In this Chapter, we will report our simulation results in two parts. One is the performance of SISO system based on IEEE 802.15.3c transmitter specification and the receiver we designed. And the second part is the simulation result for the SDMA system.
Part 1 IEEE 802.15.3c SISO system performance comparison
The HSI PHY modulation and coding scheme is listed in Table 6-1. For the FEC rates of 1/2, 5/8, 3/4 and 7/8, LDPC(672,336), LDPC(672,504), LDPC(672,420) and LDPC(672,588) codes are used respectively.
Table 6-1 HSI PHY MCS dependent parameters
We consider a SISO system with these modulation and coding schemes as shown in Table 6-1. Two channel models are considered. The first one is the AWGN channel and the other is multi-path Rayleigh fading channel.
The number of iterations for the LDPC code is critical. The higher the numbers, the better performance we will have. However, the computational complexity will
grow along with the number of the iterations. We then compare the performance for LPDC codes with different numbers of iterations in each modulation and coding schemes. Figure 6-1 to Figure 6-7 show the simulation results for the AWGN channel, and Figure 6-8 to Figure 6-14 show the simulation results for the multi-path Rayleigh fading channel. Here, we let the inner receiver be ideal. In other words, there are not synchronization or channel estimation errors. From the figures, we can find that the performance of the LDPC code have a convergent tendency. There is a tradeoff that can be considered between the system complexity and performance.
Figure 6-1 BER comparison of LDPC iteration for coding rate 1/2 in QPSK AWGN channel
Figure 6-2 BER comparison of LDPC iteration for coding rate 3/4 in QPSK AWGN channel
Figure 6-3 BER comparison of LDPC iteration for coding rate 7/8 in QPSK AWGN channel
Figure 6-4 BER comparison of LDPC iteration for coding rate 1/2 in 16QAM AWGN channel
Figure 6-5 BER comparison of LDPC iteration for coding rate 3/4
Figure 6-6 BER comparison of LDPC iteration for coding rate 7/8 in 16QAM AWGN channel
Figure 6-7 BER comparison of LDPC iteration for coding rate 5/8 in 64QAM AWGN channel
Figure 6-8 BER comparison of LDPC iteration for coding rate 1/2 in QPSK multipath Rayleigh fading channel
Figure 6-9 BER comparison of LDPC iteration for coding rate 3/4
Figure 6-10 BER comparison of LDPC iteration for coding rate 7/8 in QPSK multipath Rayleigh fading channel
Figure 6-11 BER comparison of LDPC iteration for coding rate 1/2 in 16QAM multipath Rayleigh fading channel
Figure 6-12 BER comparison of LDPC iteration for coding rate 3/4 in 16QAM multipath Rayleigh fading channel
Figure 6-13 BER comparison of LDPC iteration for coding rate 7/8
Figure 6-14 BER comparison of LDPC iteration for coding rate 5/8 in 64QAM multipath Rayleigh fading channel
Next, we compare the simulation results between the ideal and real-world conditions. In the ideal condition, there are not synchronization or channel estimation errors and the operation of the inner receiver is bypassed (same as that in Figs 6-8 to 6-14). In the real-world condition, the inner receiver is activated to conduct timing acquisition, synchronization, and channel estimation. Also, we set the number of iteration in the LDPC decoder as 5.
Figure 6-15 Comparison of ideal and real-world condition for coding rate 1/2 in QPSK multipath Rayleigh fading channel
Figure 6-16 Comparison of ideal and real-world condition for coding rate 3/4
Figure 6-17 Comparison of ideal and real-world condition for coding rate 7/8 in QPSK multipath Rayleigh fading channel
Figure 6-18 Comparison of ideal and real-world condition for coding rate 1/2 in 16QAM multipath Rayleigh fading channel
Figure 6-19 Comparison of ideal and real-world condition for coding rate 3/4 in 16QAM multipath Rayleigh fading channel
Figure 6-20 Comparison of ideal and real-world condition for coding rate 7/8
Figure 6-21 Comparison of ideal and real-world condition for coding rate 5/8 in 64QAM multipath Rayleigh fading channel
Part 2 SDMA system in IEEE 802.15.3c
First, we show, by examples, that the digital beamforming algorithm can completely null the interference from the other user. By using the algorithm we mentioned in Chapter 4, we can have the beam pattern as
I. Configuration 1
User 1 φ = π/4 , θ =π/4
User 2 φ = -π/4 , θ =π/4 (suppose user 2 is interference)
Figure 6-22 Analog beam pattern I Figure6-23 Digital beam pattern I
Figure6-24 Hybrid beam pattern I In Configuration 1, we have only two weights per user.
