The Impact of CSI and Power Allocation on Relay Channel Capacity and Cooperation Strategies

Capacity gains from transmitter and receiver cooperation are compared in a relay network where the cooperating nodes are close together. Under quasi-static phase fading, when all nodes have equal average transmit power along with full channel state information (CSI), it is shown that transmitter cooperation outperforms receiver cooperation, whereas the opposite is true when power is optimally allocated among the cooperating nodes but only CSI at the receiver (CSIR) is available. When the nodes have equal power with CSIR only, cooperative schemes are shown to offer no capacity improvement over non-cooperation under the same network power constraint. When the system is under optimal power allocation with full CSI, the decode-and-forward transmitter cooperation rate is close to its cut-set capacity upper bound, and outperforms compress-and-forward receiver cooperation. Under fast Rayleigh fading in the high SNR regime, similar conclusions follow. Cooperative systems provide resilience to fading in channel magnitudes; however, capacity becomes more sensitive to power allocation, and the cooperating nodes need to be closer together for the decode-and-forward scheme to be capacity-achieving. Moreover, to realize capacity improvement, full CSI is necessary in transmitter cooperation, while in receiver cooperation optimal power allocation is essential.Comment: Accepted for publication in IEEE Transactions on Wireless Communication

Fundamental Limits in MIMO Broadcast Channels

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system paramaters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling

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

On the Capacity of the Wiener Phase-Noise Channel: Bounds and Capacity Achieving Distributions

In this paper, the capacity of the additive white Gaussian noise (AWGN) channel, affected by time-varying Wiener phase noise is investigated. Tight upper and lower bounds on the capacity of this channel are developed. The upper bound is obtained by using the duality approach, and considering a specific distribution over the output of the channel. In order to lower-bound the capacity, first a family of capacity-achieving input distributions is found by solving a functional optimization of the channel mutual information. Then, lower bounds on the capacity are obtained by drawing samples from the proposed distributions through Monte-Carlo simulations. The proposed capacity-achieving input distributions are circularly symmetric, non-Gaussian, and the input amplitudes are correlated over time. The evaluated capacity bounds are tight for a wide range of signal-to-noise-ratio (SNR) values, and thus they can be used to quantify the capacity. Specifically, the bounds follow the well-known AWGN capacity curve at low SNR, while at high SNR, they coincide with the high-SNR capacity result available in the literature for the phase-noise channel.Comment: IEEE Transactions on Communications, 201

Scaling up MIMO: Opportunities and Challenges with Very Large Arrays

This paper surveys recent advances in the area of very large MIMO systems. With very large MIMO, we think of systems that use antenna arrays with an order of magnitude more elements than in systems being built today, say a hundred antennas or more. Very large MIMO entails an unprecedented number of antennas simultaneously serving a much smaller number of terminals. The disparity in number emerges as a desirable operating condition and a practical one as well. The number of terminals that can be simultaneously served is limited, not by the number of antennas, but rather by our inability to acquire channel-state information for an unlimited number of terminals. Larger numbers of terminals can always be accommodated by combining very large MIMO technology with conventional time- and frequency-division multiplexing via OFDM. Very large MIMO arrays is a new research field both in communication theory, propagation, and electronics and represents a paradigm shift in the way of thinking both with regards to theory, systems and implementation. The ultimate vision of very large MIMO systems is that the antenna array would consist of small active antenna units, plugged into an (optical) fieldbus.Comment: Accepted for publication in the IEEE Signal Processing Magazine, October 201

