Chapter 3 ICI Mitigation in Doppler Spread Channel
3.2 The proposed method
First we will recapitulate why the LS estimator presented in the previous section is not adequate at combating ICI. The LS estimator with 1-D interpolation compensates for the frequency-selectivity fading channel, assuming that the channel is stationary during one symbol interval. Usually, if f T is les than 0.01, the channel can be assumed constant d during one symbol interval. But the equalizer considers the ICI as an additive Gaussian random process, the performance of equalizer degrades significantly due to ICI for larger channel variation, as for f Td ≥0.01.
To fully count the ICI effect, (2.7) should be used to solve , and it is necessary to estimate the channel matrix then calculate its matrix inverse. Nevertheless, accurate estimation of the transfer function requires complete knowledge of the time-variation of the CIR for each OFDM symbol, which is not usually available. When the OFDM symbol duration is smaller than 10% of the channel coherence time, the variation of the channel during a block period can be assumed in a linear model [10]. By utilizing the above
Xt
Ht
assumption, the estimation problem of the channel matrix can be greatly simplified, since the value of the slope of the linear model uniquely determines the ICI. The component of the channel matrix can be expressed as
Ht
It is shown in (3.7) that the main diagonal of the estimated channel matrix depends on the average of the channel frequency response during one block period and the ICI term is only determined by the channel variation and OFDM parameters. Then substitute (3.7) and (3.8) into (2.7),we get
Since only depends on OFDM parameters, it is possible to precalculate it once at initialization. There are several schemes proposed in the following. The procedure for the estimation of the channel matrix is shown in Fig. 4 and described as follows.
Φq
Fig. 4 Block diagram of the estimation of the channel matrix
First, a time domain pilot signal is inserted at the end of every symbol, as shown in Fig. 5.
A similar method can be found in [10].
0 1 0 cp1 Data1 0 1 0 cp2 Data2
LP 1 LP L LP 1 LP L
Fig. 5 Transmitted data format 1
The pilot symbol is composed of 2LP+ samples. The first 1 L samples are used to P avoid ISI, while remaining LP+ samples are inserted for CIR estimation. Then, by 1 comparing the CIR changes between the received signals corresponding to the (i−1)th pilot symbol and th pilot symbol for each path, the CIR variation during the block period is estimated using linear interpolation. Although using pseudo-delta function to do the channel estimation is straightforward, it may have some drawbacks. In order to coincide with the signal power spectrum density, the pseudo-noise can be used as time domain pilot in place of the delta function, as shown in Fig.6.
i
Fig. 6 Transmitted data format 2
Before further discussion, we assume that the length of time domain pilot is M- sample.
Assuming the channel variation during the M samples can be negligible. The time domain convolution can be expressed as a matrix vector multiplication. The linear
convolution matrix is formed from the time domain pilot.The least-square channel estimate, assuming P PH has full rank, is given by
( )
h = P Pˆ H -1P rH (3.10)
and the corresponding MSE is given byσn2tr
{ (P PH )
−1}
. Based on minimizing the channel
estimation MSE, it can be achieved if and only if has equal eigenvalues. This is
achieved when
P PH
P P =H EPI (3.11)
where denotes the linear convolution matrix. It can be observed that the time domain pilot should be a shift-orthogonal sequence. The corresponding minimum MSE is
P
2
n P
Lσ E . Then, the CIR variation for each path during the OFDM symbol can be estimated with linear interpolation, given the LS estimates at the inserted pilot symbols. Finally, the proposed method reconstructs the channel matrix and calculates its matrix inverse. Since the channel matrix can have a large size, it is difficult to process in real time. Based on the structure of the channel matrix , whose energy is concentrated on the neighborhood of the main diagonal, the computation complexity can be reduced by considering only the elements nearby the main diagonal and ignoring remaining elements, as shown in Fig. 7.
Ht
Fig. 7 Banded channel matrix with color region corresponding to ICI concentration
Another way to avoid straight matrix inversion is to divide the task into ICI reduction and a simple one-tap equalizer. In the following, the ICI reduction procedure will be described in detail. According to equation (2.7), it can be found that ICI component is determined by not only the variation of the channel but also the transmitted data. The decision-feedback techniques can be utilized to acquire the estimates of the transmitted data, then the estimated channel matrix in (3.9) is used to subtract the ICI components from the received signal. The resulting ICI reduction method is as follows
[ ] [ ] [ ]
where Dec denotes a slicer in the demapper. Assuming that the number of data carriers is large, the effect of incorrect hard decisions will not have a significant impact. Finally, the ICI-cancelled Y m can be used in a conventional one-tap equalizer. For severe Doppler t
[ ]
effects, it also can be combined with an iterative method to enhance the ICI estimation accuracy, as shown in Fig. 8. In addition, the hard decision in (4.1) can be replaced by a MMSE equalization, given by
only consider the main diagonal of the estimated channel matrix and
solve the linear equation
Fig. 8 Block diagram of the proposed ICI-reduction method
In the same manner, the computation complexity of the ICI reduction can be reduced by considering only the ICI component due to the nearby subcarriers without degrading much system performance, given by
q
Even, it can be ignored the off-diagonal elements of the estimated channel matrix and use one-tap equalizer without ICI reduction. It can be observed in (3.7) that the main diagonal elements are the average of the channel frequency response during one block period. Based the linear property, it can be obtained by
( ) 1 (3.16)
where the subscript denotes the OFDM frame and denotes the main diagonal of the matrix. Then, utilize one-tap equalizer without ICI reduction.
t tth diag()