The sum-capacity$C$of a static uplink channel with$n$single-antenna sources and an$n$-antenna destination is known to scale linearly in$n$, if the random channel matrix fulfills the conditions for the Marcenko-Pastur law: if each source transmits at power$P/n$, there exists a positive$c_{0}$, such that$\lim_{n \ura{} \infty}C/n=c_{0}$almost surely. This paper addresses the question to which extent this result carries over to multi-hop networks. Specifically, an$L+1$-hop network with$n$non-cooperative source antennas,$n$fully cooperative destination antennas, and$L$relay stages of$n_{\cal R}$(cooperative or non-cooperative) relay antennas each is considered. Four relaying strategies are assessed based on the interrelationship between two sequences. For each considered strategy${\rm XF}$, there exists a sequence$(c_{L}^{\rm XF})_{L=0}^{\infty}$, such that$c_{L}^{\rm XF}=\lim_{n \ura{} \infty}R^{\rm XF}_{L}/n$almost surely, where$R^{\rm XF}_{L}$denotes the supremum of the set of sum-rates that are achievable by the strategy over$L\!+\!1$hops. This sequence depends on the sequence$(P_{L})_{L=0}^{\infty}$, where$P_{L}$corresponds to the power of the source stage and each of the relay stages in an$L\!+\!1$-hop network. Results are summarized as follows:Decode & forward (DF): For$n_{\cal R}=n$,$c^{\rm DF}_{L}$is constant with respect to$L$, if also$P_{L}$is constant with respect to$L$.

A set of distributed non-cooperating relay antennas is known to be capable of orthogonalizing multiple source- destination pairs in space by coherent amplify-and-forward (AF) relaying techniques. Known relay gain allocation schemes for this setup require either global knowledge of the channel coefficients between all participating nodes or an excess number of relays. The required dissemination of the channel state information (CSI) introduces a major overhead, which in practice may well diminish the spatial multiplexing gain. We introduce a new distributed gradient based gain allocation scheme, which minimizes this overhead. Key to this is the proof, that the gradient of the destination signal-to-interference-plus-noise ratio (SINR) can be calculated in a distributed manner based on local CSI at the relays and very limited feedback from the destinations. In order to minimize the number of iterations in the distributed gradient algorithm we propose two distributed approaches to determine the optimal step size for each iteration. Finally we provide simulation results on the sum rate performance and identify the sequential opening of the spatial channels as a key factor that impacts speed of convergence.

We consider coherent wireless MIMO multi-hop communication where nSnon-cooperating source antennas communicate to nDfully cooperating destination antennas via L clusters of nRnon-cooperating relay antennas each. Assuming i.i.d. zero-mean (slow) fading coefficients of finite variance, the sum-capacity of this channel is proven to scale linearly in min{nS, nD} in the limit Lrarrinfin, when the receive SNR is kept constant and nRisinOmega(min{nS, nD}). This capacity scaling is achieved by a quantization based forwarding strategy. Moreover, we show that Slepian & Wolf compression allows to reduce the growth rate of the transmit power per cluster that is necessary to sustain a constant receive SNR at the destination antennas from exponential to linear in L.

It has recently been proposed to orthogonalize the data streams of n interfering source-destination pairs by employing an intermediate stage of non-cooperating coherent amplify-and-forward relays. This distributed zero-forcing scheme achieves a spatial multiplexing gain n/2 and does not require multi-antenna nodes. In this paper we generalize the concept from a single to multiple relay stages. Due to the concatenation of relay stages, the gain allocation problem becomes nonlinear. We show that the zero-forcing relay gain coefficients are given by the common roots of a set of polynomials, and we identify the set of network configurations for which such roots exist. In general, there exist multiple common roots. Based on experimental results we study the impact of the root selection and the number of relay stages on achievable rates. Finally, we propose a new scheme to achieve spatial orthogonalization in a single-hop interference network. Our proposal is based on the observation, that the mathematical model of the multihop problem is identical with the one of a single-hop network if we allow signals to be bounced forth and back between sources and destinations.

We study the potential of cooperative processing in WLAN uplink scenarios where the access points are connected to a backhaul with limited capacity. We evaluate different decoding strategies based on an outage criterion and discuss the influence of the available backhaul rate. Compared to the ergodic analyses in the literature we observe three major differences: Firstly, outage rates are much more robust to the backbone limitation. Secondly, Slepian-Wolf coding (compress & forward processing) does not improve the outage performance significantly compared to pure quantization and forwarding. Finally, quantization based approaches offer substantially higher gains compared to decoding based strategies. Because of the large number of existing WLANs, we conclude that cooperative processing is a key enabler for high rates on future WLAN uplinks: in cases of limiting backhaul capacities (e.g. ADSL broadband connections in residential environments) as well as in cases of large backhaul capacities (e.g. LAN connections in office environments).

In this correspondence, the cumulants of the mutual information of the flat Rayleigh fading two-hop amplify-and-forward multiple-input multiple-output (MIMO) relay channel under independent and identically distributed (i.i.d.) Gaussian input vectors are derived in the large array limit. The analysis is based on thereplicatrickand covers both spatially independent and Kronecker correlated fading. Beamforming at all terminals is restricted to weight matrices that are independent of the channel realization and constant over time. Expressions for mean and variance of the mutual information are obtained. Their parameters are determined by a nonlinear equation system. All higher cumulants are shown to vanish as the number of antennas per terminal,n, grows to infinity. In conclusion, the distribution of the mutual informationIbecomes Gaussian in the largenlimit. In this asymptotic regime, it is completely characterized by the expressions obtained for mean and variance ofI, which are inTheta(n) andO(1), respectively. Comparisons with simulation results show that the asymptotic results serve as excellent approximations for systems with only few antennas at each terminal.

In this paper the ergodic mutual information of the i.i.d. Rayleigh fading amplify-and-forward MIMO relay channel without direct link between source and destination is derived in the large array limit. By means of the replica method an expression is obtained, whose parameters are determined by a nonlinear equation system. This system can be solved in closed form. Comparisons with Monte Carlo simulations show that the asymptotic expression serves as an excellent approximation for systems with only very few antennas at each node.

This paper analyzes the characteristics of a multi-hop 802.11b mobile ad hoc network. We present data gathered from a mobile network of 20 devices carried by test users over 5 days in an indoor environment. The data is analyzed with regard to (i) the number of reachable devices, (ii) the node degree, (iii) the average path length, (iv) the link lifetime, (v) and the route lifetime. Despite the relatively high node density and low node mobility in our setup, we observe frequent network partitioning and considerably high path lengths (as large as 7 hops). However, the usability of these long paths is questionable as their lifetime is short. We believe that our measurements are representative for typical indoor environments and that the results can and should be used for evaluating networking protocols as well as to validate existing or to derive new mobility models