The Effect of Fading, Channel Inversion, and Threshold Scheduling onAd HocNetworks

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.

On Secrecy Outage Probability and Average Secrecy Rate of Large‐Scale Cellular Networks

“…This is because the interference reduces the channel capacity of legal link. At the same time, we can observe that the gap of the average secrecy rate between the scenarios of noncooperative eavesdroppers and cooperative eavesdroppers is becoming narrower with the increasing of / , especially the gap between the upper bound of the average secrecy rate with the exact analytical expression in (9). The reason is that the large-scale fading is gradually becoming the main cause on secrecy performance.…”

“…From Proposition 1 and the definition of , the average secrecy rate can be expressed as (9), the average secrecy rate at the typical user decreases when the value increases. Also, with the increasing of path loss exponent , the average secrecy rate increases.…”

“…The difficulty of researching the secrecy performance in such wireless networks is how to model the random locations distribution of nodes accurately. Fortunately, stochastic geometry has provided a powerful tool to address this difficulty and achieved great success in ad hoc networks [9,10], random cognitive radio networks [11,12], and largescale cellular networks [13][14][15][16][17][18][19].…”

Impact of the Secondary Network on the Outage Performance of the Primary Service in Spectrum Sharing

“…The impact of fading, power allocation, and interference cancellation on the outage probability in ad hoc networks is also studied in [9] and [10].…”

Energy-Limited vs. Interference-Limited Ad Hoc Network Capacity

“…[4], [5]. The fixed transmission distance of d is clearly not a reasonable assumption; however our prior work [1], [6] has shown rigorously that variable transmit distances do not result in fundamentally different capacity results, so a fixed distance is chosen because it is much simpler analytically and allows for crisper insights. Our model does not include fading, but our past work has shown that the effect of fading in the interference-limited regime is only a multiplicative constant; the effect of fading in the energy-limited regime is of interest but it beyond the scope of this work.…”