Low-complexity Algorithms for MIMO Multiplexing Systems

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1 Low-complexiy Algoihms fo MIMO Muliplexing Sysems Ouline Inoducion QRD-M M algoihm Algoihm I: : o educe he numbe of suviving pahs. Algoihm II: : o educe he numbe of candidaes fo each ansmied signal. : : o educe boh he numbe of suviving pahs and he numbe of candidaes. Summay 2 MIMO sucue Inoducion y= Hx+n y h, L h, N x n M = M O M M + M y N h N, h N, N x N n L N y : The eceived signal veco. H : The channel maix. x : The ansmied signal veco. n : The addiive whie Gaussian noise. Inoducion MIMO MIMO Divesiy: diffeen ansmi anennas ansmi coelaed daa. MIMO MIMO Muliplexing: diffeen ansmi anennas ansmi independen daa seams. Deecion algoihms Linea deecion algoihms: : zeo-focing (ZF( ZF) esimaion and minimum mean squae eo (MMSE( MMSE) esimaion. Non-linea deecion algoihms: : maximum likelihood (ML)) deecion, sphee decoding algoihm (SD( SD), successive inefeence cancellaion (SIC( SIC) ) deecion and QR decomposiion associaed M (QRD( QRD-M) ) algoihm. 3 4

2 QRD-M algoihm Assuming h () h ( ) L h 2 ( N ) h( N) T y = h ( ), L, h () x ( ), L, x N N () + n QR decomposiion and lef muliply he eceived signal veco wih Q H x + x + L + x + x + g = z, N,2 N, N 2, N x + g = z N, N N N The QR decomposiion based ML deecion is achieved by ( L c ) d c,, i ( c ) x% = ag min D c, L, N c, L, c N : squaed Euclidean disance (SED) of he 2 M ( L c ) pah c,, i i d( c, L, ci) = zn + i j = N + i, N j+ cj (, L, ci ) : accumulaed squaed Euclidean disance (ASED) of he pah( c, L, ci ) Dc (, L, c ) = dc ( ) + dc (, c ) + L+ dc (, L, c ) + dc (, L, c ) Dc i 2 i i Seps of QRD-M M algoihm 5 6 Two appoaches o educe he complexiy of QRD-M M algoihm To educe he numbe of suviving pahs in each sage [Kim, Yue and Ilis,, 2005; Kawai, Higuchi, Maeda and Sawahashi,, 2006]. To educe he numbe of candidaes of each ansmied signal [Higuchi, Kawai, Maeda and Sawahashi,, 2004; Nagayama and Haoi, 2006; Im,, Kim and Cho, 2007]. Kim K. J., Yue J., Ilis R. A. and Gibson J. D. (2005), A QRD-M/ Kalman File-based Deecion and Channel Esimaion Algoihm fo MIMO-OFDM Sysems, IEEE Tansacions on Wieless Communicaions, vol. 4, pp Kawai H., Higuchi K., Maeda N. and Sawahashi M. (2006), Adapive Conol of Suviving Symbol Replica Candidaes in QRM-MLD fo OFDM MIMO Muliplexing, IEEE Jounal on Seleced Aeas in Communicaions, vol. 24, pp Higuchi K., Kawai H., Maeda N. and Sawahashi M. (2004), Adapive Selecion of Suviving Symbol Replica Candidaes Based on Maximum Reliabiliy in QRM-MLD fo OFCDM MIMO Muliplexing, IEEE GLOBECOM 2004, vol. 4, pp Nagayama S. and Haoi T. (2006), A Poposal of QRM-MLD fo Reduced Complexiy of MLD o Deec MIMO Signals in Fading Envionmen, IEEE VTC 2006 Fall, pp. -5. Im T. H., Kim J. and Cho Y. S. (2007), A Low Complexiy QRM-MLD fo MIMO Sysems, IEEE VTC 2007 SPRING, pp Compuaional complexiy of QRD-M algoihm The compuaion involved in he QR decomposiion will be idenical fo all he QRD-M algoihms. Theefoe, he diffeences in he compuaional complexiy beween diffeen QRD-M M algoihms ae deemined by he numbe of SED calculaions, which ae also he dominan compuaional ask. The compuaional complexiy of he poposed and he exising QRD-M algoihms ae heefoe appoximaely evaluaed in ems of he numbe of SED calculaions. 7 8