Capacity limits of bursty interference channels

Mención Internacional en el título de doctorThis dissertation studies the effects of interference burstiness in the transmission of data in wireless networks. In particular, we investigate the effects of this phenomenon on the largest data rate at which one can communicate with a vanishing small probability of error, i.e., on channel capacity. Specifically, we study the capacity of two different channel models as described in the next sections. Linear deterministic bursty interference channel. First, we consider a two-user linear deterministic bursty interference channel (IC), where the presence or absence of interference is modeled by a block- independent and identically distributed (IID) Bernoulli process that stays constant for a duration of T consecutive symbols (this is sometimes referred to as a coherence block) and then changes independently to a new interference state. We assume that the channel coefficients of the communication and interference links remain constant during the whole message transmission. For this channel, we consider both its quasi-static setup where the interference state remains constant during the whole transmission of the codeword (which corresponds to the case whether the blocklength N is smaller than T) and its ergodic setup where a codeword spans several coherence blocks. For the quasi-static setup, we follow the seminal works by Khude, Prabhakaran and Viswanath and study the largest sum rate of a coding strategy that provides reliable communication at a basic (or worstcase) rate R and allows an increased (opportunistic) rate ΔR in absence of interference. For the ergodic scenario, we study the largest achievable sum rate as commonly considered in the multi-user information theory literature. We study how (noncausal) knowledge of the interference state, referred to as channel state information (CSI), affects the sum capacity. Specifically, for both scenarios, we derive converse and achievability bounds on the sum capacity for (i) local CSI at the receiverside only; (ii) when each transmitter and receiver has local CSI, and (iii) global CSI at all nodes, assuming both that interference states are independent of each other and that they are fully correlated. Our bounds allow us to identify regions and conditions where interference burstiness is beneficial and in which scenarios global CSI improves upon local CSI. Specifically, we show the following: • Exploiting burstiness: For the quasi-static scenario we have shown that in presence of local CSI, burstiness is only beneficial if the interference region is very weak or weak. In contrast, for global CSI, burstiness is beneficial for all interference regions, except the very strong interference region, where the sum capacity corresponds to that of two parallel channels without interference. For the ergodic scenario, we have shown that, under global CSI, burstiness is beneficial for all interference regions and all possible values of p. For local CSI at the receiver-side only, burstiness is beneficial for all values of p and for very weak and weak interference regions. However, for moderate and strong interference regions, burstiness is only of clear benefit if the interference is present at most half of the time. • Exploiting CSI: For the quasi-static scenario, local CSI at the transmitter is not beneficial. This is in stark contrast to the ergodic scenario, where local CSI at the transmitter-side is beneficial. Intuitively, in the ergodic scenario the input distributions depend on the realizations of the interference states. Hence, adapting the input distributions to these realizations increases the sum capacity. In contrast, in the quasi-static case, the worst-case scenario (presence of interference) and the best-case scenario (absence of interference) are treated separately. Hence, there is no difference to the case of having local CSI only at the receiver side. Featuring global CSI at all nodes yields an increased sum rate for both the quasi-static and the ergodic scenarios. The joint treatment of the quasi-static and the ergodic scenarios allows us to thoroughly compare the sum capacities of these two scenarios. While the converse bounds for the quasi-static scenario and local CSI at the receiver-side appeared before in the literature, we present a novel proof based on an information density approach and the Verd´u-Han lemma. This approach does not only allow for rigorous yet clear proofs, it also enables more refined analyses of the probabilities of error that worst-case and opportunistic messages can be decoded correctly. For the converse bounds in the ergodic scenario, we use Fano’s inequality as the standard approach to derive converse bounds in the multi-user information theory literature. Bursty noncoherent wireless networks. The linear deterministic model can be viewed as a rough approximation of a fading channel, which has additive and multiplicative noise. The multiplicative noise is referred to as fading. As we have seen in the previous section, the linear deterministic model provides a rough understanding of the effects of interference burstiness on the capacity of the two-user IC. Now, we extend our analysis to a wireless network with a very large number of users and we do not approximate the fading channel by a linear deterministic model. That is, we consider a memoryless flat-fading channel with an infinite number of interferers. We incorporate interference burstiness by an IID Bernoulli process that stays constant during the whole transmission of the codeword. The channel capacity of wireless networks is often studied under the assumption that the communicating nodes have perfect knowledge of the fading coefficients in the network. However, it is prima-facie unclear whether this perfect knowledge of the channel coefficients can actually be obtained in practical systems. For this reason, we study in this dissertation the channel capacity of a noncoherent model where the nodes do not have perfect knowledge of the fading coefficients. More precisely, we assume that the nodes know only the statistics of the channel coefficients but not their realizations. We further assume that the interference state (modeling interference burstiness) is known non-causally at the receiver-side only. To the best of our knowledge, one of the few works that studies the capacity of noncoherent wireless networks (without considering interference burstiness) is by Lozano, Heath, and Andrews. Inter alia, Lozano et al. show that in the absence of perfect knowledge of the channel coefficients, if the channel inputs are given by the square-root of the transmit power times a power-independent random variable, and if interference is always present (hence, it is non-bursty), then the achievable information rate is bounded in the signal-to-noise ratio (SNR). However, the considered inputs do not necessarily achieve capacity, so one may argue that the information rate is bounded in the SNR because of the suboptimal input distribution. Therefore, in our analysis, we allow the input distribution to change arbitrarily with the SNR. We analyze the asymptotic behavior of the channel capacity in the limit as the SNR tends to infinity. We assume that all nodes (transmitting and interfering) use the same codebook. This implies that each node is transmitting at the same rate, while at the same time it keeps the analysis tractable. We demonstrate that if the nodes do not cooperate and if the variances of the path gains decay exponentially or slower, then the achievable information rate remains bounded in the SNR, even if the input distribution is allowed to change arbitrarily with the transmit power, irrespective of the interference burstiness. Specifically, for this channel, we show the following: • The channel capacity is bounded in the SNR. This suggests that noncoherent wireless networks are extremely power inefficient at high SNR. • Our bound further shows that interference burstiness does not change the behavior of channel capacity. While our upper bound on the channel capacity grows as the channel becomes more bursty, it remains bounded in the SNR. Thus, interference burstiness cannot be exploited to mitigate the power inefficiency at high SNR. Possible strategies that could mitigate the power inefficiency of noncoherent wireless networks and that have not been explored in this thesis are cooperation between users and improved channel estimation strategies. Indeed, coherent wireless networks, in which users have perfect knowledge of the fading coefficients, have a capacity that grows to infinity with the SNR. Furthermore, for such networks, the most efficient transmission strategies, such as interference alignment, rely on cooperation. Our results suggest that these two strategies may be essential to obtain an unbounded capacity in the SNR.Programa Oficial de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Ignacio Santamaría Caballero.- Secretario: David Ramírez García, David.- Vocal: Paul de Kerre

