Channel Aware Random Access in Wireless Networks

1. Channel Aware Random Access in Wireless Networks Professor Ye (Geoffrey) Li School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta, GA, 30332-0250 Collaborated by G. Ganesan

2. Outline Introduction CAMCRA scheme Imperfect CSI Stability Summary

3. Outline Introduction CAMCRA scheme Imperfect CSI Stability Summary

4. Random Access - Illustration

5. Random Access Schemes Features: No centralized scheduling Efficient for bursty traffic Simple to implement Data rate ? governed by packet success probability Requirements: High uplink data rate Low packet delay Our Work: Exploit multicarrier and multi-user diversity for random access!

6. Outline Introduction CAMCRA scheme Imperfect CSI Stability Summary

7. System description Aloha ? template random access scheme Multicarrier networks only Rayleigh fading channel Capacity achieving codes

8. Aloha Most popular random access scheme. Basic idea : Transmit whenever required Simple but very powerful

9. Collision Model One packet sent ? succ. received More than one packet sent ? all packets lost Stricter model Tractable analysis

10. Channel Aware Aloha (CAA) MAC layer has complete knowledge of present channel conditions (Qin03) CAA scheme for n users Optimal H0 = H0(n) chosen s.t. Max. prob. of success

11. Example – user network SNR of the ith user ? Rayleigh fading ? Threshold of the ith user ? Channel access probability for ith user ? Equal access probability for “unequal” users! CAA applicable to non-homogenous networks!

12. Asymptotic Throughput Defined as ? throughput when network pop. is For constant rate network ? success prob. For variable rate network ? actual bit rate

13. Asymptotic Throughput N user network Assume total input process ? Poisson( ) Assume each user can hold arbitrarily large packets Theorem (Bert00): For stability of network, max. allowable input rate satisfies

14. Aloha Success Probability For Channel Aware Aloha, Max. allowable input rate =

15. Variable Rate Networks Assume adaptive modulation Assume presence of capacity achieving codes Then possible to increase throughput in Channel Aware Aloha How? Exploit Multiuser Diversity

16. Multiuser Diversity Assume users with channel gains i.i.d. Capacity when one randomly chosen user transmits (bpcu: bits per channel use) Capacity when user with best gain transmits for large N

17. Throughput of CAA Max. Achievable throughput: prob. of success × capacity ? In CAA, user with best gain always transmits Hence,

18. Novel CAMCRA scheme CAMCRA: Channel Aware Multi-Channel Random Access (Ganes05) Features: Exploits multicarrier diversity… Offers throughput gain… Robust to channel uncertainties…

20. CAMCRA scheme ? existing random access scheme for users (e.g. channel aware Aloha) ?gain of th user at th carrier For each user , , choose carriers where ?number of users assigned to th carrier Apply, on carrier , the scheme

21. Example : CAMCRA

22. Probability of collision is reduced. Without CAMCRA : ave. # of users per carrier = With CAMCRA : ave. # of users per carrier = Very low chances of collision if high!!

23. Camcra - features How about if each user selects one carrier randomly ? multicarrier diversity lost ? provides for constant rate networks ? gain only in success probability

24. Constant rate CAMCRA

25. Camcra - features Rem: In CAMCRA ? each user selects best carrier among carriers ? gain of best carrier ˜ (multicarrier diversity) ? variable rate networks

26. Variable rate CAMCRA

27. Outline Introduction CAMCRA scheme Imperfect CSI Stability Summary

28. Imperfect CSI So far…assumed perfect channel conditions and statistics… In reality…channel estimate is imperfect… Actual ? channel gain: variance: Estimated ? channel gain: variance:

29. Modelling Imperfect CSI

30. Channel Uncertainty Assume soft estimator… , ?complex Gaussian RV’s (poss. dep.) Define uncertainty ? perfect CSI ? no knowledge of CSI In practice, or

31. Imperfect CSI in CAA CAA( ) ? CAA scheme under uncertainty ? probability of successful transmission under CAA( ) scheme When , (perfect CSI), already seen… When , we have

32. Surprising Result!! For , already know that = Max. Allowable input rate as However for any , we have = Max. Allowable input rate as !!!

33. CSI uncertainty in CAa

34. More Surprising Rem: Max. Achievable throughput = prob. of success × capacity When , When , as

35. Consequences Any uncertainty in CSI in CAA zero asymptotic throughput zero maximum allowable input rate Questions: Can this be remedied? How does CAMCRA perform?

