Multiple-input multiple-output (MIMO) communiction systems Advnced Modultion nd Coding : MIMO Communiction Systems
System model # # #n #m eceive tnsmitte infobits infobits #N #N N tnsmit ntenns N (k) M (k) N (k) M (k) N eceive ntenns k : time index (k =,..., K) (coded) dt symbols n (k), E[ n (k) ] = E s Advnced Modultion nd Coding : MIMO Communiction Systems
System model m N (k) = h n= m,n n (k) + w m (k) (m =,..., N ; k =,..., K) w m (k) : complex i.i.d. AWGN, E[ w m (k) ] = N 0 h m,n : complex Gussin zeo-men i.i.d. chnnel gins (yleigh fding), E[ h m,n ] = (k) h, L h,n (k) w (k) M = M O M M + M (k) h 443 444 L N h (k) w (k) N, N,N N N 4443 443 443 (k) H (k) w(k) (k) = H (k) + w(k) ( (), L, (k), L, (K)) = H ( (), L, (k), L, (K)) + ( w(), L, w(k), L, w(k)) 4444444 3 4444444 3 4444 44443 A W = H A + W Advnced Modultion nd Coding : MIMO Communiction Systems 3
System model infobits b encode MIMO coded bits b : infomtion bitte s : symbol te pe tnsmit ntenn E b : enegy pe infobit E s : enegy pe symbol b MIMO mppe M-point constelltion N K coded symbols MIMO b log (M) MIMO = S/P s = #infobits #coded bits 0 < MIMO # #n #N N MIMO b log (M) (pe ntenn) (code te) E s = E b MIMO log (M) b = s N MIMO log (M) Advnced Modultion nd Coding : MIMO Communiction Systems 4
System model Spectum tnsmitted bndpss signl B F 0 B F f B F s (necessy condition to void ISI between successive symbols) All N tnsmitted signls e simultneously in the sme fequency intevl Bndwidth efficiency : b / s = N MIMO log (M) (bit/s/hz) Advnced Modultion nd Coding : MIMO Communiction Systems 5
ML detection Log-likelihood function ln(p( A, H) : N0 ln p( A, H) = m (k) h N K m= k= n= = H A N m,n (k) = [( H A) n H ( H A)] ML detection : Aˆ = g min H A (minimiztion ove ll symbol mtices A tht obey the encoding ule) Fobenius nom of X : X = x i, j = [ X X] = [ X X ce of sque mtix M : [ M] = m i,i i Popeties : [P Q] = [Q P], [M] = [M ] X H denotes Hemitin tnspose (= complex conjugte tnspose (X * ) ) i, j Advnced Modultion nd Coding : MIMO Communiction Systems 6 H H ]
Bit eo te (BE) BE = E[# infobit eos] # infobits tnsmitted symbol mtix A epesents N K MIMO log (M) infobits BE = N (i,0) (i) info = = ( 0) ( i ) A, A N P[ Aˆ K log A (M), A MIMO A (0) ] (i,0) N info : # infobits in which A (i) nd A (i) e diffeent # infobits encode coded bits mppe N K coded symbols S/P #n MIMO M-point constelltion #N Advnced Modultion nd Coding : MIMO Communiction Systems 7
Bit eo te (BE) ˆ (i) (0) P[, ] P[ ˆ (i) (0) A = A A = A = A = A A = A ]P[ A = A (0) ] P[ A = A (0) ] = N K log (M) MIMO = M N K MIMO [ ˆ (0) (0) P[ A A A A, H] ] ˆ (i) (0) P[ A = A A = A ] = EH = (veging ove sttistics of H) P[ Aˆ = A (i) A = A (0), H] PEP (i,0) ( H) PEP (i,0) (H) = P[ - H A (i) < - H A (0) A = A (0), H] PEP (i,0) (H) : piwise eo pobbility, conditioned on H PEP (i,0) = E H [PEP (i,0) (H)] : piwise eo pobbility, veged ove H Advnced Modultion nd Coding : MIMO Communiction Systems 8