A Simple Recursively Computable Lower Bound on the Noncoherent Capacity of Highly Underspread Fading Channels

Real-world wireless communication channels are typically highly underspread: their coherence time is much greater than their delay spread. In such situations it is common to assume that, with sufficiently high bandwidth, the capacity without Channel State Information (CSI) at the receiver (termed the noncoherent channel capacity) is approximately equal to the capacity with perfect CSI at the receiver (termed the coherent channel capacity). In this paper, we propose a lower bound on the noncoherent capacity of highly underspread fading channels, which assumes only that the delay spread and coherence time are known. Furthermore our lower bound can be calculated recursively, with each increment corresponding to a step increase in bandwidth. These properties, we contend, make our lower bound an excellent candidate as a simple method to verify that the noncoherent capacity is indeed approximately equal to the coherent capacity for typical wireless communication applications. We precede the derivation of the aforementioned lower bound on the information capacity with a rigorous justification of the mathematical representation of the channel. Furthermore, we also provide a numerical example for an actual wireless communication channel and demonstrate that our lower bound does indeed approximately equal the coherent channel capacity.The work of T. H. Loh was supported by the 2013 - 2017 Electromagnetics and Time Metrology Programme of the National Measurement Office, an Executive Agency of the U.K. Department for Business, Innovation and Skills, under Projects EMT13018This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/TWC.2016.253167