II. Configuration 2
User 1 φ = π/4 , θ =π/4
User 2 φ = -π/4 , θ =π/4 , suppose user 2 is interference
Figure 6-25 Analog beam pattern II Figure 6-26 Digital beam pattern II
Figure 6-27 Hybrid beam pattern II
In Configuration 2, we have four weights per user. As we can see from the above example, the interference from the other direction is nulled completely.
According to Chapter 4-3, we can then model this SDMA system as a MIMO system. Assume that the channel is an AWGN channel, and two transmitter antennas and two receiver antennas are used (two users). The power gains corresponding to different pointing angles using analog beamforming are listed below:
User1 User2 Main power gain Interference power gain angle
45° 44° 0.4817 0.4793 1°
45° 43° 0.4817 0.4721 2°
45° 42° 0.4817 0.4602 3°
45° 40° 0.4817 0.423 5°
45° 37° 0.4817 0.34 8°
45° 35° 0.4817 0.2740 10°
45° 30° 0.4817 0.1148 15°
45° -15° 0.4817 0.0035 60°
45° -45° 0.4817 0 90°
45° -135° 0.4817 0 180°
Table 6-2 Power gain with different angles using analog beamforming Figure 6-21 to Figure 6-25 shows the performance of the SDMA system with analog beamforming (IEEE 802.15.3c). Here, the QPSK modulation scheme is used at the transmitter and the MIMO detector is used at the receiver, including the ML, VBLAST MMSE, VBLAST ZF, MMSE and ZF detectors.
Figure 6-28 Performance of SDMA system with analog beamforming using ML
Figure 6-29 Performance of SDMA system with analog beamforming using VBLAST MMSE detector (IEEE 802.15.3c)
Figure 6-30 Performance of SDMA system with analog beamforming using VBLAST ZF detector (IEEE 802.15.3c)
Figure 6-31 Performance of SDMA system with analog beamforming using MMSE detector (IEEE 802.15.3c)
Figure 6-32 Performance of SDMA system with analog beamforming using ZF
We can find that the system can have good performance in each detector when the angle separation of the two users is larger than 15 degree.
Figure 6-26 to Figure 6-30 re-compile the results in Figure 6-21 to 6-25 and show the performance comparison for the case 90°, 60°, 15°, 10°, and 5°. We can find that if the angle is larger then 15°, the performance is almost the same between these detectors. It is because the interference is small and there is no performance gain with advanced algorithms. On the other hand, if the angle is smaller than 15°, we can find that the ML detector is better than other detectors.
Figure 6-33 Performance of analog beamforming comparison with angle 90°
Figure 6-34 Performance of analog beamforming comparison with angle 60°
Figure 6-36 Performance of analog beamforming comparison with angle 10°
Figure 6-37 Performance of analog beamforming comparison with angle 5°
The power gains corresponding to different pointing angles using digital beamforming are listed below:
User1 User2 Main power gain Interference power gain angle
45° 44° 0.0003541 0 1°
Table 6-3 Power gain with different angles using hybrid beamforming
Figure 6-31 shows the performance with hybrid beamforming in using ML detector. Note that in hybrid beamforming, although the interference can be perfectly nulled, the power in the desired beam is reduced significantly. If we assume that the main power and interference power are the same before beamforming, we can find the BER performance in Figure 6-26 is worse than that of analog beamforming in Figure 6-21. The result can be explained by the fact that the cost function to minimize in (4-11) is the interference power. However, the signal-to-interference-plus-noise-ratio (SINR), not the interference power, is the factor determining the final performance.
As a result, while the interference power may be reduced to the minimum, the SINR may also be reduced. In other words, if we can use the SINR as the criterion when designing the hybrid beamformer, the performance can be enhanced. We can expect that the performance of hybrid beamforming should be better than analog beamforming.
Figure 6-38 Performance of SDMA system with hybrid beamforming using ML detector (IEEE 802.15.3c)