In this section, we will provide the simulation results of the blind SIS equalization schemes as introduced in Chapter 4. The channel state information is assumed to be unknown to the receiver (equalizer) and is estimated/tracked using the recursive least-squares (RLS) algorithm in the simulation.
Same as the previous simulation, we assume that the CIR has unity power, i.e.
1 1
0
2 =
∑
=− Ml hl . The number of the particles Ns is 100. The Max-Log SIS weighting parameter is set asγ =0.75. The signals are transmitted equally likely with BPSK modulations. In this section, we consider four types of equalizers in the simulation:
(1). The blind SIS equalizer (Blind SIS EQ): This is the original particle filter based equalization using the Max-Log SIS algorithm as proposed in 2.2.2 with the CIR estimated by a set of RLS adaptive filters for each particle.
(2). The blind SIS decision feedback equalizer (Blind SIS DFE): This is the scheme we proposed in 4.2. The FFF and FBF filter coefficients are updated with the RLS algorithm introduced in 4.1.
(3). The blind delayed-SIS equalizer (Blind D-SIS EQ): This is the delayed-SIS algorithm proposed in [3]. The CIR here is estimated in the same way as the blind SIS EQ in (1) through RLS adaptive filters.
(4). The Max-Weight blind SIS decision feedback equalizer (MW blind SIS DFE):
This is the complexity reduced version of (2), the blind SIS DFE, as
introduced in 4.3. Only one set RLS adaptive filter coefficients is used for 100 (=Ns) particles.
Again we consider two cases of CIR and see the performance of these blind equalizers.
5.2.1 Channel with a strong LOS
First in the case of strong LOS channels, the blind SIS EQ behaves as well as the blind SIS DFE does. This is because when the channel LOS is large, there is no much difference before and after the minimum-phase pre-filtering. These two algorithms result in the similar performance.
As far as the blind D-SIS algorithm is concerned in this case, the best choice of the delay d should be 0 because the channel has the largest impulse at h0. The blind D-SIS with delay d = 0 acts exactly as the blind SIS EQ. In addition, as we have testified in previous section (the perfect CSI scenario), choosing a larger d than the channel delay would not only rise the computation complexity but also cause the performance decay. Compared with the D-SIS EQ with d = 2 in the known CSI case in Fig. 5-1, the blind D-SIS EQ with d = 2 even has worse performance, especially in low SNR. This is because when the SNR is low, the particle filters are likely to draw the particles wrongly. The adaptation of the RLS filter according to the bad particles would be erroneous. The information exchange between the RLS filters and the SIS algorithm becomes a vicious circle, the error propagates through the iteration and hence raised the BER.
0 2 4 6 8 10 12 10−5
10−4 10−3 10−2 10−1 100
SNR (dB)
Bit Error Rate
SNR vs BER of blind equalization under channel with strong LOS
(1) blind SIS EQ (2) blind SIS DFE (3) Delayed−SIS with delay 0 (3) Delayed−SIS with delay 2
Fig. 5-5 BER versus SNR plots of the different blind equalizations under channel with strong LOS.
5.2.2 Channel with a weak LOS
Now we turn to the case when the channel LOS is seriously attenuated to see how the SIS DFE and D-SIS EQ improve the situation in blind equalization.
0 2 4 6 8 10 12 14
10−5 10−4 10−3 10−2 10−1 100
SNR (dB)
Bit Error Rate
SNR vs BER of blind equalization under channel with weak LOS
(1) blind SIS EQ (2) blind SIS DFE (3) Delayed−SIS with delay 0 (3) Delayed−SIS with delay 1 (3) Delayed−SIS with delay 2 (3) Delayed−SIS with delay 5
Fig. 5-6 BER versus SNR plots of the three blind equalizations under channel with weak LOS.
First we observe the curve of the SIS EQ: It is interesting that the curve climbs up with the SNR in the range of SNR = 8~12. This phenomenon has been found earlier in the analysis in Chapter 3, as drawn in Fig. 3-2, when the error propagation factor λk( )i is quite large. As expected, the SIS EQ does not attain a desirable low BER at the high SNR when it is used in the weak-LOS channel environment.
Second, the results of the D-SIS algorithm indicate again whether the performance is good enough or not is greatly dependent on the selection of d. Only when d is selected to be close to the channel delay (in this case, the channel delay is 2.) can the D-SIS EQ have the best performance. Similar to the case of the known channel with a weak LOS in Fig. 5-4, we can see that the D-SIS EQ with delay d = 2 has the best performance compared with that with other values of delay.
We end up with the simulation for the performance comparison of the blind SIS DFE and the Max-Weight blind SIS DFE, which utilizes the maximally-weighted particle to update the only one set of adaptive filter at each iteration (see 4.3). As we expected, this method would have a little worse performance than the blind SIS DFE because of the simplification. However, we have found (in Fig. 5-7) that the performance difference is small. This is a promising result because, we can use the Max-Weight blind SIS DFE, to save a lot of computations without sacrificing much performance. As shown in Fig 5-7, we can find that the Max-Weight blind SIS DFE even outperforms the D-SIS EQ (delay = 2) in the high SNR. Under the situations when the computation resources are relatively limited, the Max-Weight SIS DFE may become one of the appealing options for blind equalization.
0 2 4 6 8 10 12 14 10−5
10−4 10−3 10−2 10−1 100
SNR (dB)
Bit Error Rate
SNR vs BER of blind equalization under channel with weak LOS
(1) blind SIS EQ (2) blind SIS DFE (3) Delayed−SIS with delay 2 (4) Max−Weight blind SIS DFE
Fig. 5-7 BER versus SNR plots of the four different blind equalizations under channel with weak LOS.
5.3 CHAPTER SUMMARY
In this chapter, we have conducted the computer simulation of the particle filter based equalization algorithm described in the previous chapters. From the simulation results, we have testified that the weak LOS problem indeed affects the performance of the SIS EQ, as indicated in the BER analysis of the SIS EQ. We have performed the simulation on the ZF and the MMSE SIS DFE algorithms, showing their performance is not affected by the weak LOS channel, We also made simple comparison between the proposed SIS DFE and the D-SIS EQ.
In the second part, we simulated the blind SIS equalizers introduced in Chapter 4.
Both the blind SIS DFE and the blind D-SIS EQ can improve the system performance under the weak LOS channel. However, the D-SIS EQ requires the knowledge of the channel delay in order to determine the best value of the delay d, and its computation complexity grows exponentially with its delay d. The blind SIS DFE can be further simplified to the Max-Weight blind SIS DFE without the significant loss of performance. The cost-effective Max-Weight blind SIS DFE can be considered a promising algorithm for the practical system implementation.