This paper addresses the following question, which is of interest in the design of a multiuser decentralized network. Given a total system bandwidth of W Hz and a fixed data rate constraint of R bps for each transmission, how many frequency slots N of size W/N should the band be partitioned into in order to maximize the number of simultaneous links in the network? Dividing the available spectrum results in two competing effects. On the positive side, a larger N allows for more parallel, non-interfering communications to take place in the same area. On the negative side, a larger N increases the SINR requirement for each link because the same information rate must be achieved over less bandwidth, which in turn increases the area consumed by each transmission. Exploring this tradeoff and determining the optimum value of N in terms of the system parameters is the focus of the paper. Using stochastic geometry, the optimal SINR threshold – which directly corresponds to the optimal spectral efficiency – is derived for both the low SNR (power-limited) and high SNR (interference-limited) regimes. This leads to the optimum choice of the number of frequency bands N in terms of the path loss exponent, power and noise spectral density, desired rate, and total bandwidth. I.

Spread spectrum communication – often called Code Division Multiple Access (CDMA) – has been widely adopted over the years for many types interference-challenged wireless communication systems including cellular and cordless telephones, wireless LANs and PANs, military applications, and global positioning systems. In this paper, we explore whether CDMA – in either its frequency hopping (FH) or direct sequence (DS) forms – is an appropriate design approach for wireless ad hoc, or mesh, networks. CDMA’s merits for centralized cellular networks were widely debated in the late 1980s through the 1990s, and greatly increased the understanding of CDMA in particular and interference-limited cellular networks in general. Such a discussion has not occurred for decentralized (ad hoc) networks, and one goal of this paper is to help provoke this debate by explaining the main advantages and disadvantages of CDMA in the context of ad hoc networks as exposed by recent research. We will argue that CDMA does not inherently improve the spectral efficiency of ad hoc networks; on the contrary, its valued interference averaging effect is not appreciable in ad hoc networks due to the irregular distribution of both the transmitters and receivers. On the positive side, both types (FH and DS) of spread spectrum allow for (i) longer hop distances and (ii) a reversal of the usual relationship that the desired transmitter must be closer to the receiver than interfering transmitters. These two facts allow for significant advantages over narrowband (NB) systems in terms of energy efficiency and end-to-end delay. We also examine the considerable effect that a spread spectrum physical layer has on MAC protocols. 1

We summarize capacity results to show merits of multihop relaying in broadband cellular mesh networks. Under the guidance of these results, we provide design perspectives on relay deployment, spectrum allocation and end-to-end optimization of certain QoS measures such as throughput, coverage, reliability and robustness. We conclude with an overview of recent standardization activities and remarks on remaining open problems and design challenges. I.

Abstract — We consider a linear multi-hop network composed of multi-state discrete-time memoryless channels over each hop, with orthogonal time-sharing across hops under a half-duplex relaying protocol. We analyze the probability of error and associated reliability function [1] over the multi-hop network; with emphasis on random coding and sphere packing bounds, under the assumption of point-to-point coding over each hop. In particular, we define the system reliability function for the multi-hop network and derive lower and upper bounds on this function to specify the reliability-optimal operating conditions of the network under an end-to-end constraint on the total number of channel uses. Moreover, we apply the reliability analysis to bound the expected end-to-end latency of multi-hop communication under the support of an automatic repeat request (ARQ) protocol. Considering an additive white

This paper applies spectral efficiency as a performance measure for routing schemes and considers how to obtain a good route in a wireless network. The objective for this study is to combine different perspectives from networking and information theory in the design of routing schemes. The problem of finding the optimum route with the maximum spectral efficiency is difficult to solve in a distributed fashion. Motivated by an information-theoretic analysis, this paper proposes two suboptimal alternatives, namely, the approximately-ideal-path routing (AIPR) scheme and the distributed spectrum-efficient routing (DSER) scheme. AIPR finds a path to approximate an optimum regular path and requires location information. DSER is more amenable to distributed implementations based on Bellman-Ford or Dijkstra’s algorithms. The spectral efficiencies of AIPR and DSER for random networks approach that of nearest-neighbor routing in the low signal-to-noise ratio (SNR) regime and that of single-hop routing in the high SNR regime. In the moderate SNR regime, the spectral efficiency of DSER is up to twice that of nearest-neighbor or single-hop routing. I. BACKGROUND AND MOTIVATION As wireless communications are extended beyond the last hop of networks, a better understand-ing of wireless relaying (including routing as a special case) is needed to deploy efficient multi-hop wireless networks. Research from different perspectives, e.g., networking and information theory, yields in different relaying paradigms for wireless networks [1]–[7]. The goal of this

