We consider power-domain multiple-input multiple-output (MIMO) nonorthogonal multiple access (NOMA) down-links in which a multiple-antenna base station applies zeroforcing beamforming to transmit data to single-antenna users. Two users whose channel correlation coefficient exceeds a threshold are paired to share the same transmit beam. We derive an approximate of the expected signal-to-interference plus noise ratio (SINR) for each user, which depends on transmit power, the correlation threshold, and the number of quantization bits for channel direction information (CDI). A max-min SINR problem is formulated as a geometric program. We show that a near-optimal SINR can be achieved by optimizing only two CDI rates: one for unpaired users and the other for user pairs. A large SINR gain can be achieved by optimizing a pairing threshold when a total CDI rate is high.

In downlink, a base station (BS) with multiple transmit antennas applies zeroforcing beamforming to transmit to single-antenna mobile users in a cell. We propose the schemes that optimize transmit power and the number of bits for channel direction information (CDI) for all users to achieve the max-min signal-to-interference plus noise ratio (SINR) fairness. The optimal allocation can be obtained by a geometric program for both non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA). For NOMA, 2 users with highly correlated channels are paired and share the same transmit beamforming. In some small total-CDI rate regimes, we show that NOMA can outperform OMA by as much as 3 dB. The performance gain over OMA increases when the correlation-coefficient threshold for user pairing is set higher. To reduce computational complexity, we propose to allocate transmit power and CDI rate to groups of multiple users instead of individual users. The user grouping scheme is based on K-means over the user SINR. We also propose a progressive filling scheme that performs close to the optimum, but can reduce the computation time by almost 3 orders of magnitude in some numerical examples.

We consider non-orthogonal multiple access (NOMA) downlink channels with zeroforcing beamforming transmission. With limited feedback rate, channel direction information (CDI) needs to be quantized and fed back from mobile users to a base station. To increase spectral efficiency, two active users in some clusters share the same beamforming vector and thus, will interfere fully with each other. We derive the approximate achievable rates and outage probability for users in 1-user and 2-user clusters. With the approximate outage probability derived as a function of feedback rate, we find the optimal feedback allocation for both types of cluster that minimizes the maximum outage probability for all users. Numerical results show that significant gain over uniform feedback allocation is achieved in moderate-to-large SNR regimes.

A receiver with perfect channel state information (CSI) in a point-to-point multiple-input multiple-output (MIMO) channel can compute the transmit beamforming vector that maximizes the transmission rate. For frequency-division duplex, a transmitter is not able to estimate CSI directly and has to obtain a quantized transmit beamforming vector from the receiver via a rate-limited feedback channel. We assume that time evolution of MIMO channels is modeled as a Gauss-Markov process parameterized by a temporal-correlation coefficient. Since feedback rate is usually low, we assume rank-one transmit beamforming or transmission with single data stream. For given feedback rate, we analyze the optimal feedback interval that maximizes the average received power of the systems with two transmit or two receive antennas. For other system sizes, the optimal feedback interval is approximated by maximizing the rate difference in a large system limit. Numerical results show that the large system approximation can predict the optimal interval for finite-size system quite accurately. Numerical results also show that quantizing transmit beamforming with the optimal feedback interval gives larger rate than the existing Kalman-filter scheme does by as much as 10% and then feeding back for every block does by 44% when the number of feedback bits is small.

With finite-rate feedback, we propose two feedback methods for transmit beamforming in a point-to-point MISO-OFDM channel. For the first method, a receiver with perfect channel information, quantizes and feeds back the optimal transmit beamforming vectors of a few selected subcarriers, which are equally spaced. Based on those quantized vectors, the transmitter applies either constant, linear, or higher-order interpolation with the remaining beamforming vectors. With constant interpolation, we derive the approximate sum achievable rate and the optimal cluster size that maximizes the approximate rate. For linear interpolation, we derive a closed-form expression for the phase rotation by utilizing the correlation between OFDM subcarriers. We also propose a higher-order interpolation that requires more than two quantized vectors to interpolate transmit beamformers, and is based on existing channel estimation methods. Numerical results show that interpolation with the optimized cluster size can perform significantly better than that with an arbitrary cluster size. For the second proposed method, a channel impulse response is quantized with a uniform scalar quantizer. With channel quantization, we also derive the approximate sum achievable rate. We show that switching between the two methods for different feedback-rate requirements can perform better than the existing schemes.

We propose two feedback methods for transmit beamforming in a point-to-point multiple-antenna OFDM channel. For the first method, a receiver with channel information quantizes and feeds back the optimal transmit beamforming vectors of a few selected subcarriers that are equally spaced. Based on those quantized vectors, the transmitter linearly interpolates the remaining beamforming vectors with different phase rotation whose expression is explicitly shown. For the second proposed method, a channel impulse response is quantized with a uniform scalar quantizer. At the transmitter, channel frequency response can be reconstructed from the quantized impulse response and the optimal beamforming vectors can then be computed. We show that switching between the two methods for different feedback-rate requirement outperforms existing methods in the literature.

Assuming perfect channel state information (CSI), the receiver in a point-to-point multiantenna channel can compute the optimal transmit beamforming vector that maximizes channel capacity. The transmitter, which is not able to estimate the CSI, obtains the quantized transmit beamforming vector via a rate-limited feedback channel. We assume that time evolution of both MIMO and MISO channels can be modeled as the first-order autoregressive process parameterized by a temporal-correlation coefficient. For a limited number of feedback bits, we would like to find out how often the feedback update should take place. Applying a large system limit and random vector quantization (RVQ), we derive the integer optimization problem, which determines the optimal feedback interval that maximizes the average capacity. The analytical results show that the optimal feedback interval depends on the temporal correlation coefficient, available feedback, and the number of transmit and receive antennas.

We consider the quantization of a transmit beamforming vector in multiantenna channels and of a signature vector in code division multiple access (CDMA) systems. Assuming perfect channel knowledge, the receiver selects for a transmitter the vector that maximizes the performance from a random vector quantization (RVQ) codebook, which consists of independent isotropically distributed unit-norm vectors. The quantized vector is then relayed to the transmitter via a rate-limited feedback channel. The RVQ codebook requires an exhaustive search to locate the selected entry. To reduce the search complexity, we apply generalized Lloyd or k-dimensional (kd)-tree algorithms to organize RVQ entries into a tree. In examples shown, the search complexity of tree-structured (TS) RVQ can be a few orders of magnitude less than that of the unstructured RVQ for the same performance. We also derive the performance approximation for TS-RVQ in a large system limit, which predicts the performance of a moderate-size system very well.