Since CE, CT and EQ methods all will influence the system performance under multipath channel, we discuss the performance of both the proposed DDCT and frequency domain-MMSE (FD-MMSE) EQ here. First the mean square error (MSE) of existing LMMSE [49], ML [51], DDCT [52] and proposed DDCT is discussed.
From MSE of CE we can know the CE accuracy and tracking effect of time-variant channel. The simulation condition of CE MSE is 6Mb/s and each packet including typical 1000 data bytes, that means the BPSK mapping is applied and each packet has about 330 data OFDM symbols. And the multipath channel is the IEEE Rayleigh fading channel with 50ns RMS delay spread [19]. The window of moving-average of proposed DDCT is set as 32, which can satisfy both the average effect and tracking accuracy. The MSE of CE under time-invariant channel (Doppler frequency = 0Hz) and time-variant channel with Doppler frequency = 50Hz are respectively shown in Figure 3-29 and Figure 3-30.
In Figure 3-29 we can find the LMMSE and ML CE scheme can reduce about 6 and 10dB MSE when compared with the basic zero-forcing (ZF) CE. We can find that the DDCT designs which use each data OFDM symbol for CT can achieve more accurate CE than LMMSE and ML design which only use preamble for CE. And both the existing DDCT design and the proposed design can reduce 8~13dB MSE when
compared with ZF CE.
Simulation Condition: BPSK, 330 OFDM Symbols per Packet RMS Delay = 50ns, Doppler Frequency = 0Hz
Figure 3-29: Mean Square Error of CE and CT schemes with 0Hz Doppler frequency
They also reduce about 6.5dB MSE of the LMMSE design in the high SNR region. In the low SNR i.e. SNR = 0dB the DDCT has higher MSE because of the larger noise injures the DDCT accuracy. The MSE of CE in the time-variant channel with 50Hz Doppler frequency is drawn in Figure 3-30. The simulation result presents the importance of channel tracking in time-variant channel. Since ZF, ML, LMMSE CE schemes only estimate channel in the initial preamble, the variation caused by Doppler effect can not be acquired. Compared with the initial CE approaches the DDCT [52] and the proposed DDCT can achieve reduce about 5~15dB MSE when SNR is higher than 5dB. We can find the CE performance of proposed DDCT and the referenced DDCT [52] are approximated to each other. But when CFO and SCO are considered in simulation, the CE accuracy of referenced DDCT will be seriously degraded. That consideration will be discussed in later PER simulations.
Simulation Condition: BPSK, 330 OFDM Symbols per Packet Multipath RMS Delay = 50ns, Doppler Frequency = 50Hz
Figure 3-30: Mean Square Error of CE and CT schemes with 50Hz Doppler frequency
After discussing the CE accuracy, we present the system PER simulation of the proposed DDCT and FD-MMSE EQ. To understand the performance degraded by serious channel variation, the PER of different CE and EQ approaches is simulated in 6Mb/s data rate, of that the packet length is longest, almost as 9x of packet length of 54MB/s. First the 6Mb/s PER in IEEE multipath channel with 50ns RMS delay spread and 0Hz Doppler frequency is shown in Figure 3-31. In this simulation we can find the performance of different CE and EQ approaches in the time-invariant channel.
In Figure 3-31 we can find the improvement of the FD-MMSE EQ design. First, the employed FD-MMSE EQ can have lower 1.2dB SNR than the basic FD-MMSE EQ for typical 10% PER. With the same ZF CE scheme the FD-MMSE EQ can achieve lower 1.7dB SNR than the LS EQ design. When the proposed DDCT is also used, the SNR can be furthermore reduced by 0.7dB. And hence the FD-MMSE EQ can achieve the same SNR as the perfect LS EQ in 10% PER.
Simulation Condition: Data Rate = 6Mb/s, PSDU = 1000, Multipath Channel RMS Delay = 50ns, CFO = 40ppm, SCO = 40ppm, Doppler Frequency = 0Hz
Figure 3-31: PER of 6Mb/s in IEEE multipath channel with 0Hz Doppler frequency
Otherwise we can also find the FD-MMSE EQ can achieve lower SNR for 10%
PER than the accurate LMMSE/ML CE scheme. Although the SNR loss of improved MMSE EQ is higher than that of conventional time-domain (TD) MMSE EQ, the complex multiplications of FD-MMSE EQ is only 1.17% of that of conventional TD-MMSE EQ as listed in Table 3-1. So the FD-MMSE EQ can achieve a nice trade-off between system performance and hardware complexity.
The 6Mb/s PER in IEEE multipath channel with 50ns RMS delay spread and 50Hz Doppler frequency is shown in Figure 3-32. First we can find if the referenced DDCT [52] is directed used, the PER will be kept as 1. That is because the referenced DDCT directly uses FFT outputs for tracking without the consideration of CFO and SCO problems. We can find the proposed DDCT can save ~1.9dB SNR loss caused by channel variations when compared with the ZF CE without tracking. If the FD-MMSE EQ is used with the proposed DDCT, the proposed design can reduce
Simulation Condition: Data Rate = 6Mb/s, PSDU = 1000, Multipath Channel RMS Delay = 50ns, CFO = 40ppm, SCO = 40ppm, Doppler Frequency = 50Hz
Figure 3-32: PER of 6Mb/s in IEEE multipath channel with 50Hz Doppler frequency
The 54Mb/s PER in IEEE multipath channel with 50ns RMS delay spread and 50Hz Doppler frequency is shown in Figure 3-33. The proposed DDCT can achieve better 0.9dB SNR than ZF CE without tracking scheme.
Simulation Condition: Data Rate = 54Mb/s, PSDU = 1000, Multipath Channel RMS Delay = 50ns, CFO = 40ppm, SCO = 40ppm, Doppler Frequency = 50Hz
Figure 3-33: PER of 54Mb/s in IEEE multipath channel with 50Hz Doppler frequency