Selective DF Relaying in Multi-Relay Networks With Different Modulation Levels Hamza Umit Sokun Salama Ikki Akram Bin Sediq Halim Yanikomeroglu Lakehead University Carleton University Canada Canada sikki@lakeheadu.ca {husokun, akram,halim}@sce.carleton.ca IEEE ICC, June 2014, Sydney, Australia 1
Outline • Motivation, Background, and Context • Contributions • Error Rate Performance Analysis • Asymptotic Performance Analysis • Simulation Results • Summary and Future Work IEEE ICC, June 2014, Sydney, Australia 2
Motivation Common assumption in cooperative relaying literature: • Same modulation levels by the source and relays – Poor spectrally efficiency Allow different modulation levels at the relays opportunistically • – Better spectrally efficiency Performance analysis Protocol design • Interest in terminal relaying in 3GPP • IEEE ICC, June 2014, Sydney, Australia 3
Background 1 relay BER-based selection is better than SNR-based selection, when the signals at branches have different modulation levels. A. Bin Sediq and H. Yanikomeroglu, “Performance analysis of selection combining of signals with different modulation levels in cooperative communications,” IEEE Trans. Veh. Technol ., vol. 60, no. 4, pp. 1880–1887, May 2011. A. Bin Sediq and H. Yanikomeroglu, “Selection combining of signals with different modulation levels in Nakagami-m fading”, IEEE Commun. Letters , vol. 16, no. 5, pp. 752- 755, May 2012. IEEE ICC, June 2014, Sydney, Australia 4
Context Multiple relays IEEE ICC, June 2014, Sydney, Australia 5
Contribution 1/4 R 1 R 2 Find biased SNRs • D S R K IEEE ICC, June 2014, Sydney, Australia 6
Contribution 2/4 R 1 R 2 Find BER for selection • D combining S R K Not straightforward • Relevance to • CoMP HARQ Relay IEEE ICC, June 2014, Sydney, Australia 7
Contribution 3/4 Find E2E BER in a network with selection combining • IEEE ICC, June 2014, Sydney, Australia 8
Contribution 4/4 Find asymptotic E2E BER in a network with selection combining • IEEE ICC, June 2014, Sydney, Australia 9
Preliminaries Point-to-Point Rayleigh BER Point-to-Point AWGN BER ( ) ( ) γ ≈ γ 2 BER c Q 2 d , M ij M M i j i i i γ 2 ( ) d 1 = ≈ − 1,1 , M 2, M ij BER c 1 i i + γ ( ) ij M 2 2 i 1 d = − where c , d 2 2 / M M ij 3 i ≥ M M i , , M 4 , i i ( ) − i 2 M 1 lo g M i 2 i Average Packet Error Rate N = − − log M PER 1 (1 SER ) 2 s SR SR i i N log2 Ms γ 2 d 1 ( ) ≈ − − − M SR 1 1 c log M 1 s i + γ M 2 s 2 2 1 s d M SR s i ≈ where log for Gray-coded constellations SER BER M 2 s IEEE ICC, June 2014, Sydney, Australia 10
