No abstract

This paper surveys and unifies a number of recent contributions that have collectively developed a metric for decentralized wireless network analysis known as transmission capacity. Although it is notoriously difficult to derive general end-to-end capacity results for multi-terminal or ad hoc networks, the transmission capacity (TC) framework allows for quantification of achievable single-hop rates by focusing on a simplified physical/MAClayer model. By using stochastic geometry to quantify the multi-user interference in the network, the relationship between the optimal spatial density and success probability of transmissions in the network can be determined, and expressed -often fairly simply -in terms of the key network parameters. The basic model and analytical tools are first discussed and applied to a simple network with path loss only and we present tight upper and lower bounds on transmission capacity (via lower and upper bounds on outage probability). We then introduce random channels (fading/shadowing) and give TC and outage approximations for an arbitrary channel distribution, as well as exact results for the special cases of Rayleigh and Nakagami fading. We then apply these results to show how TC can be used to better understand scheduling, power control, and the deployment of multiple antennas in a decentralized network. The paper closes by discussing shortcomings in the model as well as future research directions.

This paper derives the outage probability and transmission capacity of ad hoc wireless networks with nodes employing multiple antenna diversity techniques, for a general class of signal distributions. This analysis allows system performance to be quantified for fading or non-fading environments. The transmission capacity is given for interference-limited uniformly random networks on the entire plane with path loss exponent α > 2 in which nodes use: (1) static beamforming through M sectorized antennas, for which the increase in transmission capacity is shown to be Θ(M 2 ) if the antennas are without sidelobes, but less in the event of a nonzero sidelobe level; (2) dynamic eigen-beamforming (maximal ratio transmission/combining), in which the increase is shown to be Θ(M 2 α ); (3) various transmit antenna selection and receive antenna selection combining schemes, which give appreciable but rapidly diminishing gains; and (4) orthogonal space-time block coding, for which there is only a small gain due to channel hardening, equivalent to Nakagami-m fading for increasing m. It is concluded that in ad hoc networks, static and dynamic beamforming perform best, selection combining performs well but with rapidly diminishing returns with added antennas, and that space-time block coding offers only marginal gains.

No abstract

This paper addresses three issues in the field of ad hoc network capacity: the impact of i) channel fading, ii) channel inversion power control, and iii) threshold-based scheduling on capacity. Channel inversion and threshold scheduling may be viewed as simple ways to exploit channel state information (CSI) without requiring cooperation across transmitters. We use the transmission capacity (TC) as our metric, defined as the maximum spatial intensity of successful simultaneous transmissions subject to a constraint on the outage probability (OP). By assuming the nodes are located on the infinite plane according to a Poisson process, we are able to employ tools from stochastic geometry to obtain asymptotically tight bounds on the distribution of the signal-to-interference (SIR) level, yielding in turn tight bounds on the OP (relative to a given SIR threshold) and the TC. We demonstrate that in the absence of CSI, fading can significantly reduce the TC and somewhat surprisingly, channel inversion only makes matters worse. We develop a threshold-based transmission rule where transmitters are active only if the channel to their receiver is acceptably strong, obtain expressions for the optimal threshold, and show that this simple, fully distributed scheme can significantly reduce the effect of fading. arXiv:0707.3584v1 [cs.IT] 24 Jul 20072 Recent work has shown that the 1/ √ n throughput scaling of multi-hop, which essentially corresponds to linear scaling of transport capacity in an extended network, can actually be exceeded for path loss exponents between 2 and 3 [12]. As a result, transmission capacity corresponds to an achievable rate that is not order-optimal for 2 ≤ α < 3, but maximizing this quantity is still meaningful because multi-hop is currently the prevalent means of communication in ad hoc networks.

Abstract1 We consider a cooperative wireless network in the presence of one of more eavesdroppers, and exploit node cooperation for achieving physical (PHY) layer based security. Two different cooperation schemes are considered. In the first scheme, cooperating nodes retransmit a weighted version of the source signal in a decode-and-forward (DF) fashion. In the second scheme, while the source is transmitting, cooperating nodes transmit weighted noise to confound the eavesdropper (cooperative jamming (CJ)).We investigate two objectives, i.e., maximization of achievable secrecy rate subject to a total power constraint, and minimization of total power transmit power under a secrecy rate constraint. For the first design objective with a single eavesdropper we obtain expressions for optimal weights under the DF protocol in closed form, and give an algorithm that converges to the optimal solution for the CJ scheme; while for multiple eavesdroppers we give an algorithm for the solution using the DF protocol that is guaranteed to converge to the optimal solution for two eavesdroppers. For the second design objective, existing works introduced additional constraints in order to reduce the degree of difficulty, thus resulting in suboptimal solutions. In this work, either a closed form solution is obtained, or algorithms to search for the solution are proposed. Numerical results are presented to illustrate the proposed schemes and demonstrate the advantages of cooperation as compared to direct transmission. Index TermsSecrecy rate, node cooperation, physical layer based security, semi-definite programming.

No abstract

The benefit of multi-antenna receivers is investigated in wireless ad hoc networks, and the main finding is that network throughput can be made to scale linearly with the number of receive antennas n R even if each transmitting node uses only a single antenna. This is in contrast to a large body of prior work in single-user, multiuser, and ad hoc wireless networks that have shown linear scaling is achievable when multiple receive and transmit antennas (i.e., MIMO transmission) are employed, but that throughput increases logarithmically or sublinearly with n R when only a single transmit antenna (i.e., SIMO transmission) is used. The linear gain is achieved by using the receive degrees of freedom to simultaneously suppress interference and increase the power of the desired signal, and exploiting the subsequent performance benefit to increase the density of simultaneous transmissions instead of the transmission rate. This result is proven in the transmission capacity framework, which presumes single-hop transmissions in the presence of randomly located interferers, but it is also illustrated that the result holds under several relaxations of the model, including imperfect channel knowledge, multihop transmission, and regular networks (i.e., interferers are deterministically located on grids). N. Jindal is with the Univ. of Minnesota, J. Andrews is with the Univ. of Texas at Austin, S. Weber is with Drexel Univ. The contact author is N. Jindal, nihar@umn.edu. Preliminary results appeared at ICC 2009 [1]. arXiv:0809.5008v2 [cs.IT]