Mobile Communications (KECE425) Lecture Note 20 5-19-2014 Prof Young-Chai Ko
Summary Complexity issues of diversity systems ADC and Nyquist sampling theorem Transmit diversity Channel is known at the transmitter (Closed-loop transmit diversity: CLTD) Channel is unknown at the transmitter (Space-time block coding: STBC) Transmit-Receive diversity (Maximal ratio transmission)
Analog-to-Digital Converter (ADC) ADC consists of two circuit blocks: Sampling and quantization r(t) ADC ( Ts ) 0001100110100110 r(t) T s T s : sampling interval t[sec] 00 01 10 11 s 2 s 1 a n = s m at t = nt Pulse shaping " 1 X Up-converter s(t) # Band-limited channel r(t) s(t) =< a n p(t nt )e j2 f ct s 4 s 3 n= 1
Sampling interval: T s [sec/sample] Sampling rate: R s = 1 T s [samples/sec] Quantization level, n [bits/sample] Sampling rate: R s = n T s [bits/sec]
Example - 10MHz bandwidth and 16-QAM T s = 1 = 50 [ns/sample] 20 106 We need at least 4 levels for hard decision of 16-QAM symbols in each of I and Q channels R s =2 20 10 6 [bits/sec] LNA LPF X cos(2 f c t) X LPF LPF ADC ( Ts ) ADC ( Ts ) Baseband! 2R s [bits/sec] process time sin(2 f c t)
Nyquist Sampling Theorem Nyquist sampling theorem tells us two things for ISI free communications over band-limited channels: 1) The sampling rate in ADC (analog-to-digital converter) should be as fast as twice the signal bandwidth R(f) 2 r(t) ADC ( Ts ) 0001100110100110 r(t) = 0 1X W a n x(t f [Hz] nt )+n(t) T s apple 1 2W samples/sec n= 1 2) The pulse shape should satisfy the Nyquist condition 1, n =0 x(nt )= 0, n 6= 0
Diversity Combining with L ADC h 1 (t) h 2 (t) r 1 (t) RF chain W ADC R s r 2 (t) RF chain W ADC R s Baseband! 2LR s [bps] h L (t) process time r L (t) RF chain W ADC R s
Complexity Comparisons MRC, EGC and SC requires L RF chains as well as L ADCs at the receiver Only switched diversity requires only one ADC
Some Combinations of Diversity Schemes Generalized Selection Combining (GSC) - Maximal ration combining L c strongest branches out of L branches 1 2 Selection 1 2 Select L c strongest brachens in terms of SNR L c -MRC L (L c apple L) L c
Generalized switched-and-stay combining (GSSC) 1 2 SSC 1 L 1 L 2 -MRC L SSC L/2
Transmit Diversity Systems 1 h 1 2 h 2 Space- time coding L h L RX Channel known at the transmitter =) Closed-loop transmit diversity (CLTD) Channel unknown at the transmitter =) Open-loop transmit diversity (OLTD)
Transmit Diversity with Known Channel State w t1 1 s 1 (t) =w t1 x(t) X w t2 2 s 2 (t) =w t2 x(t) h 1 h 2 x(t) X h L r(t) = r(t) LX h l (t)s l (t)+n(t) l=1 w tl L s L (t) =w tl x(t) = LX h l (t)w tl x(t)+n(t) l=1 X Optimum transmit weights: w tl = c l h tl
Power constraint condition LX E[ s l (t) 2 ] apple P t l=1 - c l must be adjusted to satisfy the power constraint condition If E[ x(t) 2 ] = 1, c l = s P t L P L l=1 h l 2 Received signal r(t) =x(t) LX c l h l 2 + n(t) l=1 SNR of the received signal = P t L P l=1 2 l PL l=1 2 l 2 N 0 = P L l=1 2 l LN 0 = 1 L LX l=1 l
