Nadia Fawaz

Asymptotic Capacity and Optimal Precoding in MIMO Multi-Hop Relay Networks

A multihop relaying system is analyzed where data sent by a multi-antenna source is relayed by successive multi-antenna relays until it reaches a multi-antenna destination. Assuming correlated fading at each hop, each relay receives a faded version of the signal from the previous level, performs linear precoding and retransmits it to the next level. Using free probability theory and assuming that the noise power at relays- but not at destination- is negligible, the closed-form expression of the asymptotic instantaneous end-to-end mutual information is derived as the number of antennas at all levels grows large. The so-obtained deterministic expression is independent from the channel realizations while depending only on channel statistics. This expression is also shown to be equal to the asymptotic average end-to-end mutual information. The singular vectors of the optimal precoding matrices, maximizing the average mutual information with finite number of antennas at all levels, are also obtained. It turns out that these vectors are aligned to the eigenvectors of the channel correlation matrices. Thus, they can be determined using only the channel statistics. As the structure of the singular vectors of the optimal precoders is independent from the system size, it is also optimal in the asymptotic regime.

When network coding and dirty paper coding meet in a cooperative ad hoc network

We develop and analyze new cooperative strategies for ad hoc networks that are more spectrally efficient than classical decode & forward (DF) protocols. Using analog network coding, our strategies preserve the practical half-duplex assumption but relax the orthogonality constraint. The introduction of interference due to non-orthogonality is mitigated thanks to precoding, in particular dirty paper coding. Combined with smart power allocation, our cooperation strategies allow to save time and lead to a more efficient use of the bandwidth and to improved network throughput with respect to classical repetition-DF and parallel-DF.

Optimal relay location and power allocation for low SNR broadcast relay channels

We consider the broadcast relay channel (BRC), where a single source transmits to multiple destinations with the help of a relay, in the limit of a large bandwidth. We address the problem of optimal relay positioning and power allocations at source and relay, to maximize the multicast rate from source to all destinations. To solve such a network planning problem, we develop a three-faceted approach based on an underlying information theoretic model, computational geometric aspects, and network optimization tools. Firstly, assuming superposition coding and frequency division between the source and the relay, the information theoretic framework yields a hypergraph model of the wideband BRC, which captures the dependency of achievable rate-tuples on the network topology. As the relay position varies, so does the set of hyperarcs constituting the hypergraph, rendering the combinatorial nature of optimization problem. We show that the convex hull C of all nodes in the 2-D plane can be divided into disjoint regions corresponding to distinct hyperarcs sets. These sets are obtained by superimposing all k-th order Voronoi tessellation of C. We propose an easy and efficient algorithm to compute all hyperarc sets, and prove they are polynomially bounded. Then, we circumvent the combinatorial nature of the problem by introducing continuous switch functions, that allows adapting the network hypergraph in a continuous manner. Using this switched hypergraph approach, we model the original problem as a continuous yet non-convex network optimization program. Ultimately, availing on the techniques of geometric programming and p-norm surrogate approximation, we derive a good convex approximation. We provide a detailed characterization of the problem for collinearly located destinations, and then give a generalization for arbitrarily located destinations. Finally, we show strong gains for the optimal relay positioning compared to seemingly interesting positions.

Asymptotic capacity and optimal precoding strategy of multi-level precode & forward in correlated channels

We analyze a multi-level MIMO relaying system where a multiple-antenna transmitter sends data to a multiple-antenna receiver through several relay levels, also equipped with multiple antennas. Assuming correlated fading in each hop, each relay receives a faded version of the signal transmitted by the previous level, performs precoding on the received signal and retransmits it to the next level. Using free probability theory and assuming that the noise power at the relay levels - but not at the receiver - is negligible, a closed-form expression of the end-to-end asymptotic instantaneous mutual information is derived as the number of antennas in all levels grow large with the same rate. This asymptotic expression is shown to be independent from the channel realizations, to only depend on the channel statistics and to also serve as the asymptotic value of the end-to-end average mutual information. We also provide the optimal singular vectors of the precoding matrices that maximize the asymptotic mutual information : the optimal transmit directions represented by the singular vectors of the precoding matrices are aligned on the eigenvectors of the channel correlation matrices, therefore they can be determined only using the known statistics of the channel matrices and do not depend on a particular channel realization.

A converse for the wideband relay channel with physically degraded broadcast

We investigate the multipath fading relay channel in the limit of a large bandwidth, and in the non-coherent setting, where the channel state is unknown to all terminals, including the relay and the destination. We derive a lower bound on the capacity by proposing and analyzing a peaky frequency binning scheme. The achievable rate obtained coincides with the block-Markov lower bound on the capacity of the wideband frequency-division Gaussian relay channel. When the broadcast channel is physically degraded, this achievable rate meets the cut-set upper-bound, and thus reaches the capacity of the noncoherent wideband multipath fading relay channel. In this case, a hypergraph model of the multipath fading relay channel is proposed, and the relaying scheme of concern is shown to reach its min-cut. Even if the source treats the broadcast channel as physically degraded when it is stochastically degraded, the achievable hypergraph bound is the min-cut.

Improving Ad Hoc Networks Capacity and Connectivity Using Dynamic Blind Beamforming

We propose a dynamic blind beamforming scheme which allows to benefit from antenna directivity in large mobile ad hoc networks while avoiding heavy feedback to track mobile nodes localization. By orienting its directional antenna successively in all directions, a source surely but blindly hits its destination without knowing its exact position. Performance is analyzed in terms of total network throughput and connectivity and the optimal number of rotations allowing to maximize performance is shown to result from a trade-off between delay and improvements in terms of interference. In large ad hoc networks, known to be interference limited, we show that dynamic blind beamforming can outperform omnidirectional transmissions both in terms of capacity and connectivity.

Large system design and analysis of protocols for decode-forward relay networks

In this work we consider a relay assisted CDMA network with a large number of sources and half duplex relays and a unique destination. We propose two relaying protocols called direct relaying (DR) and full relaying (FR). By dividing the relays in groups and adopting different forwarding delays for each group both protocols introduce diversity which depends on the number of groups and on the protocol. In DR mode, the relays forward only signals received directly from the sources. In FR mode, relays forward both signals received by the sources and the other relay groups by applying network coding at the physical layer. This implies a different level of diversity at the destination for the two schemes. Then, we propose an analytical framework for the analysis of the achievable rates in such a network, as the number of nodes and relays become asymptotically large.

Capacity and positioning in dense scattering environments

We study the capacity scaling of a system where a source communicates to a destination with the help of several scatterers. Capacity expressions accounting for physical characteristics of the environment (topology, frequency band...) are provided and an asymptotic analysis is performed for an increasing size of the dense scattering environment. The capacity is shown to reach a saturation level in the asymptotic regime, suggesting a capacity-delay trade-off. Moreover the saturation point depends on the positioning of scatterers, in particular in wide band systems where topology impacts capacity in terms of both path-loss and delays. Waiting very long for retransmissions from an infinite number of scatterers is not worth and a few well located scatterers around source and destination lead to better performances than more scatterers uniformly distributed on a square area between source and destination.