3 Joint Tx/Rx MMSE Beamforming Design for Multi-user MIMO-OFDM
4.2 Robust Design of Joint Tx/Rx Beamforming
4.2.2 Robust Designs
4.2.2.3 Robust Design Using Moving Average Method
Therefore, using the two-step approach, the optimal receive beamforming that minimizes the averaged MSE matrix can be obtained as the Wiener solution
( )
u kuAnd we can obtain the transmit beamforming which has the similar form
u Combining these two robust methods, we can obtain a better performance than the naive design which designs the null-space matrix and Tx/Rx beamforming by the imperfect channel information
Hˆ
uk. By the way, for single user joint design problemunder channel estimation error, the null-space matrix becomes an identity matrix and we just need to apply the robust Tx/Rx beamforming to improve the performance.
4.2.2.3 Robust Design Using Moving Average Method
We have introduced the approach that combines robust null-space matrix which minimizes the MUI between each user and robust Tx/Rx beamforming which copes with the inter-stream interference of each user terminal. However, the combination of
these two robust methods uses the instantaneous estimated channel information
Hˆ
ukto calculus the robust null-space matrix and Tx/Rx beamforming. In other words, once we receive an OFDM packet and estimate the channel by the long preamble of the packet, we use the instantaneous estimated channel information to apply to our combined robust approach to improve the performance. Thus, we can expect that the similar performance can be obtained under fast- and slow-fading channel caused by the Doppler effect of moving user terminals.
However, under the slow time-variant environment we can apply the moving average approach (the same throughput) to improve the channel estimation error instead of using the instantaneous estimated channel information. Using the moving average approach in such multi-user joint design system, we calculus the null-space matrix and Tx/Rx beamforming by the same approach described in chapter 2 and chapter 3. The only difference is that we replace the instantaneous estimated channel information by the moving average of the estimated channel. These robust approaches to improve the system performance are simulated by computer and shown as next section. We also give some comments to these simulation results.
4.3 Simulation Results and Comments
we consider a multi-user MIMO-OFDM SDMA where the BS equipped with 6 to 7 transmit antennas communicates simultaneously with 3 users. Each user is equipped with 2 receive antennas. The other parameters are set up in the same way as that in section 3-4.
0 5 10 15 20 25 30 10−3
10−2 10−1 100
Total Tx Power / Received Noise Power
BER
Joint Tx−Rx MMSE Beamforming Design for MIMO−OFDM SDMA System Under CSI Error 0.075
M=6;N=2;U=3; Naive design
M=6;N=2;U=3; Robust null−space matrix only
M=6;N=2;U=3; Robust null−space matrix and Robust beamforming M=7;N=2;U=3; Naive design
M=7;N=2;U=3; Robust null−space matrix only
M=7;N=2;U=3; Robust null−space matrix and Robust beamforming
0 5 10 15 20 25 30
10−3 10−2 10−1 100
Total Tx Power / Received Noise Power
BER
Joint Tx−Rx MMSE Beamforming Design for MIMO−OFDM SDMA System Under CSI Error 0.05
M=6;N=2;U=3; Naive design
M=6;N=2;U=3; Robust null−space matrix only
M=6;N=2;U=3; Robust null−space matrix and Robust beamforming M=7;N=2;U=3; Naive design
M=7;N=2;U=3; Robust null−space matrix only
M=7;N=2;U=3; Robust null−space matrix and Robust beamforming
Figure 4-3 Joint Tx/Rx MMSE beamforming design for MIMO-OFDM SDMA system under CSI error 0.075
Figure 4-4 Joint Tx/Rx MMSE beamforming design for MIMO-OFDM SDMA system under CSI error 0.05
0 5 10 15 20 25 30 10−3
10−2 10−1 100
Total Tx Power / Received Noise Power
BER
Joint Tx−Rx MMSE Beamforming Design for MIMO−OFDM SDMA System Under CSI Error 0.025
M=6;N=2;U=3; Naive design
M=6;N=2;U=3; Modified null−space matrix only
M=6;N=2;U=3; Robust null−sapce matrix and Robust beamforming M=7;N=2;U=3; Naive design
M=7;N=2;U=3; Modified null−space matrix only
M=7;N=2;U=3; Robust null−sapce matrix and Robust beamforming
Figure 4-3, Figure 4-4 and Figure 4-5 are the simulation results of joint Tx/Rx beamforming design for multi-user MIMO-ODFM SDMA downlink system when the variances of channel estimation error are 0.075, 0.05 and 0.025 respectively.