Bit eo te (BE) 0 BE (0) (i,0) (i,0) P[ A = A ] NinfoPEP A i 0 N K log (M) MIMO Define eo mtix : (i,0) = A (0) - A (i) PEP (i,0) ( H) = Q H N (i,0) 0 H exp 4N (i,0) 0 Aveging ove yleigh fding chnnel sttistics : PEP (i,0) (i,0) [ PEP ( H) ] = E det H I N + = (i,0) ( 4N (i,0) 0 ) H N N λ + 4N (i,0) n n= 0 N (i,0) { λ n,n = 0,..., N} set of eigenvlues of N xn mtix (i,0) ( (i,0) ) H (these eigenvlues e el-vlued non-negtive) Advnced Modultion nd Coding : MIMO Communiction Systems 9
o be futhe consideed Single-input single-output (SISO) systems : N = N = Single-input multiple-output (SIMO) systems : N =, N Multiple-input multiple-output (MIMO) systems : N, N Sptil multiplexing : ML detection, ZF detection Spce-time coding : tellis coding, dely divesity, block coding Advnced Modultion nd Coding : MIMO Communiction Systems 0
Single-input single-output (SISO) systems Advnced Modultion nd Coding : MIMO Communiction Systems
SISO : obsevtion model infobits b encode SISO coded bits b SISO mppe coded symbols s = SISO b log (M) Obsevtion model : (k) = h (k) + w(k) k =,..., K Bndwidth efficiency : b / s = SISO log (M) (bit/s/hz) Advnced Modultion nd Coding : MIMO Communiction Systems
SISO : ML detection {â(k)} = g min {(k)} k (k) h (k) = g min {(k)} k u(k) (k) (k)h u(k) = h * = (k) h (k) x * h = h h u(k) ML detecto looks fo codewod tht is closest (in Eucliden distnce) to {u(k)} K log (M) SISO K SISO # codewods = = M In genel : decoding complexity exponentil in K (tellis codes, convolutionl codes : complexity line in K by using Vitebi lgoithm) Advnced Modultion nd Coding : MIMO Communiction Systems 3
SISO : PEP computtion Conditionl PEP : PEP (i,0) (h) h d exp 4N E,(i,0) 0 d K (0) (i) E,(i,0) = (k) (k) k= squed Eucliden distnce between codewods { (0) (k)} nd { (i) (k)} d E = E,(i,0) s SISO log (M) E b Avege PEP, AWGN ( h = ) : PEP (i,0) d exp 4N E,(i,0) 0 deceses exponentilly with E b /N 0 Avege PEP, yleigh fding : PEP (i,0) + d E,(i,0) 4N 0 invesely popotionl to E b /N 0 (occsionlly, h becomes vey smll lge PEP) Advnced Modultion nd Coding : MIMO Communiction Systems 4
SISO : numeicl esults.e+00.e-0 SISO BPSK, uncoded.e-0 BE.E-03.E-04.E-05 AWGN AWGN bound yleigh fding yleigh fding bound.e-06 0 5 0 5 0 5 30 Eb/N0 (db) BE fding chnnel >> BE AWGN chnnel Advnced Modultion nd Coding : MIMO Communiction Systems 5
SISO : numeicl esults.e+00.e-0 SISO BPSK, coded.e-0 BE.E-03 AWGN uncoded.e-04 AWGN Ext. Hmming (8,4) AWGN Shnnon limit yleigh fding uncoded.e-05 yleigh fding, ext. Hmming (8,4) yleigh fding, Shnnon limit.e-06-5 0 5 0 5 0 5 30 Eb/N0 (db) coding gin on fding chnnel << coding gin on AWGN chnnel Advnced Modultion nd Coding : MIMO Communiction Systems 6
Single-input multiple-output (SIMO) systems Advnced Modultion nd Coding : MIMO Communiction Systems 7
