1. Performance Bounds for AF Multi-Hop Relaying over Nakagami Fading WCNC 2010 Gayan Amarasuriya, Chintha Tellambura and Masoud Ardakani {amarasur, chintha, ardakani}@ece.ualberta.ca 6/16/2015 University of Alberta, Canada 1

2. Outline: Introduction motivation proposed bounds analysis numerical results conclusion 6/16/20152

3. Multi-hop amplify-and-forward relaying: 6/16/2015  The gain of a channel assisted amplify-and-forward (CA-AF) relay is given by [Laneman, 2003].  For CA-AF relays, the end-to-end SNR is given by [Hasna, 2003].  The gain of an ideal CA-AF relays is given by and the end-to-end SNR is given by [Hasna, 2003].  Note that. 3

4. 6/16/2015 Prior related research: - minimum bound  [Hasna, 2003]. - geometric mean bound  [Karagiannidis, 2006].  First category: Bounds of the end-to-end SNR  Third category: Asymptotic analysis - for Rayleigh fading  [Ribeiro, 2005] - for Nakagami fading  [Fang, 2008]  Second category: Numerical techniques - relate the MGF of to . [Di Renzo, 2009] 4

5. Motivation:  minimum bound  weakens for less severe fading and higher number of hops in low-to-moderate SNR regime.  geometric mean bound  weakens for high SNRs and higher number of hops.  numerical techniques  involves at least one numerical integration.  asymptotic analysis  valid for only high SNRs.  We would like to have a bound which offers better trade-offs among:  severity of fading  number of hops  SNR regimes 6/16/20155

6. Proposed bound: - harmonic mean of minimum of the first hop SNRS and minimum of the remaining hop SNRs  - here is a free parameter and can be chosen to obtain the tightest bound. - we observe that is a good choice. - this bound is asymptotically exact. 6

7. Analysis:  The following statistics of can be derived in closed-forms:  CDF  PDF  MGF  Generalized moments  The following performance metrics can also be derived in closed-forms:  outage probability  average SER 6/16/20157

8. Analysis (ctd):  the CDF of over i.n.i.d Rayleigh fading  where, and.  the average SER over i.n.i.d Rayleigh fading  where and are the modulation dependent constants of the conditional error probability;. 6/16/20158

9. Analysis (ctd):  the CDF of over i.i.d Nakagami fading   the average SER over i.i.d Nakagami fading  6/16/20159

10. Numerical results: 6/16/2015  Average BER of BPSK over i.n.i.d. Rayleigh fading 10

11. Numerical results (ctd): 6/16/2015  Outage probability over i.n.i.d. Rayleigh fading 11

12. 6/16/2015 Numerical results (ctd):  Impact of severity of fading on the BER bounds over i.i.d. Nakagami fading 12

13. 6/16/2015 Numerical results (ctd):  Impact of number of hops on the outage bounds over i.i.d. Nakagami fading 13

14. 6/16/2015 Numerical results (ctd):  Average BER for different P values over i.i.d. Nakagami fading 14

15. Conclusion: Our bounds – asymptotically exact – outperforms the existing bounds in most of the cases Future directions – can be used to analyze  multi-hop multi-branch AF relay networks  optimal power allocation  multi-hop relay networks with MIMO-enabled terminals  blind/semi-blind relays 6/16/201515

16. References: 1.[Laneman, 2003] J. N. Laneman and G. W. Wornell, “Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks,” IEEE Trans. Inf. Theory, vol. 49, no. 10, pp. 2415–2425, Oct. 2003. 2.[Hasna, 2003] M. O. Hasna and M. S. Alouini, “Outage probability of multihop transmission over Nakagami fading channels,” IEEE Commun. Lett.,vol. 7, no. 5, pp. 216–218, May 2003. 3.[Karagiannidis, 2006] G. K. Karagiannidis, T. A. Tsiftsis, and R. K. Mallik, “Bounds for multihop relayed communications in Nakagami-m fading,” IEEE Trans. Commun., vol. 54, no. 1, pp. 18– 22, Jan. 2006. 4.[Hasna, 2003] M. O. Hasna, “Average BER of multihop communication systems over fading channels,” in 10th IEEE International Conference on Electronics, Circuits and Systems ICECS., vol. 2, Dec. 2003, pp. 723–726. 5.[Di Renzo, 2009] M. Di Renzo, F. Graziosi, and F. Santucci, “A unified framework for performance analysis of CSI - assisted cooperative communications over fading channels,” IEEE Trans. Commun., vol. 57, no. 9, pp. 2551–2557, Sep. 2009. 6.[Ribeiro, 2005] A. Ribeiro, X. Cai, and G. B. Giannakis, “Symbol error probabilities for general cooperative links,” IEEE Trans. Wireless Commun., vol. 4, no. 3, pp. 1264–1273, May 2005. 7.[Fang, 2008] Z. Fang, L. Li, and Z. Wang, “Asymptotic performance analysis of multihop relayed transmissions over Nakagami-m fading channels,” IEICE Trans. Commun., vol. E91B, no. 12, Dec. 2008. 6/16/201516

17. 6/16/2015 Thank You! 17