3 Algoihm I: o educe he numbe of suviving pahs a each sage Idea: o deemine he numbe of suviving pahs in each sage adapively accoding o he channel condiion of he ansmied signal. Sep : Paiion he pobabiliy densiy funcion of he diagonal elemen i,i hn + i, 0 hn + i,2 hn + i, hn + i, K n + i Algoihm I: o educe he numbe of suviving pahs ( ) ( ) ( ) ( ) p d = K ii, ii, n + i p d = K M ii, ii, n + i ( ) ( ) p d = K ii, ii, n + i Algoihm I: o educe he numbe of suviving pahs Sep 2: Map he insananeous i,i ino he paiioned subegions. Sep 3: Deemine he numbe of suviving pahs in each sage accoding o he sub-egion index. Mn + i = Kn + i,0 i, i < hn + i, M = K, h < h M Mn + i =, hn + i, Kn i + i, i< n + i n + i n + i, i, i n + i,2 9 0 p.d.f of i,i Algoihm I: o educe he numbe of suviving pahs p.d.f of, p.d.f of 2,2 p.d.f of 3,3 p.d.f of 4, i,i. The p.d.f of 4,4 is equally paiioned. 2. The insananeous 4,4 is mapped o he sub-egions. 3. The numbe of suviving pahs is deemined accoding o he index of he sub- egion. Simulaion condiions of algoihm I Sysem Channel Refeence algoihm Modulaion Numbe of ansmi and eceive anennas Channel gain Noise CSI QRD-M algoihm wih fixed numbe of suviving pahs 6QAM o 64QAM 3 ansmi and 3 eceive anennas 4 ansmi and 4 eceive anennas i.i.d Rayleigh disibued. Complex Gaussian, zeo mean, uni vaiance. Leas squaes channel esimaion [Kim and Ilis,, 2002] 2

4 Algoihm I: o educe he numbe of suviving pahs Simulaion esuls of algoihm I Algoihm I: o educe he numbe of suviving pahs Simulaion esuls of algoihm I 0 0 (4,4) sysem, 6QAM modulaion (3,3) sysem, 64QAM modulaion ML deecion fixed QRD M deecion, M=8 fixed QRD M deecion, M=4 adapive QRD M deecion, aveage M=8.5 adapive QRD M deecion, aveage M=4.375 adapive QRD M deecion, aveage M= ML deecion fixed QRD M deecion, M=64 fixed QRD M deecion, M=32 fixed QRD M deecion, M=8 adapive QRD M deecion, M=32.33 adapive QRD M deecion, M=6.24 adapive QRD M deecion, M= SNR SNR 3 4 Algoihm II: o educe he numbe of candidaes Algoihm II: o educe he numbe of candidaes fo each ansmied signal Idea: o selec pa of he consellaion poins insead of all he consellaion poins o save he compuaion. Refeence algoihm [Nagayama and Haoi, 2006] Sep : calculae he signal esimae on each pah. Sep 2: deemine which quadan does he signal esimae falls ino. Sep 3: choose he candidaes accoding o he quadan. 5 6