SIMO : obsevtion model Sme tnsmitte s fo SISO; N ntenns t eceive infobits b encode SIMO coded bits b SIMO mppe coded symbols s = SIMO b log (M) Obsevtion model : m (k) = h m (k) + w m (k) m =,..., N ; k =,..., K Bndwidth efficiency : b / s = SIMO log (M) (bit/s/hz) Advnced Modultion nd Coding : MIMO Communiction Systems 8
SIMO : ML detection {â(k)} = g min {(k)} N m (k) h m(k) = g min {(k)} m= k k u(k) (k) u(k) = N m= N h m= * m h m m (k) (k) m (k) x * h x Σ x u(k) ML detecto looks fo codewod tht is closest to {u(k)} N (k) * h m x N m= h m * h N Sme decoding complexity s fo SISO Advnced Modultion nd Coding : MIMO Communiction Systems 9
SIMO : PEP computtion Conditionl PEP : PEP (i,0) ( h) N exp d E,(i,0) 4N ( h 0 ) vg ( h ) vg = N N m= h m PEP, AWGN ( h m = ) : PEP (0,i) Nd exp 4N E,(i,0) 0 deceses exponentilly with E b /N 0 totl eceived enegy pe symbol inceses by fcto N s comped to SISO sme PEP s with SISO, but with E b eplced by N E b ( y gin of 0log(N ) db) PEP, yleigh fding : PEP (i,0) + d E,(i,0) 4N 0 N invesely popotionl to (E b /N 0 )^N PEP is smlle thn in SISO setup with E b eplced by N E b - y gin of 0log(N ) db - dditionl divesity gin (divesity ode N ) : pobbility tht ( h ) vg is smll, deceses with N Advnced Modultion nd Coding : MIMO Communiction Systems 0
SISO : sttisticl popeties of < h >.4. Pobbility density function of < h > pdf 0.8 0.6 0.4 N_ = N_ = N_ = 3 N_ = 5 N_ = 0 0. 0 0 0.5.5.5 3 3.5 4 x Advnced Modultion nd Coding : MIMO Communiction Systems
SISO : sttisticl popeties of < h > 0.9 0.8 0.7 P[< h > < x] 0.6 0.5 0.4 0.3 0. 0. N_ = N_ = N_ = 3 N_ = 5 N_ = 0 Cumultive distibution function function of < h > 0 0 0.5.5.5 3 x Advnced Modultion nd Coding : MIMO Communiction Systems
SIMO : numeicl esults.e+00.e-0 SIMO AWGN Uncoded BPSK.E-0 BE.E-03.E-04 N_ = N_ = N_ =3 N_ = 4.E-05.E-06 0 3 4 5 6 7 8 9 0 3 4 5 Eb/N0 (db) AWGN chnnel : y gin of 0 log(n ) db Advnced Modultion nd Coding : MIMO Communiction Systems 3
SIMO : numeicl esults.e+00.e-0 SIMO, N_ = uncoded BPSK y gin.e-0 BE.E-03.E-04.E-05 SISO y gin only bound coect divesity gin.e-06 0 5 0 5 0 5 30 Eb/N0 (db) fding chnnel : y gin + divesity gin Advnced Modultion nd Coding : MIMO Communiction Systems 4
SIMO : numeicl esults.e+00.e-0 SIMO, N_ = 3 uncoded BPSK.E-0 BE.E-03.E-04.E-05 SISO y gin only bound coect.e-06 0 5 0 5 0 5 30 Eb/N0 (db) fding chnnel : y gin + divesity gin Advnced Modultion nd Coding : MIMO Communiction Systems 5
SIMO : numeicl esults.e+00.e-0.e-0 SIMO, N_ = 4 uncoded BPSK SISO y gin only bound coect BE.E-03.E-04.E-05.E-06 0 5 0 5 0 5 30 Eb/N0 (db) fding chnnel : y gin + divesity gin Advnced Modultion nd Coding : MIMO Communiction Systems 6
SIMO : numeicl esults.e+00.e-0 SIMO, N_ = BPSK.E-0 BE.E-03.E-04.E-05.E-06 SISO uncoded uncoded Shnnon limit Ext. Hmming (8,4) 0 5 0 5 0 5 30 Eb/N0 (db) fding chnnel : coding gin inceses with N Advnced Modultion nd Coding : MIMO Communiction Systems 7
SIMO : numeicl esults.e+00.e-0 SIMO, N_ = 3 BPSK.E-0 BE.E-03.E-04.E-05 SISO uncoded uncoded Shnnon limit Ext. Hmming (8,4).E-06 0 5 0 5 0 5 30 Eb/N0 (db) fding chnnel : coding gin inceses with N Advnced Modultion nd Coding : MIMO Communiction Systems 8
