# Access Control and Pilot Allocation for Machine-Type Communications in Crowded Massive MIMO Systems
## 4 Simulation Results  
We implement Monte-Carlo simulations to compare the performance of the proposed method with several benchmark schemes. In the simulations, the radius of cell is 250 m, the MTCDs are uniformly located in the cell with distance of 25 m from BS. In the simulation, the urban micro scenario in [29] is used to model the pathloss of the uncorrelated Rayleigh fading with pathloss exponent 3.8. Consider a crowded scenario with \(\tau_{p}=50\) during \(I_{A}=100\) slots. To illustrate the efficiency of our proposed DACB-SUCR method, we consider comparisons with the following approaches:* SUCRe: This method was proposed in [12]. It can resolve pilot collisions when devices select pilot sequence at random to access the network. Each device with the strongest channel gain will be assigned one pilot.
* RA w/o ACB: This is a traditional random access procedure without controlling the number of arrival devices. In an access attempt, if more than one device selects the same pilot sequence, they will fail to access the network.
* SUCRe with fixed ACB: We use a fixed ACB factor (\(p_{ACB}=0.5\)) to limit the number of arrival devices and apply the SUCRe protocol for pilot allocation.
* RA with fixed ACB: Similar to SUCRe with fixed ACB, an access control using a fixed ACB factor (\(p_{ACB}=0.5\)) is applied.
* SUCRe with traffic-aware ACB: access control is realized based on traffic-aware ACB factor before the SUCRe protocol will make pilot allocation.
* RA with traffic-aware ACB: random access procedure based on controlling the number of new arrivals by traffic-aware ACB scheme.  
Figure 4 shows the variance of the access success rate when the total number of active MTCDs increases. In this simulation, the number of antennas is set as \(M=100\). It shows that the access success rate improvement achieved by the proposed DACB-SUCR is remarkably higher than others. At first, when the number of MTCDs is small, most of MTCDs can access the network successfully with all methods. Clearly, the access success rate drops as the number of total MTCDs increases. However, the access success rate of proposed DACB-SUCR is still higher than others. That is because the number of access devices is controlled efficiently by dynamically adjusting the ACB factor. We find that two schemes, when the total number of MTCDs is 10,000, SUCRe with traffic-aware ACB and proposed DACB-SUCR, can handle up to 45% of the MTCDs. While others just allow less than 25% of the MTCDs to be accessed successfully.  
Figure 5 shows the variance of the access success rate when \(M\) increases. The total number of MTCDs is set as \(N=10\),000. The access success rate is small at \(M=1\), but increases significantly  
Figure 4: Access success rate.  
when the number of BS antennas gets larger. However, the system performance saturates for \(M\geq 15\). Since the number of pilot sequences is finite, the access success rate reaches the saturation even if the number of BS antennas is greater than 30. The increasing number of BS antennas cannot enhance the success access rate indefinitely. Therefore, we need to consider the reasonable number of BS antennas corresponding to the available number of pilot sequences.  
Through Table 1, we can obviously see that the SUCRe with any ACB schemes bring higher performances as compared to the original SUCRe scheme. Among four investigated methods, the proposed DACB-SUCR achieve the highest access success rate. When increasing the number of BS antennas from 5 to 100, SUCRe's performance only increases by around 5%, while the proposed DACB-SUCR's performance increases by more than 10%. Obviously, the proposed DACB-SUCR brings the highest efficiency among these methods.