reduce quantization error by applying linear ZF precoding at Tx side, but these are not efficient enough to apply nonlinear interference cancellation schemes such as THP on the BS side because of more quantization error.…”

Widely linear channel estimation for LD‐STBC MB‐OFDM UWB systems

“…Combination of MB‐OFDM UWB and Multiple‐Input Multiple‐Output (MIMO) technologies has been well investigated in the literature . Indeed, it provides error performance improvement and high data rates.…”

On Transmit Beamforming for MISO-OFDM Channels With Finite-Rate Feedback

“…In [4], [9], [15], [18], the optimal transmit beamforming vectors of selected subcarriers, which are a few subcarriers apart, are quantized while the remaining ones are approximated to equal the quantized vector of the closest subcarrier. The remaining transmit beamforming vectors are proposed to be linearly interpolated in [5], [12] and spherically interpolated in [6], [11], [13].…”