## 4 Simulation and Analysis
### Real Data Tests  
Real data tests are conducted to prove that the novel carrier loop algorithm has significantly good performance in an actual environment. We start our actual tests in a comprehensive test platform, which is shown in Figures 12 and 13. The test platform consists of a modified base station and the TC-OFDM receiver. Figure 12 describes each component of the modified base station in detail. The time distributor, the counter and the industrial personal computer collaborative work together in order to ensure synchronization between the modified base stations. Each modified base station equipped with an atomic clock with an output frequency of 10 MHz. The synchronization accuracy between the modified base stations is up to 5 ns (1\(\sigma\)). Meanwhile, the time distributor generates the positioning data messages containing UTC, air pressure, base station number and base station coordinates which are necessary for positioning. The function of the actuator is to modulate the TC-OFDM signal into RF signal and finally the RF signal is transmitted by the transmitter. We use the TC-OFDM receiver developed by us which is shown in Figure 13 to test the positioning accuracy. An overview of the internal and external structures of the TC-OFDM receiver is shown in Figure 13a. Figure 13b shows that the TC-OFDM receiver and mobile phone communicate through the Bluetooth protocol to transmit useful data messages. Then the phone exhibits the final positioning result via the map. An architecture based on FPGA and ARM is adopted in the TC-OFDM receiver for baseband processing and data demodulation. The FPGA is used to perform the main logic operations and ARM is responsible for controlling the circuit logic. The IF signal is processed into a zero-digital IF signal for subsequent FPGA processing. The LM iterative and KF algorithm used in the proposed carrier loop are implemented in the ARM processor. The main computational load is in LM. In each LM iteration, sine, cosine operations and matrix calculations are needed. The above calculations are easily calculated in ARM which can meet real tracking requirements for carrier loop. Figure 11: Comparison of the tracking probabilities between the three algorithms. In addition, we implement the proposed algorithm in our own developed TC-OFDM receiver. The EKF algorithm and two-order FLL assisted three-order PLL algorithm are also implemented to make a comparison. The performance when the three algorithms track weak TC-OFDM signals can be evaluated in practical applications as shown in Figure 14. The modified base station is utilized to generate TC-OFDM signals. Then the TC-OFDM signal is sent to a signal attenuator. The signal attenuator is used to set different signal power. Then the receiver receives TC-OFDM signal of different signal power for subsequent baseband processing. Finally, the useful data is transmitted to the mobile phone for positioning. We use signal attenuator to gradually reduce the signal power to test the ability of tracking weak signal performance of three algorithms. The test results are shown in Table 3, where it can be seen that the proposed algorithm has better tracking sensitivity for weak TC-OFDM signals by 2-4 dB. In the real TC-OFDM system, the weak signal power is generally between \(-125\) dBm to \(-130\) dBm. But, under the special cases, the signal power is low to \(-136\) dBm. Therefore, the sensitivity improvement of the proposed algorithm is modest, and it can satisfy the use of existing TC-OFDM systems. Meanwhile, the proposed carrier loop tracking algorithm in this paper is implemented in the receiver's ARM structure. The ARM development resources of existing TC-OFDM receivers can meet the complexity and computational burden of the proposed algorithm. Furthermore, from Table 3, the proposed algorithm can effectively track the TC-OFDM signal when the signal power is \(-136\) dBm. The signal power using the algorithm of FLL-assisted PLL and pure EKF is \(-132\) dBm and \(-134\) dBm,  
Figure 12: Each component of the modified base stations.