1. ISIT 2007 — 1 Throughput (bits/sec/Hz) of Capture- Based Random-Access Systems with SINR Channel Models ______________________________________________ This work was supported by the Office of Naval Research. Jeffrey E. Wieselthier and Gam D. Nguyen Information Technology Division Naval Research Laboratory Anthony Ephremides Electrical and Computer Engineering Department and Institute for Systems Research University of Maryland ISIT 2007 — June 2007

2. ISIT 2007 — 2 Random-Access System Collision channel  no capture General Multiple-Access channel  all users “succeed” In-between: Reception in the presence of interference  SINR-based model  One or more users can be successful Receiver

3. ISIT 2007 — 3 SINR-based Capture Model A packet from user j is successful if and only if b = 0: Perfect capture single detector: largest always successful multiple detectors: all are successful b = ∞: No capture (collision channel) when 2 or more transmit, none are successful P(j) = Power at receiving node from user j b = Threshold that depends on many system parameters (increasing function of rate) Receiver j

4. ISIT 2007 — 4 Measures of Throughput Scenario:  Single destination  Random-access transmissions “Packet throughput” (ISIT 2006) Expected number of successful packets in a slot:  S n = E{number of successful packets | n simultaneous transmissions}  Performance depends on threshold b “Bit throughput” (this paper) Spectral efficiency (bits/sec/Hz)  We address impact of:  b  Specified BER  Modulation scheme Destination

5. ISIT 2007 — 5 Packet Throughput: E{Successful packets | n } All packets for which SINR > b are successful S n = n Pr{SINR(1) > b} We addressed this problem at ISIT 2006  Model for b < 1  Performance evaluated via simulation  Shape of curves is dramatically different from previous results  Because of our propagation model  = 2

6. ISIT 2007 — 6 What is the Significance of the Parameter b ? Small value of b  high packet throughput  But we pay a price to achieve small values of b :  Fewer bits in each packet  Expand BW  Relax BER requirement How does b relate to spectral efficiency (bits/sec/Hz)?  Impact of specified BER  Impact of modulation scheme

7. ISIT 2007 — 7 Key Modeling Assumptions Modulation scheme: M -ary PSK  Minimum symbol duration: t = 1/W  W = channel bandwidth Ways to vary data rate R b  Choice of k = log 2 M  Increase symbol duration t s > t  This does NOT affect channel BW No error-control coding Other-user interference is uniform Gaussian in BW W = 1/t  We neglect background noise  Equivalent noise spectral density:

8. ISIT 2007 — 8 E s /N 0 and its Relationship to b Evaluate E s /N 0 Noise spectral density (background noise = 0): Bit energy: Symbol-energy-to-interference ratio: Relationship to b For signal i to be successful, we require:  Specifying a value of b is equivalent to requiring:

9. ISIT 2007 — 9 Impact of BER Constraint on Achievable Data Rate Define: Esno(BER,k) = value of E s /N 0 that is needed to achieve the specified BER when M -ary PSK is used  Spectral efficiency (bits/sec/Hz) is a function of BER, k and b :

10. ISIT 2007 — 10 Alternative Approximate Model: Shannon Capacity Shannon capacity  C = W log 2 (1+b) Simple, inaccurate model  Does not address finite packet length  Addresses operation at BER = 0

11. ISIT 2007 — 11 Spectral Efficiency of M -ary PSK vs b Shannon capacity provides a decent approximation for spectral efficiency for BER = 0.1 BER = 0.01 BER = 0.1

12. ISIT 2007 — 12 Spectral Efficiency of Binary PSK (in presence of other-user interference) Relax BER constraint  increase spectral efficiency Curves show value of n that provides highest spectral efficiency BER = 0.01BER = 0.1 Spectral Efficiency (Bit Throughput per Hz):

13. ISIT 2007 — 13 Spectral Efficiency of Binary PSK (in presence of other-user interference) BER = 0.01BER = 0.1 Spectral Efficiency (Bit Throughput per Hz):

14. ISIT 2007 — 14 Summary and Conclusions  Addressed spectral efficiency of capture-based random-access systems  Relationships between “packet throughput” and “bit throughput”  Impact of threshold b  Impact of BER  Developed basis of trade-offs in scheduled vs random-access systems  Model easily extended to multiple-destination networks with overlapping user populations  Using approach of our MILCOM 2006 paper  Provides link between information theory and networking