Closed-form Output Statistics of MIMO Block-Fading Channels

The information that can be transmitted through a wireless channel, with multiple-antenna equipped transmitter and receiver, is crucially influenced by the channel behavior as well as by the structure of the input signal. We characterize in closed form the probability density function (pdf) of the output of MIMO block-fading channels, for an arbitrary SNR value. Our results provide compact expressions for such output statistics, paving the way to a more detailed analytical information-theoretic exploration of communications in presence of block fading. The analysis is carried out assuming two different structures for the input signal: the i.i.d. Gaussian distribution and a product form that has been proved to be optimal for non-coherent communication, i.e., in absence of any channel state information. When the channel is fed by an i.i.d. Gaussian input, we assume the Gramian of the channel matrix to be unitarily invariant and derive the output statistics in both the noise-limited and the interference-limited scenario, considering different fading distributions. When the product-form input is adopted, we provide the expressions of the output pdf as the relationship between the overall number of antennas and the fading coherence length varies. We also highlight the relation between our newly derived expressions and the results already available in the literature, and, for some cases, we numerically compute the mutual information, based on the proposed expression of the output statistics.Comment: 16 pages, 5 figure

Output Statistics of MIMO Channels with General Input Distribution

The information that can be conveyed through a wireless channel, with multiple-antenna equipped transmitter and receiver, crucially depends on the channel behavior as well as on the input structure. In this paper, we derive analytical results, concerning the probability density function (pdf) of the output of a single-user, multiple-antenna communication. The analysis is carried out under the assumption of an optimized input structure, and assuming Gaussian noise and a Rayleigh block-fading channel. Our analysis therefore provides a quite general and compact expression for the conditional output pdf. We also highlight the relation between such an expression and the results already available in the literature for some specific input structure

Optimum Pilot Overhead in Wireless Communication: A Unified Treatment of Continuous and Block-Fading Channels

The optimization of the pilot overhead in single-user wireless fading channels is investigated, and the dependence of this overhead on various system parameters of interest (e.g., fading rate, signal-to-noise ratio) is quantified. The achievable pilot-based spectral efficiency is expanded with respect to the fading rate about the no-fading point, which leads to an accurate order expansion for the pilot overhead. This expansion identifies that the pilot overhead, as well as the spectral efficiency penalty with respect to a reference system with genie-aided CSI (channel state information) at the receiver, depend on the square root of the normalized Doppler frequency. Furthermore, it is shown that the widely-used block fading model is only a special case of more accurate continuous fading models in terms of the achievable pilot-based spectral efficiency, and that the overhead optimization for multiantenna systems is effectively the same as for single-antenna systems with the normalized Doppler frequency multiplied by the number of transmit antennas.Comment: Submitted to IEEE Trans. Wireless Communication

Finite Random Matrix Theory Analysis of Multiple Antenna Communication Systems

Multiple-antenna systems are capable of providing substantial improvement to wireless communication networks, in terms of data rate and reliability. Without utilizing extra spectrum or power resources, multiple-antenna technology has already been supported in several wireless communication standards, such as LTE, WiFi and WiMax. The surging popularity and enormous prospect of multiple-antenna technology require a better understanding to its fundamental performance over practical environments. Motivated by this, this thesis provides analytical characterizations of several seminal performance measures in advanced multiple-antenna systems. The analytical derivations are mainly based on finite dimension random matrix theory and a collection of novel random matrix theory results are derived. The closed-form probability density function of the output of multiple-input multiple-output (MIMO) block-fading channels is studied. In contrast to the existing results, the proposed expressions are very general, applying for arbitrary number of antennas, arbitrary signal-to-noise ratio and multiple classical fading models. Results are presented assuming two input structures in the system: the independent identical distributed (i.i.d.) Gaussian input and a product form input. When the channel is fed by the i.i.d. Gaussian input, analysis is focused on the channel matrices whose Gramian is unitarily invariant. When the channel is fed by a product form input, analysis is conducted with respect to two capacity-achieving input structures that are dependent upon the relationship between the coherence length and the number of antennas. The mutual information of the systems can be computed numerically from the pdf expression of the output. The computation is relatively easy to handle, avoiding the need of the straight Monte-Carlo computation which is not feasible in large-dimensional networks. The analytical characterization of the output pdf of a single-user MIMO block-fading channels with imperfect channel state information at the receiver is provided. The analysis is carried out under the assumption of a product structure for the input. The model can be thought of as a perturbation of the case where the statistics of the channel are perfectly known. Specifically, the average singular values of the channel are given, while the channel singular vectors are assumed to be isotropically distributed on the unitary groups of dimensions given by the number of transmit and receive antennas. The channel estimate is affected by a Gaussian distributed error, which is modeled as a matrix with i.i.d. Gaussian entries of known covariance. The ergodic capacity of an amplify-and-forward (AF) MIMO relay network over asymmetric channels is investigated. In particular, the source-relay and relay-destination channels undergo Rayleigh and Rician fading, respectively. Considering arbitrary-rank means for the relay-destination channel, the marginal distribution of an unordered eigenvalue of the cascaded AF channel is presented, thus the analytical expression of the ergodic capacity of the system is obtained. The results indicate the impact of the signal-to-noise ratio and of the Line-of-Sight component on such asymmetric relay network

