Advances in MIMO Techniques for Mobile Communications—A Survey <s> Partial Feedback Schemes <s> This paper presents optimum MIMO precoder designs based on transmit and receive correlation matrices to maximize the ergodic channel capacity for both frequency-flat and frequency-selective fading channels. It is shown that the optimum MIMO precoder in a frequency-flat fading channel is an eigen beamformer with beams referred to the eigen-modes of the transmit correlation matrix. By using the multi-path representation of a frequency-selective fading channel, the corresponding optimum precoding structure is derived. For a frequency-selective fading channel that can be represented by L uncorrelated effective paths, the optimum precoding structure consists of P+L parallel eigen-beamformers. Simulation results show that the proposed precoders can improve the ergodic capacity of both frequency-flat and frequency-selective fading channels, especially for channels with high spatial correlation. <s> BIB001 </s> Advances in MIMO Techniques for Mobile Communications—A Survey <s> Partial Feedback Schemes <s> Close loop transmission incorporating preceding, rate and power loading etc, can improve the performance of multiple-input multiple-output (MIMO) antenna system and draw much attention in recent research. However, the feedback overhead of channel information may significantly reduce the system throughput especially in FDD mode. In this paper, a statistical information based partial feedback scheme is proposed for MIMO communication system to reduce the amount of channel information feedback, which can be used to improve the scheduling and rate control of traffic. Simulations demonstrate that the proposed scheme overhead can be reduced greatly and still tracking the variation of channel. <s> BIB002 </s> Advances in MIMO Techniques for Mobile Communications—A Survey <s> Partial Feedback Schemes <s> The closed-loop transmit diversity technique is used to improve the performance of the downlink channel in multiple-input multiple-output (MIMO) communication systems. The wideband code-division multiple-access standard endorsed by the Third Generation Partnership Project (3GPP) adopts a downlink closed-loop scheme based on partial channel state information (CSI) known as mode 1. The information is fed back from the mobile unit to the base station through a low-rate uncoded feedback bit stream. In this paper, several reconstruction techniques are introduced to improve the performance of mode 1 of 3GPP in the presence of feedback error by taking advantage of the redundancy available in the bit stream of the CSI. We propose a number of algorithms for the reconstruction of beamforming weights at the base station with the constraint of a constant transmit power. The performance is examined within a simulated 3GPP framework. It is demonstrated that the proposed algorithms have substantial gain over the conventional method for low, moderate, and high mobile speeds. It is also shown that the proposed algorithms can substitute the antenna weight verification process done at the mobile unit in many cases. The proposed approach is applicable to other feedback schemes as well. <s> BIB003 </s> Advances in MIMO Techniques for Mobile Communications—A Survey <s> Partial Feedback Schemes <s> We have been proposing multi-beam MIMO (MB-MIMO) as an evolved UTRA downlink MIMO scheme for 3GPP long term evolution (LTE). MB-MIMO is a pre-coding MIMO scheme that uses a simple combination of multi-beam multiple-data-stream transmission and user equipment (UE)-based adaptive beam selection. The scheme benefits from its simple uplink feedback signaling, because MB-MIMO requires only a subset of the beam (codebook) indices to be fed back. However, a hardware calibrator (HW-CAL), which increases the complexity of RF components at a transmitter, should be installed in order to achieve a high beam-forming gain with a small codebook size. In this paper, we propose a novel codebook design for MB-MIMO, which realizes a superior performance without any HW-CAL with a small increase of the codebook size and the feedback signaling. We performed a computer simulation to evaluate the throughput performance of the proposed scheme, considering the phase variation between antenna elements in a spatially distributed multi-path fading channel model. <s> BIB004
