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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”).

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

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  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?

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