This paper investigates the delay-reliability tradeoff for multihop underwater acoustic networks. The propagation medium of underwater acoustic channel exhibits distinct characteristics when contrasted with other common propagation media such as copper, fiber, and radio. In particular there are the extremely slow propagation speed of sound in water, high signal attenuation due to absorption, significant delay spreads and intersymbol interference, and range-dependent transmission bandwidth. These features make the delayreliability tradeoff for underwater acoustic channels fundamentally different from other channels. The approach is based on error-exponents which enable a physical-layer comparison of multihopping versus no hops while considering the overall throughput. The analysis shows that for typical network parameters, increasing the number of hops dramatically improves both the achievable information rate and the achievable reliability function, which quantitatively captures the decay rate of the decoding error probability as the coding block length increases asymptotically. Numerical results are presented to illustrate the analysis.

Abstract — This paper addresses the following question, which is of interest in the design of a multiuser decentralized network: given a total system bandwidth of W Hz and a fixed data rate constraint of R bps for each transmission, how many frequency slots N of size W/N should the band be partitioned into to maximize the number of simultaneous transmissions in the network? Dividing the available spectrum reduces the number of users on each band and therefore decreases multiuser interference level, but also increases the SINR requirement for each transmission because the same information rate must be achieved over a smaller bandwidth. Exploring this tradeoff between bandwidth and SINR and determining the optimum value of N in terms of the system parameters is the focus of the paper. Using stochastic geometry, we analytically derive the optimal SINR threshold on this tradeoff curve and show that it is a function of only the path loss exponent. Furthermore, the optimal SINR point lies between the low-SINR (power-limited) and high-SINR (bandwidth-limited) regimes. I.

Abstract — We consider a dense fading multi-user network with multiple active multi-antenna source-destination pair terminals communicating simultaneously through a large common set of K multi-antenna relay terminals in the full spatial multiplexing mode. We use Shannon-theoretic tools to analyze the tradeoff between energy efficiency and spectral efficiency (known as the power-bandwidth tradeoff) in meaningful asymptotic regimes of signal-to-noise ratio (SNR) and network size. We design linear distributed multi-antenna relay beamforming (LDMRB) schemes that exploit the spatial signature of multi-user interference and characterize their power-bandwidth tradeoff under a systemwide power constraint on source and relay transmissions. The impact of multiple users, multiple relays and multiple antennas on the key performance measures of the high and low SNR regimes is investigated in order to shed new light on the possible reduction in power and bandwidth requirements through the usage of such practical relay cooperation techniques. Our results indicate that point-to-point coded multi-user networks supported by distributed relay beamforming techniques yield enhanced energy efficiency and spectral efficiency, and with appropriate signaling and sufficient antenna degrees of freedom, can achieve asymptotically optimal power-bandwidth tradeoff with the best possible (i.e., as in the cutset bound) energy scaling of K −1 and the best possible spectral efficiency slope at any SNR for large number of relay terminals. Furthermore, our results help to identify the role of interference cancellation capability at the relay terminals on realizing the optimal power-bandwidth tradeoff; and show how relaying schemes that do not attempt to mitigate multi-user interference, despite their optimal capacity scaling performance, could yield a poor power-bandwidth tradeoff. Index Terms — Relay networks, dense networks, distributed beamforming, power-bandwidth tradeoff, energy efficiency, spectral efficiency, scaling laws, fading channels, bursty signaling, spatial multiplexing, multiple antennas I.

Abstract—We evaluate the peak and average power savings due to relay deployments in cellular systems via a simulation study. The peak power savings translate to cost reduction in power amplifiers. The average power savings lead to savings in electricity bills. Half-duplex relays are placed one per sector in a 19-cell, 57-sector cellular network. In the baseline case, the base stations control their transmit powers to achieve a common rate among users. When relays are present in the system, optimal powers are found when the relays get the complete message to be relayed to the user. The codebooks at the relays are chosen such that the users obtain a rate corresponding to the sum of the received powers from the base station and the relay. We observe that when power control is employed, the peak power saving is 2.6 dB and the average total power in the system can be reduced by 3 dB. I.

Abstract — Multihop relaying in cellular networks is seen as a viable strategy to address the need for higher data rates and better coverage. In this paper, we analyze the system-level performance of multicellular multihop networks in the presence of co-channel interference, and build upon prior work in [1]-[2], which considered multihop relaying in a single-cell setting. Considering an opportunistic hop-count routing algorithm, we study cellular sum capacity under different multiuser scheduling algorithms such as MaxCap, proportional fair, and round robin. We numerically investigate the competing interaction between multihop diversity and multiuser diversity, and discuss the areal diversity aspect as a byproduct of multihop relaying. Finally, we provide further practical design insights on cellular planning through our empirical results on interference statistics in multicellular multihop networks. I.