Partial feedback schemes for MIMO systems are based on the feedback of statistical channel information along with some instantaneous channel quality indicator (CQI) e.g. SNR, SINR etc. to the transmitter. A partial feedback scheme for MIMO-OFDM systems involving the decomposition of MIMO channel covariance matrix is presented in BIB002 . The covariance matrix R is calculated from the estimated MIMO channel matrix H (for the k-th subcarrier) at the receiver and is given by The matrix R is then decomposed using SVD which is given by where is a diagonal matrix containing the singular  where x is the transmit data vector, H is the MIMO channel matrix for the k-th subcarrier, A is a diagonal matrix with diagonal elements determined by the matrix feedback for power allocation to the active spatial streams, and the BIB002 . The MIMO channel covariance and the corresponding channel singular values do not vary rapidly with time even at vehicular speeds around 100 km/h BIB002 . This greatly reduces the feedback load on the system and makes this closed-loop MIMO-OFDM system suitable for mobile environments. Figures 21 and 22 show the simulated frame error rate (FER) performance of the proposed MIMO-OFDM system in comparison with open-loop SM and perfect CSI feedback MIMO-OFDM systems, for 2 u 2 and 4 u 4 MIMO configurations respectively. The figures include FER performance curves for QPSK and 64-QAM modulation in a low speed mobile scenario using the ITU PB channel profile with vehicular speeds of 3 km/h. The OFDM scheme is based on 512-point FFT with 15 subchannels for data transmission each consisting of 20 continuous subcarriers, for a total bandwidth of 5 MHz. The frame duration is about 0.5ms. Turbo coding is employed for FEC and MMSE detection is used at the receiver. Equal power allocation is used for the open-loop SM system while water-filling is used for the closed-loop systems. Ideal channel knowledge is assumed at the receiver for all systems and antenna correlations are not considered BIB002 . As seen from the results, the proposed system operates quite close to the perfect CSI feedback system and shows substantial performance gain over the open-loop system. The small performance loss in comparison with the perfect feedback system is primarily due to the quantization error associated with limited feedback BIB002 . Efficient feedback reconstruction algorithms for improvement of the closed-loop transmit diversity scheme constituting the mode 1 of 3GPP's wideband code-division multiple access (WCDMA) 3G standard are presented in BIB003 . These algorithms efficiently reconstruct the beamforming weights at the transmitter while considering the effect of feedback error. Performance results for vehicular speeds up to 100 km/h are provided. The proposed techniques are applicable to closed-loop MI-MO diversity systems and may possibly be extended to 4G systems. In BIB001 , the optimal MIMO precoder designs for frequency-flat and frequency-selective fading channels are presented, assuming partial CSI at the transmitter consisting of transmit and receive correlation matrices. The elements of transmit and receive correlation matrices are determined from the respective transmit and receive antenna spacing and angular spread. It is shown that from the capacity maximization perspective, the optimal precoder for a frequency-flat fading channel is an eigen-beamformer. On the other hand, the optimal precoder for a frequency-selective fading channel represented by L uncorrelated effective paths consists of P + L parallel eigen-beamformers where P is an arbitrary value depending on the no. of vectors in a transmission data block BIB001 . A closed-loop limited feedback MIMO scheme called multi-beam MIMO (MB-MIMO) is proposed in BIB004 for 3GPP LTE E-UTRA downlink. MB-MIMO employs multiple fixed beams at the base station (Node B) to transmit multiple data streams. The no. of beams and data streams to be used are adaptively selected using a codebook at the UE. The selected precoding vectors or beam indices constituting a precoding matrix are then fed back to the Node B. The MB-MIMO scheme can adaptively switch between MIMO SM and transmit beamforming (Tx-BF) modes. Tx-BF is used if a single beam is selected and SM is used if multiple beams are selected. The proposed scheme eliminates the need for a hardware calibrator (HW-CAL) at Node B that was required for a previously proposed MB-MIMO implementation. HW-CAL compensates the phase variations caused by RF components and was needed to align the phase condition of each transmit antenna element for maximizing the transmit beamforming gain. The proposed scheme uses a larger codebook based on an extended precoding matrix which includes phase terms that can be controlled to align the phase condition of the 4 node B antenna elements. This results in high beamforming gain even without HW-CAL. However, 4 additional bits or a total of 8 bits are required for feedback, which is still a small number.