6 research outputs found
Coverage probability in wireless networks with determinantal scheduling
We propose a new class of algorithms for randomly scheduling network
transmissions. The idea is to use (discrete) determinantal point processes
(subsets) to randomly assign medium access to various {\em repulsive} subsets
of potential transmitters. This approach can be seen as a natural extension of
(spatial) Aloha, which schedules transmissions independently. Under a general
path loss model and Rayleigh fading, we show that, similarly to Aloha, they are
also subject to elegant analysis of the coverage probabilities and transmission
attempts (also known as local delay). This is mainly due to the explicit,
determinantal form of the conditional (Palm) distribution and closed-form
expressions for the Laplace functional of determinantal processes.
Interestingly, the derived performance characteristics of the network are
amenable to various optimizations of the scheduling parameters, which are
determinantal kernels, allowing the use of techniques developed for statistical
learning with determinantal processes. Well-established sampling algorithms for
determinantal processes can be used to cope with implementation issues, which
is is beyond the scope of this paper, but it creates paths for further
research.Comment: 8 pages. 2 figure
Throughput Analysis of Wireless Ad-Hoc Cognitive Radio Networks
In this dissertation we consider the throughput performance of cognitive radio
networks and derive the optimal sensing and access schemes for secondary users that
maximizes their sum-throughput while guaranteeing certain quality of service to primary
networks. First, we consider a cognitive radio network where secondary users
have access to N licensed primary frequency bands with their usage statistics and
are subject to certain inter-network interference constraint. In particular, to limit
the interference to the primary network, secondary users are equipped with spectrum
sensors and are capable of sensing and accessing a limited number of channels
at the same time. We consider both the error-free and erroneous spectrum sensing
scenarios, and establish the jointly optimal random sensing and access scheme, which
maximizes the secondary network expected sum throughput while honoring the primary
interference constraint. We show that under certain conditions the optimal
sensing and access scheme is independent of the primary frequency bandwidths and
usage statistics; otherwise, they follow water-filling-like strategies.
Next, we study the asymptotic performance of two multi-hop overlaid ad-hoc
networks that utilize the same temporal, spectral, and spatial resources based on
random access schemes. The primary network consists of Poisson distributed legacy
users with density λ^(p) and the secondary network consists of Poisson distributed
cognitive radio users with density λ^(s) = (λ^(p))^(β) that utilize the spectrum opportunistically.
Both networks employ ALOHA medium access protocols where the
secondary nodes are additionally equipped with range-limited perfect spectrum sensors
to monitor and protect primary transmissions. We study the problem in two
distinct regimes, namely β > 1 and 0 < β < 1. We show that in both cases, the
two networks can achieve their corresponding stand-alone throughput scaling even
without secondary spectrum sensing ; this implies the need for a more comprehensive
performance metric than just throughput scaling to evaluate the influence of
the overlaid interactions. We thus introduce a new criterion, termed the asymptotic
multiplexing gain, which captures the effect of inter-network interference . With this
metric, we clearly demonstrate that spectrum sensing can substantially improve the
overlaid cognitive networks performance when β > 1. On the contrary, spectrum
sensing turns out to be redundant when β < 1 and employing spectrum sensors
cannot improve the networks performance.
Finally, we present a methodology employing statistical analysis and stochastic
geometry to study geometric routing schemes in wireless ad-hoc networks. The techniques
developed in this section enable us to establish the asymptotic connectivity
and the convergence results for the mean and variance of the routing path lengths
generated by geometric routing schemes in random wireless networks