# A Receiving Antenna Allocation Scheme for Downlink MU-MIMO-OFDM Transmission
## 4 Performance Evaluation
### Analysis of Receiving Antenna Decision Method  
Figure 8 plots the overhead time versus the number of STAs. In the conventional downlink MU-MIMO-OFDM transmission assumed in this paper, each STA needs to acquire information of the allocated antennas before actual data transmission. Therefore, this paper assumes the inclusion of allocated antenna information per subcarrier in L-SIG or VHT-SIG-A. Therefore, the overhead time of the conventional method is calculated by using binary phase shift keying (BPSK) and coding rate of \(\
icefrac{{1}}{{2}}\), as specified in IEEE 802.11. From this figure, the conventional method incurs more overhead as the number of STAs increases. For a massive antenna system with a great many spatial streams, the transmission efficiency is greatly degraded by the overhead increase. On the other hand, the proposed method performs to decide the receiving antenna comparing the received powers of the fixed preambles multiplied the proposed pre-coding, as shown in Section 3.2. Although the pre-coding value may change in accordance with the STA combination, the length of preambles with the proposed  
Figure 6: Total channel capacity and reduction rate vs. threshold value.  
Figure 7: CDF of the total channel capacities of the downlink MU-MIMO-OFDM transmission with the proposal and random/optimum antenna allocations.  
pre-coding does not change. In next generation wireless systems [3; 4], discussions of increasing the number of streams beyond eight have been started. For example, when the number of streams is 16 and data length is 500 \(\upmu\)s, we confirmed that the transmission efficiency of the system performance improves by about 24%. Assuming more stream numbers, further improvement can be expected.  
Finally, we present the effectiveness of the proposed method. Figure 9 shows the CDF of the total channel capacity of the downlink MU-MIMO-OFDM transmission with a receiving antenna allocation by using the proposed method. Plots for five antenna decision variants are shown. The first uses the optimum antenna allocation without antenna decision error. The other four variants are the combinations of with/without the proposed pre-coding weight, which presents the receiving antenna decision method in Section 3.2, and the receiving antenna allocation with/without considering the antenna decision error in the limited CSI feedback sequence. It is clear that without the pre-coding, the proposed method has a greatly reduced performance because of the many antenna decision errors created by frequency selective fading. With the pre-coding, the channel capacity of the proposed method almost triples as the CDF value of 10%. However, since the pre-coding cannot perfectly mitigate the received power, antenna decision error still occurs in response to the propagation environment. Moreover, the offsets from the optimal channel capacity are less than 20% at a CDF value of 50% because the decision error is improved. In detail, the proposal roughly quadruples the channel capacity at the CDF value of 10%.  
Figure 8: Overhead time vs. number of STAs.  
Figure 9: CDF of total channel capacities of the downlink MU-MIMO-OFDM transmission with/without the proposed pre-coding.