Transcript 下載/瀏覽

Performance analysis with a timing error
 Next related problem is the effect of timing offset on the error
probability for OFDM system.
 Assume that the complex envelope is given by
N 1
x(t )   (a n  jbn )e
j
2
nt
T
n 0
 Complex envelope of the signal at the input of the receiver is
N 1
2
r (t )   X n exp( j
nt )  n(t )
T0
n 0
 Assume that the receiver makes a timing error  in the
sampling process and the OFDM is cyclically extended, then
the sample of the received signal is equal to:
N 1
T0
2
rk  r (t ) t k T0    X n exp( j
n(k   ))  nk
T0
N
N
n 0
Wireless Communication Technologies 2.5.3
1
Performance analysis with a timing error
 Using these samples to compute the DFT, we have
1 N 1
2
2
~
X m   rk exp(  j
mk )  X m exp( j
m )  nm
N k 0
N
T0
1
n

where m
N
N 1
 nk exp(  j
k 0
2
mk ) .
N
 From Eq. we can see that when timing offset does not exceed
the duration of guard interval, the timing offset does not
violate the orthogonality of the subcarriers.
 The result of this effect is a phase rotation of the subcarriers
which linearly changes with subcarrier orders.
Wireless Communication Technologies 2.5.3
2
Performance analysis with a timing error
 Assume the modulation is QPSK and a n , bn  {1,  1} , the
probability of a correct decision on the mth subcarrier is [5]
Pc / m 
 1 
 1 

2
2
2
2



m  bm sin
m )  Q 2SNR (cos
m  bm sin
m )  
1  Q 2SNR (cos
T0
T0
T0
T0
 2 

 2 
 1 
 1 

2
2
2
2
m  am sin
m )  Q 2SNR (cos
m  am sin
m ) 
1  Q 2SNR (cos
T0
T0
T0
T0
 2 

 2 
where SNR represents the signal-to-noise ratio per information
bit at the input of the decision device.
 The error probability is obtained by averaging the probability
on every subcarrier, that is
1 N 1
Pe   (1  Pc / m )
N m 0
Wireless Communication Technologies 2.5.3
3
Performance analysis with a timing error
 Fig. represents error probability as a function of the relative
timing offset and Eb / N o at the input of the decision device.
 It can be seen that the performance is more sensitivity at high
SNR.
Eb / N o  0dB
Eb / N o  4dB
Eb / N o  8dB
Eb / N o  12dB
QPSK , N  32
 /T
Wireless Communication Technologies 2.5.3
4
Performance analysis with a timing error
 Fig. shows the error probability versus the normalized timing
offset and the number of subcarriers.
 It can be seen that the increase of the number, that is, at the higher bit rates,
the performance is more sensitivity to the timing offset.
N  128
N  64
BER
N  32
QPSK , Eb / N o  10dB
 /T
Wireless Communication Technologies 2.5.3
5