SIMO : numeicl esults.e+00.e-0 SIMO, N_ = 4 BPSK.E-0 BE.E-03.E-04.E-05.E-06 SISO uncoded uncoded Shnnon limit Ext. Hmming (8,4) 0 5 0 5 0 5 30 Eb/N0 (db) fding chnnel : coding gin inceses with N Advnced Modultion nd Coding : MIMO Communiction Systems 9
Multiple-input multiple-output (MIMO) systems Advnced Modultion nd Coding : MIMO Communiction Systems 30
MIMO : obsevtion model # m infobits b N (k) = h n= encode MIMO m,n n coded bits (k) + w b MIMO m (k) mppe M-point constelltion N K coded symbols MIMO b log (M) S/P (m =,..., N ; k =,..., K) s = #n #N N MIMO b log (pe ntenn) (M) = H A + W t ny eceive ntenn, symbols fom diffeent tnsmit ntenns intefee Bndwidth efficiency : b / s = N MIMO log (M) (bit/s/hz) Advnced Modultion nd Coding : MIMO Communiction Systems 3
MIMO : ML detection ML detecto : Aˆ = g min H A A # diffeent symbol mtices A = N MIMO log (M) K = M N MIMO K detecto complexity in genel inceses exponentilly with N MIMO nd K Advnced Modultion nd Coding : MIMO Communiction Systems 3
MIMO : PEP computtion PEP, yleigh fding : PEP (i,0) det I N + (i,0) 4N (i,0) H 0 N = N λ + 4N (i,0) n n= 0 N # nonzeo eigenvlues equls nk( (i,0) ), with nk( (i,0) ) N PEP (i,0) invesely popotionl to (E b /N 0 )^(N nk( (i,0) )) PEPs tht dominte BE e those fo which (i,0) = A (0) -A (i) hs minimum nk. divesity ode (i,0) = N min nk( ) (i,0) Advnced Modultion nd Coding : MIMO Communiction Systems 33
MIMO : sptil multiplexing Advnced Modultion nd Coding : MIMO Communiction Systems 34
Sptil multiplexing infobits b S/P N N b b encode encode N b N b mppe mppe # #N s = N b log (M) A = M N MIMO encode : MIMO = (pe ntenn) n = ( n (), L, n (k), L, n (N)) codewod tnsmitted by ntenn #n codewods tnsmitted by diffeent ntenns e sttisticlly independent Aim : to incese bndwidth efficiency by fcto N s comped to SISO/SIMO Bndwidth efficiency : b / s = N log (M) Advnced Modultion nd Coding : MIMO Communiction Systems 35
Sptil multiplexing : ML detection ML detecto : Aˆ = g min H A A = g min A N n,n' = ) e N ( H H H) n,n' ( H n n' n= H n u n (u n ) : n-th ow of H H As H H H is nondigonl, codewods on diffeent ows must be detected jointly insted of individully # diffeent symbol mtices A = N log (M) K = M N K ML detecto complexity inceses exponentilly with N s comped to SISO/SIMO Advnced Modultion nd Coding : MIMO Communiction Systems 36
Sptil multiplexing : PEP computtion (i,0) nonzeo nk( (i,0) ) nk( (i,0) ) = when ll ows of (i,0) e popotionl to common ow vecto δ = (δ(),..., δ(k),..., δ(k)). Exmple : (i,0) hs only one nonzeo ow; this coesponds to detection eo in only one ow of A min nk( i 0 (i,0) ) = Denoting the n-th ow of nk- eo mtix (i,0) by α n δ, the bound on the coesponding PEP is PEP (i,0) + δ 4N 0 n α n N dominting PEPs e invesely popotionl to (E b /N 0 )^N divesity ode N (sme s fo SIMO) Advnced Modultion nd Coding : MIMO Communiction Systems 37