Fundamental Limits of Cooperation

Cooperation is viewed as a key ingredient for interference management in wireless systems. This paper shows that cooperation has fundamental limitations. The main result is that even full cooperation between transmitters cannot in general change an interference-limited network to a noise-limited network. The key idea is that there exists a spectral efficiency upper bound that is independent of the transmit power. First, a spectral efficiency upper bound is established for systems that rely on pilot-assisted channel estimation; in this framework, cooperation is shown to be possible only within clusters of limited size, which are subject to out-of-cluster interference whose power scales with that of the in-cluster signals. Second, an upper bound is also shown to exist when cooperation is through noncoherent communication; thus, the spectral efficiency limitation is not a by-product of the reliance on pilot-assisted channel estimation. Consequently, existing literature that routinely assumes the high-power spectral efficiency scales with the log of the transmit power provides only a partial characterization. The complete characterization proposed in this paper subdivides the high-power regime into a degrees-of-freedom regime, where the scaling with the log of the transmit power holds approximately, and a saturation regime, where the spectral efficiency hits a ceiling that is independent of the power. Using a cellular system as an example, it is demonstrated that the spectral efficiency saturates at power levels of operational relevance.Comment: 27 page

One-Bit Massive MIMO: Channel Estimation and High-Order Modulations

We investigate the information-theoretic throughout achievable on a fading communication link when the receiver is equipped with one-bit analog-to-digital converters (ADCs). The analysis is conducted for the setting where neither the transmitter nor the receiver have a priori information on the realization of the fading channels. This means that channel-state information needs to be acquired at the receiver on the basis of the one-bit quantized channel outputs. We show that least-squares (LS) channel estimation combined with joint pilot and data processing is capacity achieving in the single-user, single-receive-antenna case. We also investigate the achievable uplink throughput in a massive multiple-input multiple-output system where each element of the antenna array at the receiver base-station feeds a one-bit ADC. We show that LS channel estimation and maximum-ratio combining are sufficient to support both multiuser operation and the use of high-order constellations. This holds in spite of the severe nonlinearity introduced by the one-bit ADCs

Output Statistics of MIMO Channels with General Input Distribution

The information that can be conveyed through a wireless channel, with multiple-antenna equipped transmitter and receiver, crucially depends on the channel behavior as well as on the input structure. In this paper, we derive analytical results, concerning the probability density function (pdf) of the output of a single-user, multiple-antenna communication. The analysis is carried out under the assumption of an optimized input structure, and assuming Gaussian noise and a Rayleigh block-fading channel. Our analysis therefore provides a quite general and compact expression for the conditional output pdf. We also highlight the relation between such an expression and the results already available in the literature for some specific input structures

Interference Mitigation in Large Random Wireless Networks

A central problem in the operation of large wireless networks is how to deal with interference -- the unwanted signals being sent by transmitters that a receiver is not interested in. This thesis looks at ways of combating such interference. In Chapters 1 and 2, we outline the necessary information and communication theory background, including the concept of capacity. We also include an overview of a new set of schemes for dealing with interference known as interference alignment, paying special attention to a channel-state-based strategy called ergodic interference alignment. In Chapter 3, we consider the operation of large regular and random networks by treating interference as background noise. We consider the local performance of a single node, and the global performance of a very large network. In Chapter 4, we use ergodic interference alignment to derive the asymptotic sum-capacity of large random dense networks. These networks are derived from a physical model of node placement where signal strength decays over the distance between transmitters and receivers. (See also arXiv:1002.0235 and arXiv:0907.5165.) In Chapter 5, we look at methods of reducing the long time delays incurred by ergodic interference alignment. We analyse the tradeoff between reducing delay and lowering the communication rate. (See also arXiv:1004.0208.) In Chapter 6, we outline a problem that is equivalent to the problem of pooled group testing for defective items. We then present some new work that uses information theoretic techniques to attack group testing. We introduce for the first time the concept of the group testing channel, which allows for modelling of a wide range of statistical error models for testing. We derive new results on the number of tests required to accurately detect defective items, including when using sequential `adaptive' tests.Comment: PhD thesis, University of Bristol, 201