# Temporal Encoding to Reject Background Signals
## 2 Results
### Robustness to Noise  
A major advantage of this transmission scheme is that it is expected to be robust against background counts, as ambient light is generally uncorrelated on the time scale of 10 s of ns. To verify this, BER measurements were taken for increasing levels of background light using a secondary 450 nm light source, as shown in Figure 2b. As background counts increase, the probability of detecting noise correlations increases. The threshold applied to the correlation histogram must be increased to avoid erroneous detection of bits, requiring higher received average power to maintain the same BER performance.  
The results in Figure 5a show the incident optical power required to maintain a BER of \(1\times 10^{-3}\) for 10 and 50 kb/s with increasing levels of background optical power. The signal power requirements do increase, however, they are still very low. At high background levels, the required signal power is significantly lower than the power received from background illumination, with equal levels indicated by the solid line. Here, the interplay between number of pulse repetitions, photons detected per pulse and background counts becomes important. As discussed in Section 2.3, higher levels of background power increases the number of bit errors, as the overlap of Poisson distributions increases. While the target BER can be recovered by increasing received photons per bit, equivalent to increasing the signal power, it can also be recovered by increasing the number of transmitted pulses, equivalent to reducing the data rate. The result is that given a certain level of background optical power, a signal can always be transmitted at a power level below that of noise, at the expense of data rate.  
Figure 4: (**a**) BER as a function of received signal power for varying data rates. (**b**) Received photons per bit required to achieve a BER of less than \(10^{-3}\) for varying data rates, fitted with a \(x^{-\frac{1}{2}}\) relationship. The standard quantum limit for OOK at this BER is also shown.  
The system was also measured under modulated background illumination. Since the number of detected correlation counts depends on the square of received power, a high modulation rate background should interfere in the same manner as a DC signal at the root-mean-squared (RMS) of its count rate. For this reason, background signals were set to maintain similar RMS photon count rates for comparison to DC measurements. The RMS background optical power was approximately 15 pW for all measurements. The power required to maintain a BER of \(10^{-3}\) is shown in Figure 5b, and displays two distinct groups of results. The high background modulation rates of 1 and 10 MHz show similar required signal power to constant background conditions, while when the background modulation rate is close to the correlation link data rate, the BER performance is degraded, requiring approximately 40% more received power. This reduction in performance occurs as the background signal is now generating different levels of noise correlations from one bit period to the next, making it more difficult to choose a correlation threshold. At higher background modulation rates the background signal completes many cycles within a single bit period of the correlation link, and the dead time of the SPAD restricts the number of photons that can be detected per background cycle, causing the signal to interfere in the same manner as constant background. Nevertheless, all conditions still reach a BER of less than \(10^{-3}\) for less than 14 pW of received signal power.  
Under all background conditions, the signal is transmitted with a lower photon count rate than the background signal, demonstrating low power performance even with high power modulated background interference.