Summary of fundamental ideas presented
Wireless network is the interconnection of computing nodes without any physical linkages. Multipath effect is a challenge that faces wireless linkages. To enhance reliability of communication through wireless network there are a number of factors to consider and these include formulation of outage probability so as to simulate individual reliability of a linkage over slow changing channel. Ergodic capacity is time independent and so it may not be suitable for improving wireless linkage over slowly changing channel. Hindrance between numerous sessions ought to be attended through employment of various techniques of medium access at the MAC layer. To do this various route algorithms have to be formulated and tradeoffs between reliability resulting from outage probability and energy consumption under certain conditions be studied.
For point-to-point communication connection, a model of probabilistic link has to be formulated. This is to ensure that a message that is transmitted by one node in the network is not received by any other node and this event is called node disconnect. Reliability-power tradeoff can be improved by exploring the concept of route diversity seen in the multi-hope routing.
Issues addressed and how they may have been addressed in the past
The prevailing problems of wireless networks are communication reliability ant that of diversity of multi-hope. To ensure message delivery to the intended destination event of node disconnect could have been applied. Algorithms could have been designed to determine an appropriate route between a source and destination under specific limits of reliability and power usage. Route diversity can exploit the benefit exhibited by wireless broadcast future and the freedom of fade constraints between unlike pairs of nodes to basically adjust the existing trade-off.
Discussion of 1 or 2 core ideas presented
Probabilistic link model
Considering the model of outage probability, the following expression gives the probability of successfully receiving Rayleigh fading link:
Where do is distance of separation between nodes, snr is the signal to noise ratio at the transmitter, and k is the path-loss exponent.
For outage (unsuccessful transmission), the probability is: POutage (d, snr) = 1–exp (-dk/snr). Outage probability in high-snr is approximately: POutage (d, snr)dk/snr. This form of approximating is employed in assessing the outage probality and power level trade-off.
This shows that for any point-to-point link having single transmiting and receiving anntenae, the outage probability decays as snr-1. For constant noise level, then the existing relationship is lnear between the snr and the transmitted power.
Network Disconnect Probability
The idea here is that message transimmitted by a specific source node should not be received by any other node in the same network . The area of concern is the trade-off between disconnect probability and the transmitted power level. Any gain is attributed to the space diversity that is created by the existance of numerous receiving nodes thus giving space diversity gain in a network.
Considering a sinle dimensional network, let the source be fixed and then measure distances of all other nodes with respect to that node. Let the Disconnect (x, dx, snr) be the event whereby source node is not connected to any node in the network segment of (x, x+dx). A shortline segment of length dx contains no node or contains only one node, and this happens with probability λdx.
Using independence of the fading for line segment containing a node, the probability is: 1-PSucc(x, snr)λdx ≤ PDisconnect (x, dx, snr) ≤ 1-PSucc(x+dx, snr) λdx, wherePSucc (d, snr) is given by (1).
For disconnected event Disconnect (L, snr), the probability is: PDisconnect (L, snr) = Taking logs of both sides,
As dx tends to 0, the sum can be substitued with an integral and the lower and upper bounds converge. From ln (1-p)-p for small values of p, then
Disconnect probability of large networks, L tends to , disconnect probability is:
Where ┌ the Gamma function. For di-sided disconnect, the following theorems apply:
1. In a Poisson line network, density λ and path-loss exponent k, the probability of node being disconnected is: .
2. In a 2 dimensional Poisson network, density λ, and path-loss exponent k, probility of node disconect is: .
The expressions in theorem 1 and theorem 2 are applicable to any value of snr, thus there is no need of high-snr approximations during derivation.
Potential applications of technology presented (or) potential issues created
Wireless network technology can be applied in cellular telephony that facilitates easy private communication, two-way radios, PDAs, inter-continental network systems using radio satellites for communication, and emergency services like police to enhance communication.
Future directions suggested or ones that you might infer from the topic
For faster search, optimal algorithms should be designed to aid the same. The lossy character of wireless communication medium also calls for well-defined protocols and strategies.
There is need to consider closed form estimations of optimal position of response handlers with changing parameter of packet length.
Use of channel state information within the network layer, efficient routing protocol for equal-power and optimal-power allocation in a multi-hop network in fading channels and using end-to-end outage probability from source to destination as criteria for optimization will further the wireless technology.
Works Cited
Shah, Syed Ijlal Ali and Mohammad Ilyas. Pervasive Communications Handbook. New york City: CRC Press, 2010.