5 Algoihm II: o educe he numbe of candidaes The poposed algoihm. Sep : calculae he signal esimae on each pah. Sep 2: deemine a cicle ceneing a he signal esimae. Sep 3: choose he consellaion poins wihin he cicle. Simulaion condiions of algoihm II Sysem Modulaion Numbe of ansmi and eceive anennas 6QAM 4 ansmi and 4 eceive anennas Channel Refeence algoihm Channel gain Noise CSI QRD-M algoihm o educe he numbe of candidaes by he quadan of signal esimae in he consellaion i.i.d Rayleigh disibued. Complex Gaussian, zeo mean, uni vaiance. Leas squaes channel esimaion [Nagayama and Haoi, 2006] 7 8 Algoihm II: o educe he numbe of candidaes Simulaion esuls of algoihm II Algoihm II: o educe he numbe of candidaes Simulaion esuls of algoihm II QAM modulaed (4,4) sysem The poposed algoihm, 2 =0.8 The poposed algoihm, 2 =.6 The algoihm in [6], sub-se wih 7 poins The algoihm in [6], sub-se wih poins Compuaional complexiy Complexiy of he efeence algoihm Complexiy of he poposed algoihm 0-4 The poposed algoihm, 2 =0.8 The poposed algoihm, 2 =.6 The algoihm in [6], sub-se wih 7 poins The algoihm in [6], sub-se wih pioins QAM modulaed (4,4) sysem

6 : o educe boh he numbe of suviving pahs and he numbe of candidaes fo each ansmied signal This algoihm has combined boh appoaches o educe he complexiy. Reducion of he numbe of candidaes fo each ansmied signal. Le pah ( c = x, L, ci = xi ) be he coec pah a he ( i ) h sage Esimae of he signal Acual value of he signal Esimaion eo i ( = L = ) = ( j = ) xˆ pah c x,, c x z c i i i N + i N + i, N j+ j N + i, N + i i ( j= ) x = z x g i N + i N + i, N j+ j N + i N + i, N + i ( L ) ˆ,, εi = xi xi pah c = x ci = xi = gn + i N + i, N + i The pobabiliy p of he coec candidae falling wihin a cicle wih cene a x ˆ ( i pah c = x L ci = xi ) and adius Γ can be calculaed by Γ P( xˆ i pah( c = x, L, c ), ) exp( ) exp ( ), i = x i Γ = σ d = λ Γ 0 σ 2 0 The poin wihin he cicle ceneing σ = σn a x ˆ ( N + i, N + i λ =Γ,, i pah c = x L ci σ= xi ) wih adius Γ = λσ has high pobabiliy o be he e coec n N, + i N + i candidae. Only he consellaion poins wihin he cicle aound he signal esimae will be seleced as candidaes. The consellaion poins ouside he cicle will be discaded ( L i ) xˆ i pah c,, c Reducion of he numbe of suviving pahs. h The e oal numbe of possible pahs a he i sage is M accodingly educed fom Mi C o i. Theefoe, he j = m i, j h numbe of suviving pahs a he i sage can be se M as M min Mˆ, i m. i { j i, j} = = When he channel condiion is good and/o he noise powe is low, M i ˆ mi, j< M and he numbe of suviving pahs is educed. j= λσ n N + i, N + i The e numbe of candidaes fo each ansmied signal as well as he numbe of suviving pahs in each sage ae adapively and independenly conolled accoding o he channel condiions and noise powe

7 Implemenaion fo algoihm II and III How o deemine he cicle? To calculae he eal ime Euclidean disance beween he signal esimae and he consellaion poins will cause addiional calculaions. This wok is done off-line by using a look up able Simulaion condiions of algoihm III Sysem Channel Refeence algoihms Paamees Modulaion Numbe of anennas Channel gain Noise SNR 6QAM modulaed 4,4 sysem 64QAM modulaed 3,3 sysem 6QAM and 64QAM 3 ansmi and 3 eceive anennas 4 ansmi and 4 eceive anennas i.i.d Rayleigh disibued. Complex Gaussian, zeo mean, uni vaiance. 0dB-30dB CSI Leas squaes channel esimaion QRD-M algoihm wih fixed [Kim and Ilis, 2002] numbe of suviving pahs QRD-M algoihm o educe he [Kawai, Higuchi, Maeda and numbe of suviving pahs in Sawahashi, 2006] each sage =.5, 2, 2.5; k=2, 3, 4; M=2 =2, 2.5, 3; k=2, 3, 4; M= SNR = 0dB Lowe bound fo SNR = 0dB SNR = 5dB Lowe bound fo SNR = 5dB SNR = 20dB Lowe bound fo SNR = 20dB λ The effec of λ on he pefomance fo a 6QAM modulaed d sysem, N = 4, N = 4 Simulaion esuls of algoihm III: he effecs of λ 27 28

