# Hybrid Beamforming for Reduction of Inter-Beam Interference in Millimeter-Wave Cellular Systems
## 3 Simulation
If the number of _RF_ chains is smaller than 12, performance may degrade due to the remaining IBI. Figure 5 shows the achievable rate of Type-3 precoder when the number of _RF_ chains varies. In simulation, the number of _RF_ chains is changed from 4 to 12. As can be seen in the figure, the achievable rate decreases as the number of _RF_ chains decreases. When the number of _RF_ chains is 4, the performance of Type-3 precoder is similar to that of \"Analog-only Beamforming\" because Type-3 precoder cannot remove the IBI due to the insufficient number of _RF_ chains. Figure 4: BER comparison of proposed hybrid beamforming techniques. Figure 5: Achievable rates of Type-3 precoder when the number of radio frequency (_RF_) chains varies. Figure 6 shows the performance comparison when we used the CBRS technique and the time-division beam switching (TDBS) technique for channel estimation in the environment of Figure 2. In the CBRS technique, multiple beams with the same CID but different BIDs are transmitted simultaneously from neighboring _BSs_. In the TDBS technique, single Tx beams are individually transmitted from the _BS_ until all of the Tx beams are transmitted. This process is repeated for neighboring _BSs_. The processing time required for beam transmission in TDBS increases proportionally to the product of the number of Tx beams and the number of neighboring _BSs_. As can be seen in Figure 6, the performances of two different channel estimation techniques are similar. It can be seen that the CBRS technique allows us to estimate the effective network channel with a minimal IBI in a multicell environment. In Table 1, we compare the processing times required for channel estimation in the CBRS and TDBS techniques. Here, it is assumed that the subcarrier spacing \(\Delta f=75\) kHz and the symbol time \(T_{5}~{}=~{}\frac{1}{75\,\mathrm{kHz}}\simeq 13.33~{}\upmu\)s [13]. In the CBRS technique, the processing time required for channel estimation is one orthogonal frequency-division multiplexing (OFDM) symbol period because the CBRSs are transmitted simultaneously from neighboring _BSs_ with multiple beams. Here, we ignore the time required to calculate the value of the channel estimate. The processing time required for beam transmission in the TDBS technique increases as the number of Tx beams and the number of neighboring _BSs_ increase. When the TDBS technique is used for channel estimation and Type-1/Type-2/Type-4 precoders are used for interference reduction, the processing time required for channel estimation is increased by \(B\times U\) because each _BS_ needs to send one beam at a time to _U MSs_ in the serving cell. In the Type-3 case, the processing time is increased by \(\left(B\right)^{2}\times U\) because each _BS_ needs to send beams in the direction of not only _MSs_ in the serving cell but also _MSs_ in neighboring cells. For example, when \(B=3\) and \(U=5\), the TDBS technique with the Type-1 and Type-3 precoders requires processing times that are 15 and 45 times longer, respectively, than with the CBRS technique. Figure 6: Performance comparison of channel estimation between cell and beam reference signal (CBRS) and time-division beam switching (TDBS) techniques. Table 2 compares the sizes of the matrix and computational complexities required for proposed precoders. Since the digital precoders are designed using the estimated effective network channel matrices, the computational complexity of the proposed precoder is proportional to the size of the effective network channel matrices. As shown in Table 2, Type-2 and Type-3 precoders require the highest computational complexity. The followings are Type-1 and Type-4 precoders. The computational complexity is important in sensor networks because processing resources are constrained in most sensor nodes. The proposed precoders except Type-4 precoder do not require processing resources at the sensor node. All the computations required for the design of precoder are performed at the \(BS\). The \(MS\) needs only to feedback the channel information to the \(BS\).