Comparing these simulation results, we give the following comments:
z The naive design of course has worst performance due to the imperfect design of null-space matrix and beamforming which induces the MUI and inter-stream interference respectively. However, using the robust null-space matrix to resist the MUI, we can obtain the performance improvement.
z Furthermore, combining the robust null-space matrix with the robust Tx/Rx beamforming to simultaneously resist the MUI and inter-stream interference,
Figure 4-5 Joint Tx/Rx MMSE beamforming design for MIMO-OFDM SDMA system under CSI error 0.025
we certainly obtain a better performance than above two designs.
z When the variance of channel estimation error increases, the performance becomes worse. The improvement of the combined robust approach is observable.
z The effect of improvement of the robust null-space matrix is larger than the robust beamforming design since the MUI will cause the more performance loss than the inter-stream interference.
z
For the under-loaded case, we can see the performance improvement caused by the increase of diversity gain.0 5 10 15 20 25 30
10−3 10−2 10−1 100
Total Tx Power / Received Noise Power
BER
Joint Tx−Rx MMSE Beamforming Design for MIMO−OFDM SDMA System Under CSI Error 0.05
M=6;N=2;U=3; Naive design
M=6;N=2;U=3; Robust null−space matrix only
M=6;N=2;U=3; Robust null−space matrix and Robust beamforming M=7;N=2;U=3; Naive design
M=7;N=2;U=3; Robust null−space matrix only
M=7;N=2;U=3; Robust null−space matrix and Robust beamforming M=6;N=2;U=3; Moving average approach for 10 times
M=7;N=2;U=3; Moving average approach for 10 times
In the sequel, we are going to apply the moving average approach to the
Figure 4-6 Joint Tx/Rx MMSE beamforming design for MIMO-OFDM SDMA system under CSI error 0.05
slow-fading environment. Total 100 MIMO channel realizations are simulated and, we apply the moving average approach 10 times to each channel realization. We can see that the moving average approach is superior to the original robust methods in Figure 4-6. But this approach is only suitable for the slow-fading channel. That means only the slight Doppler Effect caused by slow-moving user terminals exists.
We also consider the single user case (Figure 4.7, 4.8 and 4.9), where the null-space matrix is an identity matrix and only the robust beamforming matrix is used.
0 5 10 15 20 25 30
10−3 10−2 10−1 100
Total Tx Power / Received Noise Power
BER
Joint Tx−Rx MMSE Beamforming Design for Single−user MIMO−OFDM System Under CSI Error 0.1
M=6;N=6;U=1; Naive design M=6;N=6;U=1; Bobust beamforming M=7;N=6;U=1; Naive design M=7;N=6;U=1; Bobust beamforming
Figure 4-7 Joint Tx/Rx MMSE beamforming design for single user MIMO-OFDM system under CSI error 0.1
0 5 10 15 20 25 30 10−3
10−2 10−1 100
Total Tx Power / Received Noise Power
BER
Joint Tx−Rx MMSE Beamforming Design for Single−user MIMO−OFDM System Under CSI Error 0.075
M=6;N=6;U=1; Naive design M=6;N=6;U=1; Bobust beamforming M=7;N=6;U=1; Naive design M=7;N=6;U=1; Bobust beamforming
0 5 10 15 20 25 30
10−3 10−2 10−1 100
Total Tx Power / Received Noise Power
BER
Joint Tx−Rx MMSE Beamforming Design for Single−user MIMO−OFDM System Under CSI Error 0.05
M=6;N=6;U=1; Naive design M=6;N=6;U=1; Bobust beamforming M=7;N=6;U=1; Naive design M=7;N=6;U=1; Bobust beamforming
Figure 4-8 Joint Tx/Rx MMSE beamforming design for single user MIMO-OFDM system under CSI error 0.075
Figure 4-9 Joint Tx/Rx MMSE beamforming design for single user MIMO-OFDM system under CSI error 0.05
0 5 10 15 20 25 30 10−3
10−2 10−1 100
Total Tx Power / Received Noise Power
BER
Joint Tx−Rx MMSE Beamforming Design for Single−user MIMO−OFDM System Under CSI Error 0.05
M=6;N=6;U=1; Naive design M=6;N=6;U=1; Bobust beamforming M=7;N=6;U=1; Naive design M=7;N=6;U=1; Bobust beamforming
M=6;N=6;U=1; Moving average approach for 10 times M=7;N=6;U=1; Moving average approach for 10 times
Figure 4-10 shows that the moving average approach enhances the performance when the channel error variance is 0.05. We can see that the moving average approach is also superior to the original robust methods. However this approach is only suitable for the slow-fading channel.