36. How About CAMCRA? More robust to imperfect CSI? Non-zero asymptotic success probability?

37. Interesting fact (Guocong05)1: OFDM with carriers with perfect CSI ( ) max. capacity = When , obviously… max. capacity < In fact, max. capacity = where and ? estimation errors with

38. lower bound Theorem (Ganes06): for any , where . Capacity retains the same order! However, the bound is loose!

39. Interpretation ? extra SNR needed to offset channel uncertainty Multicarrier network ? very robust to imperfect CSI in downlink direction Throughput utmost reduced by a constant factor…i.e. max. capacity =

40. CAMCRA Throughput Theorem (Ganes06): In CAMCRA, when as Throughput reduced utmost by constant factor!! Rem. in CAA: When , as !

41. CAA vs CAMCRA (? = 10%)

42. CAA vs CAMCRA (? = 50%)

43. Robustness of CAMCRA to channel imperfections

44. Outline Introduction CAMCRA scheme Imperfect CSI Stability Summary

45. Two user aloha -assumptions Two users U1 and U2 Total N carriers Total Bandwidth = B Hz ai ? fraction of carriers selected by Ui Rayleigh fading, independent across carriers Stability Region: set of allowable input rate vectors s.t. the lengths of queues are finite

46. Major results CASCRA1 ? If Ui chooses ai of his carriers randomly Net (normalized) throughput = ai CAMCRA2 ? If Ui chooses ai of his best carriers Net (normalized) throughput = C(ai) ? Later we show, C(ai) > ai ? Leads to enlarged stability region!

47. Assumptions for Throughput analysis adaptive modulation capacity achieving codes

48. Throughput analysis (contd) When Ui selects ai of his carriers randomly…(CASCRA) ? Max. possible throughput = ai ? Max. allowable input rate = ai Normalized input rate : = ai

49. theorem (Ganes07): When Ui selects ai of his best carriers …(CAMCRA) ? Max. (normalized) throughput = C(ai) ? Max. (normalized) input rate = C(ai) where

50. Throughput comparison

51. observations C(a) : concave function of a We have C(a) > a For same bandwidth, CAMCRA can support higher data rate than CASCRA Can this lead to larger stability region?

52. Assumptions for Stability analysis Assume buffer can hold arbitrarily large number of packets Assume input arrival rate ? Poisson process Input arrival process independent from user to user

53. Two user aloha Stability region (SALOHA): Set of all input rate vectors “supported” by Aloha “Supported” ? Loosely implies buffer of each user does not overflow Two user system: SALOHA ? well known (single carrier)

54. Stability region (CASCRA vs. CAMCRA) , ? normalized input rates for two user systems… CASCRA stability region (Tysb78) : CAMCRA Exploits presence of multiple carriers Closed form expression not compact Larger stability region!!

55. Stability region

56. Outline Introduction CAMCRA scheme Imperfect CSI Stability Summary

57. Summary (camcra) Multicarrier diversity useful in random access schemes Probability of collision reduced ? throughput improvement Throughput improvement by 50% in Channel Aware Aloha

58. Summary (imperfect CSI) Studied effect of imperfect CSI on CAA and CAMCRA… Showed ? CAA highly sensitive to CSI imperfection… Asymptotic throughput ? 0 in CAA under imperfect CSI… However ? CAMCRA very robust to imperfection in CSI Asymptotic throughput utmost reduced by a constant factor!!

59. Summary (stability region) Studied effect of multicarrier (m/c) diversity… Derived throughput expressions for two user networks with m/c diversity Characterized stability region of two user networks with m/c diversity Showed enlargement of stability region using multiple carriers

60. References G. Ghurumuruhan, Y. (G.) Li, and F. W. Vook, “Stability region of multicarrier channel aware Aloha,” Proc. of IEEE Wireless Commun. and Networking Conf., Hong Kong, China, March 2007 / also to appear in IEEE Trans. Inf. The., June 2007. G. Ghurumuruhan, Y. (G.) Li, and A. Swami, “Channel aware Aloha with imperfect CSI,” Proc. of IEEE 2006 Global Telecommun. Conf., San Francisco, CA Nov. 2006 /also submitted to IEEE Trans. Inf. The. G. Ghurumuruhan, G.-C. Song and Y. (G.) Li, “Asymptotic throughput analysis of distributed multichannel random access schemes,” Proc. of 2005 IEEE International Conf. on Commun., pp. 3637-3641, Seoul, South Korea, May 2005 //also submitted to IEEE Trans. Inf. The.