Optimal Number Of Training Symbols Research Articles

LMMSE Receivers in Uplink Massive MIMO Systems With Correlated Rician Fading

We carry out a theoretical analysis of the uplink (UL) of a massive MIMO system with per-user channel correlation and Rician fading, using two processing approaches. First, we examine the linear-minimum-mean-square-error receiver under training-based imperfect channel estimates. Second, we propose a statistical combining technique that is more suitable in environments with strong line-of-sight (LoS) components. We derive closed-form asymptotic approximations of the UL spectral efficiency (SE) attained by each combining scheme in single and multi-cell settings, as a function of the system parameters. These expressions are insightful in how different factors such as LoS propagation conditions and pilot contamination impact the overall system performance. Furthermore, they are exploited to determine the optimal number of training symbols, which is shown to be of significant interest at low Rician factors. The study and numerical results substantiate that stronger LoS signals lead to better performances, and under such conditions, the statistical combining entails higher SE gains than the conventional receiver.

Optimal Training-Based Scheme for MIMO Full-Duplex Wireless Links

In a multiple-input-multiple-output (MIMO) full-duplex (FD) wireless link, training-based schemes are the most effective with digital self-interference (SI) cancellation methods after antenna and analog SI cancellations, and they help receiver to know responses of both residual SI channel for digital cancellation and transmission channel for demodulation. In this situation, the open issue is that how much training is needed in MIMO FD wireless links-too little training will cause the imperfect digital SI cancellations and the transmission channels are also improperly learned, too much training and the links have no time left for the data transmission before the fading channel changes. We compute a capacity lower bound of a MIMO FD channel that is learned at the receiver by training without any feedbacks, and maximize the bound as a function of the received signal-to-noise ratio $\rho $ , fading coherence time $T$ , and numbers of link antennas $M$ , $N$ . When training power is equal to data power, numerical results show that the optimal number of training symbols $T_{o}$ is $T_{o}\geq 2\mathrm {max}(M,N)$ if $T \gg \mathrm {max}(M,N)$ under appropriate $\rho $ . Conversely, if $T\approx 2\max (M,N)$ , $T_{o} .

Outage Probability and Power Allocation of Two-Way Amplify-and-Forward Relaying with Channel Estimation Errors

We consider a two-way amplify-and-forward (AF) relaying system consisting of two source nodes and a half-duplex relay. We assume that the source nodes are equipped with the linear minimum mean squared error (LMMSE) channel estimators. We investigate the effect of uncertainty due to channel estimation error on the system outage probability, considering the imposed bandwidth and energy costs of channel estimation. For a fixed transmission block length and a total transmit power constraint, we provide a compact-form expression for the system outage probability upper bound and we explore the optimal number of training symbols, the optimal power allocation between data and training, and the optimal power allotment between the two users and the relay, such that this bound is minimized. Our numerical results show that channel estimation error does not limit the performance in high signal-to-noise ratio (SNR). Also, the optimal power allocation between data and training and between the users and the relay provides a significant SNR improvement, compared with the suboptimal schemes, including fixed power allocation. The optimization gain increases as the relay moves away from the middle point.

How Does Channel Estimation Error Affect Average Sum-Rate in Two-Way Amplify-and-Forward Relay Networks?

This paper studies the impact of channel estimation error on the performance of a two-way amplify-and-forward (AF) relay network and investigates the optimal transmit resource allocation that minimizes the impact. In particular, we consider a three node network, consisting of two user terminals \mathbb{T}_A and \mathbb{T}_B and a half duplex relay node \mathbb{R}, where only \mathbb{T}_A and \mathbb{T}_B are equipped with channel estimators. Assuming block flat fading channel model, we adopt two estimation theoretic performance metrics, namely the Bayesian Cramer-Rao lower bound (CRLB) and the mean-squared error (MSE) of the linear minimum mean square error (LMMSE) channel estimate, and an information theoretic performance metric, namely the average sum-rate lower bound, as our optimality criteria. For a fixed transmission block length and under the total transmit power constraint, we investigate the optimal training vector design, the optimal number of training symbols in the training vector, the optimal power allocation between training and data in a transmission block, and the optimal power allotment between three nodes, such that these performance metrics are optimized, via utilizing bi-objective optimization methods. Our simulation results demonstrate that the optimal solutions corresponding to each performance metric vary, as the relay location and the system signal-to-noise ratio (SNR) change. They also reveal interesting symmetry relationship between these optimal solutions and the relay location.

Transmission Resource Allocation for Training Based Amplify-and-Forward Relay Systems

For a three node amplify-and-forward (AF) relay system in which only destination D is equipped with a channel estimator, we derive lower bound on training-based mutual information per transmission block. For a given transmission block length and a fixed total transmit power constraint between source S and relay R, we investigate jointly optimal number of training symbols, optimal power allocation between training and data, and optimal power allotment between S and R, such that the mutual information lower bound is maximized. For the AF relay system without direct link we provide analytical solutions to the joint optimization problem and relate the solutions to the relay location. For the AF relay system with direct link we resort to numerical evaluations to find the optimal solutions.

Space-time coded asynchronous DS-CDMA with decentralized MAI suppression: performance and spectral efficiency

Multiple-input, multiple-output (MIMO) techniques are considered in an asynchronous code-division multiple- access system with a flat fading channel. A unified maximum- likelihood receiver, based on chip-level oversampling, is proposed to jointly suppress the multiple-access interference and perform the space-time decoding. Analysis shows that the system performance is determined by the product measure of the space- time code and the effective signal-to-interference-plus-noise- ratio (SINR). Three expurgated union bounds are proposed to approximate the bit error rate for different MIMO schemes and SNRs. Next, spectral efficiency is analyzed by applying a Gaussian approximation to the multiple-access interference. Numerical results show that the chip-level oversampling, together with MIMO techniques, can effectively increase the spectral efficiency. The impact of channel estimation error on spectral efficiency is also investigated both analytically and numerically. Two tradeoffs are found in a lower bound of spectral efficiency. In the first tradeoff to optimize spectral efficiency, the increase of the number of users is shown to dominate the degradation of SINR. In the second tradeoff, increasing the number of training symbols in a fixed-length packet is shown to yield a higher SINR but a reduction in the amount of transmitted information. An optimal number of training symbols is found numerically as a function of the SNR and the packet length.

How much training is needed in multiple-antenna wireless links?

Multiple-antenna wireless communication links promise very high data rates with low error probabilities, especially when the wireless channel response is known at the receiver. In practice, knowledge of the channel is often obtained by sending known training symbols to the receiver. We show how training affects the capacity of a fading channel-too little training and the channel is improperly learned, too much training and there is no time left for data transmission before the channel changes. We compute a lower bound on the capacity of a channel that is learned by training, and maximize the bound as a function of the received signal-to-noise ratio (SNR), fading coherence time, and number of transmitter antennas. When the training and data powers are allowed to vary, we show that the optimal number of training symbols is equal to the number of transmit antennas-this number is also the smallest training interval length that guarantees meaningful estimates of the channel matrix. When the training and data powers are instead required to be equal, the optimal number of symbols may be larger than the number of antennas. We show that training-based schemes can be optimal at high SNR, but suboptimal at low SNR.