4.4 Conclusions
In this chapter, we address the problem of joint Tx/Rx beamforming design for multi-user MIMO-OFDM SDMA downlink system with channel estimation errors.
Imperfect CSI will cause significant performance degradation. The performance degradation is caused by the erroneous null-space matrix and Tx/Rx beamforming
Figure 4-10 Joint Tx/Rx MMSE beamforming design for single user MIMO-OFDM system under CSI error 0.05
which will induce the MUI among users and the inter-stream interference of each user respectively. To handle these two kinds of interference, we combine two robust approaches to improve the performance. The combination of these two robust methods utilizes the instantaneous estimated channel information. The similar performance can be obtained under both the fast time-variant and the slow time-variant environments.
Under the slow time-variant environment, we also apply the moving average method to calculus the null-space matrix and transmit and receive beamforming.
Using the average approach, we obtain a better performance than the method using the instantaneous channel estimate under slow time-variant environment. But the performance improvement is not obvious for the fast time-variant environment.
---Chapter 5
Conclusions and Perspective
---
In this thesis, we have considered the MIMO wireless communication systems which adopt multiple antennas at both the transmit and the receive sides. Such MIMO systems are thought as the promising structure to provide a significant capacity.
Furthermore, the OFDM is a popular technique for achieving high data rate, spectral efficiency, and combating multi-path fading effects in wireless communications. Thus, the MIMO-OFDM based systems become a trend for future wireless communications.
All joint design problems discussed in this thesis were based on the MIMO-OFDM system.
5.1 Conclusions
We have clearly introduced the conventional joint Tx/Rx MMSE beamforming design for single user MIMO-OFDM system in chapter 2 and then extend it to multi-user MIMO-OFDM SDMA system in chapter 3. Both of them assume that exact channel information is known at transmitter and receiver. In this thesis, we furthermore consider the practical case in which the channel estimate contains errors may cause significant performance loss.
For a multi-user joint beamforming design system, the performance loss is caused by the multi-user interference induced by the erroneous null-space matrix and the inter-stream interference caused by imperfect CSI. Consequently, we address the problem of designing joint Tx/Rx beamforming for multi-user MIMO-OFDM SDMA downlink system with imperfect channel information at both terminals.
We then combined two robust approaches to suppress these two interferences and obtained performance improvement. The original robust design utilizes the instantaneous estimated channel. It can be applied to fast time-variant and slow time-variant environments and has similar performances. Furthermore, we apply the moving average approach to the slow fading channel environment and obtain performance improvement.
5.2 Perspective
Future wireless applications are requested to provide higher data rate and good link quality wireless access. Owing to the advantages of MIMO and OFDM techniques, some standards such as 802.11n and 802.16e adopt MIMO-OFDM based system to increase capacity, reliability and range etc. Space-time coding and spatial multiplexing are promising techniques for achieving high data rates over MIMO systems. However, the joint Tx/Rx beamforming design scheme can also applied to some applications where the CSI can be available at both transmitter and receiver.
This scheme makes that the number of antennas, size of the coding block, and transmit power can be scalable and the solutions are shown to convert the mutually
cross-coupled MIMO transmission system into a set of parallel eigen subchannels system. Thus, this scheme may also become a popular solution for future wireless communications.
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