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We present some simulation results on signal detection performance in this section.

As in Sec.3.2, we let subcarrier spacing fs = 10.94 kHz and sample period Tsa= 714 ns. The subcarriers are QPSK-modulated with Gray-coded bit-to-symbol mapping.

There is no channel coding. The channels are multipath Rayleigh-faded WSSUS channels having the PDPs shown in Table4.1.

Unless otherwise noted, we let N = 128 and assume that the receiver has perfect knowledge of the channel state information (CSI), which includes the channel matrix within band K and the covariance matrix Kz of the residual ICI plus noise.

To start, consider the extreme case of K = 0 in absence of channel noise.

Through this we look at the limit imposed by the ICI to the performance of the conventional detection method. We also look at the possible gain from blockwise whitening of the full ICI followed by MLSE with p = q = 1, at infinite signal-to-noise ratio (SNR). The ICI covariance matrix in this case is given by

Kz = simu-lation results for the TU6 channel. The numerical performance for the SUI4 channel is very similar. These results show that ICI-whitening detection (the proposed tech-nique) yields some advantage over conventional detection: the error probability is reduced by about 2.2 times.

Significantly higher gain can be obtained by ICI-whitening MLSE with K = 1.

In Fig. 4.3 we compare the corresponding performance of the proposed technique with that of MLSE which treats the residual ICI as white [4], over TU6 and SUI4 channels in the noise-free condition (i.e., SNR = ∞). For the proposed technique, two parameter settings are considered, viz. {q = 1, p = 2} and {q = 1, p = 1}, for

which the covariance matrices Kz of residual ICI are given by, respectively,

Consider the case p = q = 1 first. In this case, the proposed method shows a remarkable gain of roughly three to four orders of magnitude in error performance compared to treating residual ICI as white. The error floor induced by the residual ICI can be driven to below 10−5 even at the very high normalized peak Doppler frequency of 0.32.

Very interestingly, Fig. 4.3 also shows that the setting {q = 1, p = 2} yields a worse performance than p = q = 1, even though the former setting may seem more natural in its associated band channel matrix structure (compare (4.2) with (4.3)), which captures all the ICI terms within the modeling range (K = 1). Moreover, its corresponding trellis has more states than the latter setting (45 vs. 43). The reason will be explored in the next section. For now, we note that the above results appear to indicate the suitability of setting p = q = K = 1 in practical system design.

It yields good performance without undue complexity. With this observation, we now present some more simulation results under this setting. The aims are to examine the proposed technique’s performance at finite SNR and to compare it with a benchmarking upper bound. For this, we first consider how it varies with Doppler spread and then how it varies with SNR.

Fig. 4.4 shows some results for the TU6 channel with p = q = K = 1 at several SNR values. The results for SUI4 show similar characteristics and are omitted. We compare the performance of the proposed method with a benchmark: the matched-filter bound (MFB), i.e., signal detection with perfect knowledge of the interfering symbols. To make the MFB a more-or-less absolute lower bound, it is obtained with the residual ICI outside band K fully cancelled. Other than these, the same MLSE as in the proposed technique is used. For all three finite SNR values shown, note that the MFB drops monotonically with increasing fd, i.e., with increasing time-variation

of the channel. This is in line with the fact that faster channel variation yields greater time diversity, as various researchers have observed [15,17,18]. However, such time diversity can show clearly only when ICI is sufficiently small (e.g., after ICI cancellation). For the proposed technique, its error performance at Eb/N0 = 15 and 28 dB tracks that of the MFB reasonably closely, deviating by less than a multiplicative factor of three for normalized peak Doppler frequencies up to 0.18 (fd ≤ 2000 Hz). At Eb/N0 = 45 dB, the performance improves with fd until fd

reaches about 1500 Hz (normalized peak Doppler frequency ≈ 0.14). Afterwards, the residual ICI dominates in determining the performance, as can be seen by the closeness between the corresponding curves for Eb/N0 = 45 dB and ∞.

Next, consider how the performance of the proposed method varies with SNR.

The solid lines in Fig. 4.5 show results at fd = 1500 Hz (normalized peak Doppler frequency ≈ 0.14) under perfect CSI. It is seen that the proposed method at K = 1 can yield a substantial performance gain compared to nonwhitening MLSE [4] at K = 2. The dash-dot lines in Fig. 4.5 depict some results under imperfect CSI.

Limited by space, we cannot elaborate on the many possible channel estimation methods and their performance. Hence the results shown pertain to a typical con-dition only. For this, we note that the mean-square channel estimation error is typically proportional to the variance of the unestimatable channel disturbance, with the proportionality constant inversely dependent on the sophistication of the channel estimation method [19]. In our case, the unestimatable channel distur-bance includes residual ICI (mostly that beyond K = 1) and additive channel noise (AWGN). At a normalized peak Doppler frequency of 0.14 (fd = 1500 Hz), the first term is approximately 20 dB below the received signal power. The proportionality constant is set to 1/8. The channel estimation error limits the performance of all detection methods and the residual ICI-free bound in the form of error floors. The floor of the proposed method at K = 1 is seen to be lower than that of nonwhitening MLSE at K = 2 and is relatively close to the bound. We further note that, while Fig.4.5has been obtained with N = 128, the results obtained with N = 1024 (eight times the bandwidth) are very close.

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Figure 4.2: Error performance in TU6 channel of the conventional OFDM signal detection method and ICI-whitening MLSE (the proposed method) with K = 0 and p = q = 1 in noise-free condition.

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Figure 4.3: Comparison of proposed technique in TU6 and SUI4 channels with that treating residual ICI as white; SNR = ∞.

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Figure 4.5: Performance versus Eb/N0 of different methods in the TU6 channel, with N = 128, Tsa = 714 ns, fd = 1500 Hz (normalized peak Doppler frequency fdTsaN = 0.1371) and QPSK subcarrier modulation. (Results with N = 1024 are very close.)

4.4 Dependence of Detection Performance on