Simulated and Experimental Decoding BER in a SFH System

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In this section, we conduct simulations for both SFH and FFH scenarios. From our exper- imental data gathered in the previous section and simulation data obtained in this section, we compute the decoding BER as a function of γ. We vary the value of γ from 0 to 10 to observe the corresponding decoding BER for the adversary. Then we compare the simulated and experimental results.

Simulated Decoding BER

The simulation follows the identical setup as the experiment. We use 905MHz as the carrier frequency for the active eavesdropper to broadcast his CW. We allocate 910MHz - 922.5MHz for a total of 50 available hopping channels. Each channel is separated by 250kHz from the two adjacent channels. We have simulated with 3 different hopping channels. They are N = 5, 10 and 50. The tag replies with the same 64-bit Miller modulated subcarrier code from the 8-bit message. Moreover, from the experiment, we have identified that all channels have equal gains and observed that the value of 20 log₁₀(η1−η0)gk

σk is approximately 8.5dB on each channel. Therefore, we set this value also to 8.5dB across all hopping channels including the eavesdropper’s channel in the simulation. Furthermore, we have mentioned earlier that in the experiment, the sampling rate is set at 1MHz, the tag’s data rate is 100kbps. This implies theoretically, each Miller coded bit contains 10

samples. Therefore, in the simulation section, we also set each bit to contain 10 samples. Each bit is decoded by taking the average of 10 consecutive samples and using the threshold decision rule as shown in (8.4). Finally, the BER is calculated over 105 with Miller coded bits and 10₈5 with message bits.

We plot BER vs γ in Figure 8.11. We observe initially BER decreases as γ increases for all cases. This is expected because according to our analysis,

√ ∆E

2σef f always increases for γ < N .

Moreover, from this figure, we have observed that the smaller the number of available hopping channels N , the lower the decoding error probability. This is also expected because at one time instance, only one hopping channel contains the signal, all other channels contain only noise. Therefore, the greater the amount of hopping channels, the lower the combined SNR will be. This in turn would result in a higher decoding BER.

Finally, we see in general, BER of decoded message bits is lower than the Miller coded bits. This is expected because the purpose of coding at the expense of reducing the rate is to improve the decoding BER. The only exception is at the lower γ with 50 hopping channels. In this case, BER of decoded message bits is slightly higher than the Miller coded bits. The reason for this is because the hamming distance between codewords 0 and 1 is 4 for our Miller modulated subcarrier codes. This implies only one error can be corrected according to the classic coding theory [47]. Since the received coded bits have exceeded the error correction capability, we can expect the decoded message bits to have a higher BER.

Experimental Decoding BER

In this section, we compare the simulated and experimental results. We take the experi- mental data where the active eavesdropper’s received signal strength from his own CW is comparable to the reader’s CW. The BER is calculated from 105 _{Miller coded message bits.} The corresponding number of decoded message bits are 10₈5. Moreover, we have taken the simulation results for N = 5 from the previous section. The comparison on the decoding BER as a function of γ for both the simulated and experimental results is shown in Figure 8.12.

In general, the simulated results agree with the experimental results. By comparing both the Miller coded bits and the decoded message bits between the experimental and simulated results, we can observe they almost overlap with each other at lower value of γ. However, there exist some discrepancies as γ increases. The BER for the experimental result decreases slower than the simulated results. The reason is that from the experimen-

0 2 4 6 8 10 10−5 10−4 10−3 10−2 10−1 100 γ BER

Miller coded bits with N=5 Miller coded bits with N=10 Miller coded bits with N=50 Decoded message bits with N=5 Decoded message bits with N=10 Decoded message bits with N=50

Figure 8.11: Simulation Results for Decoding BER in a SFH System with Three Different Hopping Channels

tal observations, we have discovered not all Miller coded bits contain exactly 10 samples. In some cases one coded bit contains 9 samples. In other cases, it contains 11 samples. However, in our decoder, we did not make this adjustment. Each bit is decoded by averag- ing and using threshold decision rule over exactly 10 consecutive samples. The imperfect sampling interval induced BER is a constant and it dominate at higher values of γ. This imperfect sampling intervals can lead to additional decoding errors, which are unaccounted for in the simulated result. Thus, this additional source of errors causes the discrepancy between the simulated and experimental results. This is especially noticeable at higher value of γ.