2006 Корея ImpulseSymbolBasedChannelEstimationinOFDMSystems
2006 Корея ImpulseSymbolBasedChannelEstimationinOFDMSystems
2006 Корея ImpulseSymbolBasedChannelEstimationinOFDMSystems
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The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)
y ( n)
where hn,l is equal to h(n, l). H is converted in the frequency
Y (k ) Parallel Y y Overlap y′ Serial
to FFT and to ⊕ domain by using the N -point FFT matrix FN . The element at
Serial Add Parallel
z ( n) ith row and jth column is
1 j2π(i−1)(j−1)
Fij = √ e− N (11)
Figure 2: Block diagram of ZP-OFDM system N
The system model from X to Y can be represented in the fre-
From (2), the frequency symbols, X are transformed to x = quency domain
[x(0) x(1) · · · x(n) · · · x(N − 1)]T .
To avoid interference between adjacent OFDM symbol Y = FN HFH
N X + Z = GX + Z (12)
blocks, the length of CP, G should be longer than the length
where G = FN HFH
N is the channel matrix in the frequency
of the channel impulse response. In CP-OFDM system, the
domain; Z is FFT of z.
last G − 1 elements are appended ahead of x as following
By multiplying the matrix inversion of G with Y, the mit-
x = [x(N − G + 1) · · · x(N − 2) x(N − 1) xT ]T (3) igation of ISI and ICI is achieved. In this case, there are two
methods: the zero-forcing (ZF) and minimum mean squared
Under the assumption that the channel impulse response is con- error (MMSE) linear detection. The mathematical representa-
stant and its length is L, the receive signal y(n) is given by tions of them are given by
L−1
y(n) = x(n) ∗ h(n) + z(n) = h(l)x(n − l) + z(n) (4) ZF : X̃ = [G]+ Y (13)
−1
l=0 σ2
MMSE : X̃ = GH G + Z 2 IN GH Y (14)
where ∗ denotes the linear convolution; z(n) is the AWGN. σX
The serial to parallel converter outputs y = [y(N − G +
where σZ 2
and σX2
are the noise power and the signal power,
1) · · · y(N − 2) y(N − 1) y(0) y(1) · · · y(N − 1)]T . Af-
respectively; IN is the N × N identity matrix.
ter removing the CP from y , y(n) can be represented by the
circular convolution between x(n) and h(n). B. ZP-OFDM
y(n) = x(n) h(n) + z(n), n = 0, · · · , N − 1 (5) Fig. 2 depicts the block diagram of the ZP-OFDM system. The
structure of ZP-OFDM is similar to that of CP-OFDM. How-
where denotes the circular convolution. The vec-
ever, the methods inserting the guard interval are different be-
tor y is transformed to the vector Y where y = tween two systems. In ZP-OFDM system, G − 1 null symbols
[y(0) y(1) · · · y(n) · · · y(N − 1)]T ; Y = are appended behind x,
[Y (0) Y (1) · · · Y (k) · · · Y (N − 1)]T . For the frequency
domain representation, (5) can be expressed to x = [xT 0G−1 ]T (15)
Y (k) = X(k)H(k) + Z(k), k = 0, · · · , N − 1 (6) where 0G−1 represents the 1×(G−1) null vector. The received
where H(k) is the FFT of h(n) and Z(k) is the FFT of z(n). signal is y = [y(0) y(1) · · · y(N − 1) y(N ) · · · y(N +
The equalization is performed by dividing in the frequency do- G − 2)]T . In ZP-OFDM, the guard interval is not removed. In
main addition, the vector y is obtained by overlap and add method.