8 Compuaional Complxiy SNR = 0dB SNR = 5dB SNR = 20dB Uppe bound of compuaional complexiy λ Simulaion esuls of algoihm III: he effecs of The effec of λ on he compuaional complexiy fo a 6QAM modulaed sysem, N = 4, N = 4 λ Simulaion esuls of algoihm III: compaison wih he efeence algoihms The KHMS QRD-M algoihm,k=2 The KHMS QRD-M algoihm,k=3 The KHMS QRD-M algoihm,k=4 The poposed algoihm,λ =.5 The poposed algoihm,λ =2 The poposed algoihm,λ =2.5 The KI QRD-M algoihm,m= The pefomance fo a 6QAM modulaed sysem, N = 4, N = Simulaion esuls of algoihm III: compaison wih he efeence algoihms Simulaion esuls of algoihm III: compaison wih he efeence algoihms Compuaional Complexiy The KHMS QRD-M algoihm,k=2 The KHMS QRD-M algoihm,k=3 The KHMS QRD-M algoihm,k=4 The poposed algoihm,λ =.5 The poposed algoihm,λ =2 The poposed algoihm,λ =2.5 The KI QRD-M algoihm,m=2 The poposed algoihm can achieve moe han an ode of educion in compuaional complexiy a SNR=6dB The KHMS QRD-M algoihm,k=2 The KHMS QRD-M algoihm,k=3 The KHMS QRD-M algoihm,k=4 The poposed algoihm,λ=2 The poposed algoihm,λ=2.5 The poposed algoihm,λ=3 The KI QRD-M algoihm,m= The compuaional complexiy fo a 6QAM modulaed sysem, N = 4, N = The pefomance fo a 64QAM modulaed sysem, N = 3, N =

9 Simulaion esuls of algoihm III: compaison wih he efeence algoihms Compuaional Compuaional Complexiy Complexiy The KHMS QRD-M algoihm,k=2 The The KHMS KHMS QRD-M algoihm,k=2 algoihm,k=3 The The KHMS KHMS QRD-M algoihm,k=3 algoihm,k=4 The The KHMS poposed QRD-M algoihm,λ algoihm,k=4 =.5 The The poposed algoihm,λ =2 =2 The The poposed poposed algoihm,λ =2.5 =2.5 The The poposed KI QRD-M algoihm,λ algoihm,m=2 =3 The KI QRD-M algoihm,m= The poposed algoihm can achieve a 93% educion in he compuaional complexiy a SNR=20dB. The compuaional complexiy fo a 64QAM modulaed sysem, N = 3, N = 3 Summay Thee algoihms ae poposed o educe he compuaional complexiy of QRD-M M algoihm. Algoihm I educes he numbe of suviving pahs a each sage; Algoihm II educes he numbe of candidaes fo each ansmied signal; educe boh he numbe of suviving pahs and he numbe of candidaes fo each ansmied signal. The hee algoihms can achieve a educion of complexiy of QRD-M M algoihms when compaed wih he exising algoihms, and hey have diffeen applicaions: When he channel sae infomaion (CSI) and channel disibuion infomaion (CDI) ae available a he eceive, Algoihm I can be applied. When only he CSI is available a he eceive, Algoihm II can be applied. When CSI and he noise powe ae available a he eceive, can be applied Thank you! 35

MIMO Cognitive Radio Capacity in. Flat Fading Channel. Mohan Premkumar, Muthappa Perumal Chitra. 1. Introduction

MIMO Cognitive Radio Capacity in. Flat Fading Channel. Mohan Premkumar, Muthappa Perumal Chitra. 1. Introduction Inenaional Jounal of Wieless Communicaions, ewoking and Mobile Compuing 07; 4(6): 44-50 hp://www.aasci.og/jounal/wcnmc ISS: 38-37 (Pin); ISS: 38-45 (Online) MIMO Cogniive adio Capaciy in Fla Fading Channel