Sptil multiplexing : zeo-focing detection Complexity of ML detection is exponentil in N Simple sub-optimum detection : zeo-focing (ZF) detection line combintion of eceived ntenn signls m (k) to eliminte mutul intefeence between symbols n (k) fom diffeent tnsmit ntenns nd to minimize esulting noise vince Condition fo ZF solution to exist : nk(h) = N (this equies N N ) (k) = H(k) + w(k) nk(h) = N (H H H) - exists z(k) = (H H H) - H H (k) = (k) + n(k) n(k) = (H H H) - H H w(k) z(k) : no intefeence between symbols fom diffeent tnsmit ntenns E[n(k)n H (k)] = N 0 (H H H) - : n i (k) nd n j (k) coelted when i j Advnced Modultion nd Coding : MIMO Communiction Systems 38
Sptil multiplexing : zeo-focing detection (k) z (k) detecto { â (k)} m (k) z (H H H) - H H n (k) detecto { â n (k)} N (k) zn (k) detecto { â N (k)} Sequences { n (k)} e detected independently insted of jointly, ignoing the coeltion of the noise on diffeent outputs : {â (k)} = gmin (k) zn n (k) n n (k) k Complexity of ZF detecto is line (insted of exponentil) in N Pefomnce penlty : divesity equls N -N + (insted of N ) Advnced Modultion nd Coding : MIMO Communiction Systems 39
Sptil multiplexing : numeicl esults BE (bound).e+00.e-0.e-0.e-03 N_ =, N_ = N_ = 5, N_ = N_ =, N_ = N_ = 5, N_ = N_ =, N_ = 3 N_ = 5, N_ = 3 N_ =, N_ = 4 N_ = 5, N_ = 4.E-04.E-05.E-06 Sptil multiplexing uncoded BPSK ML detection 0 5 0 5 0 5 30 Eb/N0 (db) ML detection : penlty w..t. SIMO deceses with incesing N Advnced Modultion nd Coding : MIMO Communiction Systems 40
Sptil multiplexing : numeicl esults.e+00.e-0 (N_, N_) = (,), (,), (3,3),... (N_, N_) = (,), (3,), (4,3),... (N_, N_) = (3,), (4,), (5,3),... (N_, N_) = (4,), (5,), (6,3),....E-0 BE.E-03.E-04.E-05 Sptil multiplexing uncoded BPSK ZF detection.e-06 0 5 0 5 0 5 30 Eb/N0 (db) ZF detection : sme BE s SIMO with N -N + eceive ntenns Advnced Modultion nd Coding : MIMO Communiction Systems 4
MIMO : spce-time coding Advnced Modultion nd Coding : MIMO Communiction Systems 4
Spce-time coding # infobits b encode MIMO coded bits b MIMO mppe coded symbols MIMO b log (M) S/P #n #N Aim : to chieve highe divesity ode thn with SIMO ny (i,0) must hve nk lge thn (mx. nk is N, mx. divesity ode is N N ) coded symbols must be distibuted ove diffeent tnsmit ntenns nd diffeent symbol intevls ( spce-time coding) s = N MIMO b log (pe ntenn) Popety : MIMO /N is necessy condition to hve nk N fo ll (i,0) t mx. divesity, b / s log (M) b / s limited by bndwidth efficiency of uncoded SIMO/SISO (M) Advnced Modultion nd Coding : MIMO Communiction Systems 43
hee clsses of spce-time coding : spce-time tellis codes (SC) dely divesity spce-time block codes (SBC) Advnced Modultion nd Coding : MIMO Communiction Systems 44