Feedback channel for acquiring the downlink channel at the transmitter c 1 h 1 1 s 1 (t) =w t1 x(t) X c 2 h 2 2 s 2 (t) =w t2 x(t) h 1 h 2 x(t) X h L Receiver c L h L L s L (t) =w tl x(t) Channel Estimator X Feedback channel - Hence we call this as closed-loop diversity system
Channel state information (CSI) - We call h l for l =1,,L as the channel state information (CSI) - There are two separate CSI: amplitude and phase of the channel h l Channel direction information (CDI): \(h l ) Channel quality information (CQI): h l CSI feedback CSI Estimation at the receiver CSI Quantization at the receiver Precoding at the transmitter CSI update
CSI quantization - n 1 -bit and n 2 -bit level quantization for CQI and CDI, respectively - Total n-bit level quantization which means we have 2 n di erent channel state CSI update - CSI should be updated every coherence time
Performance of closed-loop diversity systems - Received SNR is LX t = 1 L l=1 l - Hence, the BER/SER of closed-loop transmit diversity will be the same as the one of MRC by substituting /L into - For iid Rayleigh channel with BPSK, we have P (e) = apple 1 µ 2 L LX 1 k=0 apple L 1+k 1+µ k 2 k where µ = s /L 1+ /L = r L +
BER of BPSK using MRC and closed-loop TD over Rayleigh channels P (e) 10 0 No diversity L=2 L=3 L=4 10 1 MRC with L=2 MRC with L=3 MRC with L=4 10 2 10 3 10 4 10 5 10 6 0 5 10 15 20 25 30 Received SNR per branch ( )[db]
PDF of the combined output SNR p t ( t )= t for L branches MRC 1 (L 1)!( ) L L 1 t e t/ 1 09 08 L=1 L=2 L=3 L=4 L=10 07 06 05 04 03 02 01 0 0 1 2 3 4 5 6 7 8 9 10 t
PDF of the combined output SNR t for L branches CLTD p t ( t )= 1 L 1 (L 1)!( /L) L t e L t/ 12 L=1 L=2 L=3 L=4 L=10 1 08 06 04 02 0 0 05 1 15 2 25 3 35 4 45 5 t
Open-Loop Transmit Diversity There are many open loop transmit diversity schemes Out of them, we only study the space-time block coding (STBC) with dual transmit antennas Alamouti devised the STBC with two antennas in 1998 and it is often called as Alamouti coding
Alamouti coding (2 1) TX antenna 1 h 1 r 1 = s 0 h 1 + s 1 h 2 + n 1 antenna 1 s 1 s 0 TX antenna 2 r 2 = s 1h 1 + s 0h 2 + n 2 antenna 2 s 0 s 1 h 2 [Space-time block code (STBC) antenna1 antenna2 time t time t+t s 0 s 1 s 1 s 0
QPSK example 00! s 1 = 1+j 01! s 2 = 1 j 11! s 3 = 1+j 10! s 4 = 1 j [Space-time block code (STBC) antenna1 antenna2 time t s 0 s 1 time t+t s 1 s 0 data: 01001011 =) s 0 s 1 s 2 s 4 = s 2 s 1 s 4 s 3 time T 2T 3T 4T ant1 ant2 1 j 1+j 1+j 1+j 1 j 1+j 1+j 1+j r 1 = s 0 h 1 + s 1 h 2 + n 1 r 2 = s 1h 1 + s 0h 2 + n 2 r 3 = s 2 h 1 + s 3 h 2 + n 1 r 4 = = s 3h 1 + s 2h 2 + n 2
Detection of space-time block coding signal r 1 = s 0 h 1 + s 1 h 2 + n 1 r 2 = s 1h 1 + s 0h 2 + n 2 v 1 = h 1r 1 + h 2 r 2 v 2 = h 2r 1 h 1 r 2 v 1 = ( h 1 2 + h 2 2 )s 0 + h 1n 1 + h 2 n 2 v 2 = ( h 1 2 + h 2 2 )s 1 + h 2n 1 h 2 n 2