Capacity of ad-hoc wireless Networks. Vicky Sharma. Introduction . Ad hoc Networking has been an area of active research during the past decade . There has been a drastic increase in application scenarios for ad hoc networking (e.g. defense applications)
* Reliable data delivery
* Robust to dynamic channel conditions
* Allow for Scaling. Network services (e.g. throughput, delay) should not degrade rapidly as network grows.
* An upper bound on the total network capacity
that can be achieved.
* An upper bound on the per – node throughput that is possible.
* How do these limits vary as the network grows.
What is the maximal achievable throughput for ad-hoc wireless networks and how does it scale ?
The total network bit-distance product under the optimal conditions is :-
A throughput (n) is feasible for a network if 9 T < 1 s.t. every node can send (n)T bits in a time interval
[(i - 1)T,iT] 8 i 2 Z
A network transports 1 bit-meter if 1 bit is moved to 1 meter towards its destination.
The throughput capacity of a class of networks is of order (f(n)) bps if 9 c > 0, c’ < 1 s.t.
limn !1 P((n) = cf(n) is feasible) = 1
limn !1 P((n) = c’f(n) is feasible) < 1
A network where n nodes are arbitrarily placed. Each node has a destination that is chosen arbitrarily. The transmission range of each node can be different and is arbitrarily chosen.
A network where n nodes are randomly located on a 2D surface (either surface of a sphere S2 or a planar disk R2). Each node has a randomly chosen destination where it sends data at (n) bps. The destinations are independently chosen. The transmission ranges for each node are the same, however.
If a node i at position Xi transmits to node j at Xj at some time in a sub-channel m. If another node k at Xk is transmitting in the same sub-channel at the same time, then the condition for node j to receive from i is as follows:-
|Xk – Xj| ¸ (1 + ) |Xi – Xj|
where > 0 is the guard zone
We will denote nodes by their positions in the following slides.
If transmission power of node xi is denoted by Pi and it decays by exponential factor , then a node xj recieves from xi if :-
Where = minimum SIR needed for reception
N = channel noise and > 2
= set of nodes transmitting at the same time in the same sub-channel
* There are M sub-channels with a sub-channel m capable of Wm bps and m = 1,2 .. M Wm = W
* Network is Multi-hop. Bits may be stored at any relay node before being transmitted to the next hop.
* Transmissions synchronized with slots of length
* Network transports (n) nT bits over T seconds
Where Lav = average distance between source and destination. Also
Where Im(b,h) is the indicator function for transmission
of bit b on sub-channel m at hop h
|xi – xl| ¸ (1 + )|xk – xl| (1)
|xk – xr| ¸ (1 + )|xi – xr| (2)
|xr – xl| ¸ |xr – xk| - |xl – xk| (3)
|xl – xr| ¸ |xl – xi| - |xr – xi| (4)
Hence, we have
|xl – xr| ¸ (/2)(|xk – xl| + |xi – xr|)
* Average hops is of order O(pn)
* reception and transmission is omni-directional
* nodes are stationary
where c is constant