SC : tellis epesenttion A = ( ( ), L, (k), L, (K) ) (k) = ( (k), L, (k), L, (k)) n N ( b (k),,b (k)) b( k) = L L L input bits t beginning of k-th symbol intevl S(k) : stte t beginning of k-th symbol intevl stte tnsitions : (S(k+), (k)) detemined by (S(k), b(k)) tellis digm : (L=) 0 b(k), (k) S(k+) S(k) 3 k k+ L bnches leving fom ech stte L bnches enteing ech stte Advnced Modultion nd Coding : MIMO Communiction Systems 45
SC : bndwidth efficiency Bndwidth efficiency : MIMO = L/(N log (M)) b / s = L (bit/s/hz) t mx. divesity : MIMO /N L log (M) #sttes N M (exponentil in N ) ML decoding by mens of Vitebi lgoithm : decoding complexity line (insted of exponentil) in K but still exponentil in N (t mx. divesity) Advnced Modultion nd Coding : MIMO Communiction Systems 46
SC : exmple Exmple fo N =, 4 sttes, 4-PSK, L = infobits pe coded symbol pi 0 3 0 0,0 0, 0, 0,3,0,,,3,0,,,3 3 3,0 3, 3, 3,3 enty i,j : dt symbols coesponding to tnsition fom stte i to stte j 0 3 ny (i,0) hs columns (0, δ ), (δ, 0) with nonzeo δ nd δ nk =, i.e., mx. nk mx. divesity (N N = N ), mx. bndwidth efficiency (L = log (M)), coesponding to mx. divesity Advnced Modultion nd Coding : MIMO Communiction Systems 47
Dely divesity : tnsmitte infobits b encode b mppe dely (n-) # #n Exmple : N = 3 dely (N -) s = #N b log (M) (pe ntenn) A () = 0 0 () () 0 (3) () () (4) (3) () L L L (K 3) (K 4) (K 5) (K ) (K 3) (K 4) 0 (K ) (K 3) 0 0 (K ) nk( (i,0) ) = N divesity ode = N N mximum possible divesity ode! Advnced Modultion nd Coding : MIMO Communiction Systems 48
Dely divesity : bndwidth efficiency Equivlent configution : infobits b encode dely (n-) mppe mppe # #n MIMO encode : MIMO = /N dely (N -) mppe s = #N b log (M) (pe ntenn) Bndwidth efficiency (fo K >> ) : b / s = N MIMO log (M) = log (M) sme bndwidth efficiency s SIMO/SISO with code te Mx. bndwidth efficiency (t mx. divesity) of log (M) chieved fo = (uncoded dely divesity) Advnced Modultion nd Coding : MIMO Communiction Systems 49
Dely divesity : tellis epesenttion Uncoded dely divesity ( = ) cn be intepeted s spce-time tellis code : stte S(k) = ((k-), (k-),..., (k-n +)) #sttes = N M input t time k : (k) output duing k-th symbolintevl : ((k), (k-),..., (k-n +)) decoding complexity : line in K, exponentil in N Advnced Modultion nd Coding : MIMO Communiction Systems 50
Spce-time block codes ML decoding of spce-time code : minimizing - HA ove ll possible codewods A A contins N K coded symbols, which coesponds to N K MIMO log (M) infobits In genel, ML decoding complexity is exponentil in N K Spce-time block codes cn be designed to yield mximum divesity nd to educe ML decoding to simple symbol-by-symbol decisions decoding complexity line (insted of exponentil) in N K Advnced Modultion nd Coding : MIMO Communiction Systems 5
Advnced Modultion nd Coding : MIMO Communiction Systems 5 SBC : exmple = * * A Exmple : N = (Almouti code ) AA H = ( + )I (A hs othogonl ows, iespective of the vlues of nd ) ML decoding (H = (h, h ), = (, ), nd i.i.d. symbols) ( ) ( ) ) )( ( )] ( ) ( e[ g min )] )( [( ]] e[[ g min gmin ),â (â * H * * H *, H H H H,, h h h h h h AA H H H A HA + + + + + = + = = * H u h h h h + + = * H u h h h h + = no coss-tems involving both nd symbol-by-symbol detection u gmin â = u gmin â =