Magnitude
h1,1 h1,0 · · · hN +1,2
1
H= .. .. .. .. (17)
. . . . 0.5
hN −1,N −1 hN −1,N −2 ··· hN −1,0 0
0 10 20 30 40 50 60
Subcarrier
Compared with CP-OFDM, the upper triangular terms are dif- Channel Impulse Response
ferent. From H, the channel matrix G is obtained by (12) and All data
its inversion used to mitigate ISI and ICI. 0.6 Selected data
Magnitude
0.4
III. OFDM C HANNEL E STIMATION 0.2
The channel frequency response is transformed to the time do- Channel Frequency Response
3
main sequence, h(n) = IFFT[g(k)]. Next, h(n) becomes the Magnitude
Interpolated Data
Estimated Data
channel impulse response composed of the components with 2
relatively high power. Moreover, the receiver discards the com-
1
ponents whose delay is more than the maximum delay. Fig. 3
shows the OFDM channel with pilot symbols in time slots. 0
0 10 20 30 40 50 60
It is assumed that there are m − 1 data symbol blocks be- Subcarrier
Channel Impulse Response
tween two pilot symbol blocks. The channel impulse response 0.6
hi = [hi (0) hi (1) · · · hi (l) · · · hi (L − 1)] is obtained at All data
Magnitude
Selected Data
i-th OFDM symbol block. The channel impulse response at 0.4
the next pilot symbol blocks is hi+m . The delay component 0.2
h(n, l) in m − 1 data symbol blocks is acquired by interpola-
tion between hi (l) and hi+m (l). As a result, the channel matrix 0
0 10 20 30 40 50 60
H is constructed by the above value and the channel matrix G Sampling Index
4
quency response, the received signal vector is divided by the
pilot symbols like (18). However, the interpolation technique is 2
required for all subcarriers, because the channel coefficients at
0
subcarriers without the pilot symbol are not acquired directly. 0 20 40 60 80
Except applying interpolation, the channel estimation process Sampling Index
Received Sequence
is the same as the previous scheme. Fig. 4 depicts the estimated 3
OFDM Symbol Part
OFDM channel with pilot symbols in subcarriers. Impulse Symbol Part
Magnitude
0
Table 1: Systems Environment. 10
Modulation QPSK
FFT/IFFT Size 64 −1
10
Guard Interval 16
System Bandwidth 500kHz
BER
−2
10
where Gij is the element at ith row and jth column of the chan- V. C ONCLUSION
nel matrix G and Ĝij is the element of the estimated channel In real environments, the receiver cannot generally know per-
matrix. fect CSI. Thus, to accurately estimate CSI, we proposed the
The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06)
0 0
10 10
−1 −1
10 10
BER
BER
−2 −2
10 10
Figure 8: BER versus SNR/bit of OFDM systems in the chan- Figure 10: BER versus SNR/bit of OFDM systems in the chan-
nel with ∆fD = 0.1 and τrms = 2µs nel with ∆fD = 0.05 and τrms = 10µs
0 0
10 10
ZP Training Block ZP Training Block
CP Training Block CP Training Block
ZP Pilot Symbol ZP Pilot Symbol
−1 −1
10 CP Pilot Symbol 10 CP Pilot Symbol
ZP Impulse ZP Impulse
−2 −2
10 10
MSE
MSE
−3 −3
10 10
−4 −4
10 10
0 5 10 15 20 25 30 0 5 10 15 20 25 30
Eb/N0 [dB] Eb/N0 [dB]
Figure 9: MSE versus SNR/bit of OFDM systems in the chan- Figure 11: MSE versus SNR/bit of OFDM systems in the chan-
nel with ∆fD = 0.1 and τrms = 2µs nel with ∆fD = 0.05 and τrms = 10µs
novel channel estimation method using the impulse symbol in [3] Yang-Seok Choi, P.J. Voltz, and F.A. Cassara, “On channel estimation
and detection for multicarrier signals in fast and selective rayleigh
the time domain. The channel impulse response is obtained fading channels,” IEEE Trans. Commun., vol. 49, no. 8, pp. 1375-
directly in the time domain. On the other hand, the existing 1387, Aug. 2001.
pilot-based OFDM system needs IFFT operation to obtain the [4] Hoojin Lee, E.J. Powers, and Joonhyuk Kang, “Efficient OFDM sym-
channel impulse response. Moreover, our proposed technique bol estimation algorithm over time-frequency-selective fading chan-
is more robust to the effect of Doppler spread and delay spread nels,” IEEE Int. Conf. Acoustics, Speech and Signal Processing, vol.
than existing channel estimation schemes. However, we can ac- 3, pp. 781-784, Mar. 2005.
quire more accurate CSI by using the impulse symbol as long [5] J.K. Cavers, “An analysis of pilot symbol assisted modulation for
rayleigh fading channels,” IEEE Trans. Veh. Techno., vol. 40, no. 4,
as the length of channel impulse response is moderate. pp. 686-693, Nov. 1991.
[6] B. Muquet, Zhengdao Wang, G.B. Giannakis, M. de Courville, and P.
ACKNOWLEDGEMENT Duhamel, “Cyclic prefixing or zero padding for wireless multicarrier
transmissions?,” IEEE Trans. Commun., vol. 50, no. 12, pp. 2136-
This research was supported by Samsung ICU Research Center. 2148, Dec. 2002.
[7] K.F. Lee and D.B. Williams, “A space-time coded transmitter diver-
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