Error Rate Performance (1/3) End-to-End Average BER ( ) P S ( ) K K ∏ ∑ ∑ r all ∏ ∏ = + − BER PER BER 1 PER PER BER SR SD SR SR comp ( ) k e e P S i o r m , all = = = ∈ ∉ k 1 r 1 m 1 e P ( S ) e P ( S ) i r m , all o r m , all For example, for a two-relay scenario, it is given as = + − + − BER PER PER BER (1 PER ) PER BER (1 PER ) PER BER SR SR SD SR SR comp { } SR SR comp { } 1 2 1 2 1 2 1 2 + − − (1 PER )(1 PER ) BER SR SR comp { } 2 1 1,2 represents the cardinality of , P S ( ) S • r all all is r-th element power set of , i.e., , ( ) P S S • r all all ( ) P S is m-th element of , P , ( S ) • r all r m all { } = is the set of all relays’ indexes, i.e., , S S 1, ..., K • all all − is the average packet error ratio in link , PER S R • SR i i − S D is average BER in link , BER • SD is average BER conditioned on the decoding set at destination terminal after BER • comp DS selection combining. IEEE ICC, June 2014, Sydney, Australia 11
Error Rate Performance (2/3) End-to-End Average BER Conditioned on the Decoding Set γ γ ≥ ρ γ = 2 c Q ( 2 d ) if , i 1,2,..., K M M SD SD i R D ≈ S S i BER comp inst , γ γ < ρ γ γ < β γ ≠ = = 2 c Q ( 2 d ) if and j i , j 1,2,..., K , for i 1,2,..., K M M RD SD i R D R D ij R D R R i j i i i An approximate and simpler 2 2 d d implementation of the instantaneous BER. M M ρ = β = R R where i and i are biasing factors. i ij 2 2 d d M M S Rj K + ∑ 1 2 = BER BER BER γ ≥ ρ γ ρ γ γ < ρ γ γ < β γ ≠ = 1 ,..., and , , 1,2,..., comp { } j i j K decoding set SD 1 R D K R D SD i R D R D ij R D K i j i = i 1 γ − − ( ) γ ρ γ 1 ρ γ 1 ∞ R D − − i SD K 1 SD K SD 1 1 ∏ ∫ ∫ ∫ γ γ = γ 2 R D BER ... c Q 2 d e e d d ... d SD i 1 γ ≥ ρ γ γ γ γ γ γ M M SD SD i R D s s SD R D R D i 1 K = γ = γ = γ = i 1 SD R D 0 0 0 i SD R D R D 1 K 2 BER γ < ρ γ γ < β γ ≠ = and , j i j , 1,2,..., K SD i R D R D ij R D i j i γ γ ρ γ β γ β γ γ ( ) ∞ − RjD − R D − i i R D i 1 R D iK R D − SD K 1 i 1 i 1 1 ∏ 1 γ ∫ ∫ ∫ ∫ γ = γ γ 2 R D ... c Q 2 d e R D e e j d d d ... d i SD γ γ γ γ γ γ γ M M R D R R i R D SD R D R D i i i 1 K = γ = γ = γ = γ = j 1 R D SD R D 0 0 0 0 R D SD R D R D i j i 1 K IEEE ICC, June 2014, Sydney, Australia 12
Error Rate Performance (3/3) End-to-End Average BER N log2 Ms γ γ 2 2 d d K 1 1 ∏ ( ) = − − − − M SR M SD 1 1 log 1 1 BER c M s k c S + γ + γ M 2 s M 2 2 2 s 1 d 2 S 1 d = k 1 M SR M SD s k S N N log2 Ms log2 Ms γ γ 2 2 d d P S ( ) K 1 1 ∑ ∑ r all ∏ ( ) ∏ ( ) M SR M SR + − − × − − − s ei s eo 1 c log M 1 1 1 c log M 1 + γ + γ M 2 s M 2 s 2 2 2 s 1 d 2 s 1 d = = ∈ ∉ r 1 m 1 e P ( S ) e P ( S ) M SR M SR i r m , all o r m , all s ei s eo P ( S ) r m , all + + P ( S ) ( ) k c r m , all k 1 k 1 ∑ ∑ ( ) × ∞ γ + − k ∞ M 2 2 , , , 1 , , , I c d I s d { } { } { } { } γ γ γ M M SD M s s s HM , P S HM , P S = = k 1 y 1 S D SD k y , SD k y , P ( S ) r m , all ( ) P ( S ) P ( S ) c + + k r m , all r m , all k 1 k 1 ∑ ∑ ∑ ( ) + ∞ γ + − k ∞ M 2 2 Ri I , c , d , 1 I , , d , { } { } { } { } γ M M R D M γ γ R R i R i i i HM , P S HM , P S = = = i 1 k 1 y 1 R D R D k y , x R D k y , x i i i IEEE ICC, June 2014, Sydney, Australia 13
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