SBC : exmple A * = * (i,0) ( (0) (i) (0) (i) * = (0) (i) (0) (i) * ( ) ) othogonl ows nk = (= mx. nk fo N = ) Assume M-point constelltion A contins 4 symbols, i.e. 4 log (M) MIMO = log (M) infobits MIMO = / (= /N ) : highest possible te fo mx. divesity Almouti spce-time block code yields - mximum divesity (i.e., N ) - mximum coesponding bndwidth efficiency (i.e., b / s = log (M)) - smll ML decoding complexity Advnced Modultion nd Coding : MIMO Communiction Systems 53
Advnced Modultion nd Coding : MIMO Communiction Systems 54 SBC : exmple Exmple : N = 3 = * * * 4 * 3 4 3 * 3 * 4 * * 3 4 * 4 * 3 * * 4 3 A AA H = ( + + 3 + 4 )I 3 ows of A e othogonl ny (i,0) hs nk = 3 mx. divesity (i.e., 3N ) ML detection of (,, 3, 4 ) : symbol-by-symbol detection (no coss-tems) Bndwidth efficiency : b / s = 4 log (M)/8 = log (M)/ i.e., only hlf of the mx. possible vlue fo mx. divesity mx. bndwidth efficiency (unde estiction of mx. divesity nd symbol-by-symbol detection) cnnot be chieved fo ll vlues of N MIMO = /6 (/N = /3)
SBC : numeicl esults.e+00.e-0 Spce-time block codes BPSK N_ = BE (bound).e-0.e-03.e-04 SISO N_ = (Almouti) N_ = 3.E-05.E-06 0 5 0 5 0 5 30 Eb/N0 (db) Advnced Modultion nd Coding : MIMO Communiction Systems 55
SBC : numeicl esults.e+00.e-0.e-0 Spce-time block codes BPSK N_ = BE (bound).e-03.e-04.e-05.e-06.e-07.e-08 SISO SIMO N_ = (Almouti) N_ = 3.E-09 0 5 0 5 0 5 30 Eb/N0 (db) Advnced Modultion nd Coding : MIMO Communiction Systems 56
SBC : numeicl esults.e+00.e-0.e-0 Spce-time block codes BPSK N_ = 3 BE (bound).e-03.e-04.e-05.e-06 SISO SIMO N_ = (Almouti) N_ = 3.E-07.E-08.E-09 0 5 0 5 0 5 30 Eb/N0 (db) Advnced Modultion nd Coding : MIMO Communiction Systems 57
SBC : numeicl esults.e+00.e-0.e-0 Spce-time block codes BPSK N_ = 4 BE (bound).e-03.e-04.e-05.e-06 SISO SIMO N_ = (Almouti) N_ = 3.E-07.E-08.E-09 0 5 0 5 0 5 30 Eb/N0 (db) Advnced Modultion nd Coding : MIMO Communiction Systems 58
Summy : SISO/SIMO/MIMO Bndwidth efficiency Divesity ode (ML detection) ML detecto complexity SISO SISO log (M) in genel : expon. in K (tellis : line in K) SIMO SIMO log (M) N in genel : expon. in K (tellis : line in K) MIMO N MIMO log (M) (i,0) in genel : N mx nk( ) (i,0) expon. in N K Advnced Modultion nd Coding : MIMO Communiction Systems 59
Summy : MIMO Bndwidth efficiency Divesity ode (ML detection) ML detecto complexity sptil multiplexing N log (M) N in genel : expon. in N K (tellis : line in K, expon. in N ) SC log (M) (*) N N expon. in N, line in K dely log divesity (M) N N if uncoded ( = ) : expon. in N, line in K SBC log (M) (*) N N symbol-by-symbol decision (*) ssuming mx. divesity N N is chieved emk : sptil multiplexing with ZF detection - complexity line in N - divesity ode is N -N + Advnced Modultion nd Coding : MIMO Communiction Systems 60