1 / 17

On the Optimal SINR in Random Access Networks with Spatial Re-Use

On the Optimal SINR in Random Access Networks with Spatial Re-Use. Navid Ehsan and R. L. Cruz UCSD. An Analogy…. On Public Speaking. The 85% Rule Should I be talking now?. The bottom line, almost…. Horizontal throughput (bit meter/sec) versus link reliability. Model (“infinite density”).

irma
Download Presentation

On the Optimal SINR in Random Access Networks with Spatial Re-Use

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. On the Optimal SINR in Random Access Networks with Spatial Re-Use Navid Ehsan and R. L. Cruz UCSD

  2. An Analogy… On Public Speaking • The 85% Rule • Should I be talking now?

  3. The bottom line, almost… Horizontal throughput (bit meter/sec) versus link reliability

  4. Model (“infinite density”) • Slotted system, users distributed throughout infinite plane • In each slot, the set of transmitting users forms a 2-D Poisson point process with spatial intensity  (includes re-transmissions) • Each transmission is to a fixed receiver at distance r

  5. Model, cont’d • Flat fading channel model. Power attenuation between two points separated by distance x isl(x) = (1 + Ax)- path loss exponent, > 2 A = constant (we later assume A=1)

  6. Model, cont’d • Each active transmitter transmits with power P • Thermal noise power at each receiver is 2 • Assume interference from different transmitters are uncorrelated

  7. Model, cont’d • Total interference from all transmissions at a given receiver at position x:I = i Pl( | yi - x | ) • random sum of received powers • => interference power in each slot is random • approximate I as Gaussian, can get mean and variance of I from Campbell’s theorem

  8. Model, cont’d • Signal to Interference and Noise Ratio SINR =  = Pl(r ) / (2 + I ) • SINR in each slot is random

  9. Model, cont’d • Target SINR: target • If target then transmission is successful, otherwise it is not successful • Information rate:  •  = W log2 (1 + target ) (Shannon) • Assumes noise + interference is Gaussian • W = Bandwidth, assume = 1 Hz.

  10. Optimization Problem • Horizontal Throughput per unit area: • J = max{  r Psucc :  r , target } • Psucc = Prob (> target ) • Theorem

  11. Optimal Parameters • * =  , * = 0, target =0 (- dB) , P*succ=1, r* = 1/[A(a-1)]. •  = G, (offered info load per unit area) • Optimal load:

  12. Finitely Dense Networks • Model • Location of nodes in each slot is a 2D Poisson point process with intensity 0 . • Each node transmits with probability  / 0 in each slot, so that set of transmitting nodes in each slot is a 2D Poisson point process with intensity . • Psucc = ( 1 -  / 0 )Prob{  > target } • 0 ≤  ≤ 0 ==>  is finite

  13. J*(  ) as a function of  for various values of 0

  14. The bottom line… Horizontal throughput (bit meter/sec) versus target SINR 0 = 30

  15. Horizontal throughput (bit meter/sec) versus target SINR 0 = 15,60

  16. The bottom line, almost… Horizontal throughput (bit meter/sec) versus link reliability

  17. Six is a magic number?

More Related