## 3 Efficient OFDM BER Floor with Joint Near-Optimal Time Sampling and CFO
### Simulation Setup  
We used the industry-standard, system-level software simulator SystemVue from Keysight Technologies, tailored for LTE (i.e., 5G NR numerology 0) physical layer tests [19]. Specifically, we configured it for measuring BER on the OFDM-based LTE Frequency-Division Duplex (FDD) downlink, with channel bandwidth of 5 MHz, packet switching, and 16 QAM exemplar modulation type [19]. We conducted the embedded framed BER tests on a specific Single-Input Single-Output (SISO) LTE downlink channel (PDSCH 1 (UE 1)), whereas the reference channels complied to TS 36.101, and the faded one to the definition in Annex B of TS 36.101 (Figure 3). However, some embedded assumptions of the professional tool operation were not a good match for the analytical model verification. In this regard, we needed to disable the embedded CP data protection [19] (which we could only do by manipulating input data so as to mimic operation beyond the normal CP length of 4.69 \(\upmu\)s), as well as disable the hybrid automatic repeat request (HARQ) protocol error control at physical (PHY) and Medium-Access Control (MAC) layers. As the simulator setup provides sampling just at the very beginning of the delay profile with no other option, the only available means to simulate impact of various sample delay positions on BER was \"nesting\" progressive additional delays in the profile, while tracking BER reduction to the minimum. We used two test power delay profiles, namely the extended pedestrian A (EPA) standard power delay profile model (Table 1, Figure 4) and the delay-limited exponential model (Figure 5), where for the latter, the a priori chosen probability \(p=99\%\) determines the maximal delay to be 4.6 times the rms delay spread, thus leaving just \(1\%\) of the corresponding delay-unlimited exponential profile to remain beyond the span of the limited one [19]. Figure 3: Long-Term Evolution (LTE) FDD downlink BER simulator setup. Figure 4: Extended pedestrian A (EPA) power delay profile. Figure 5: Exponential profile; rms delay spread \(\sigma_{\tau}=2T_{S}\); \(T_{\rm S}=76\) ns. After verifying Equation (12), we see in Figures 5 and 6 that the curves around the minima are rather smooth and flat, so that we expect the optimal sample point to be quite close to the mean delay. Indeed, sampling at the mean delay (Equation (13)), exhibits negligible worsening of BER with regard to the optimal sampling; just about 0.2% on average, for all three modulation types and both profiles, as evident in Figure 8, where the BER floor is graphed as a function of rms delay spread, adopting Equations (12) and (13). This finally verifies the use of the mean delay as the near-optimal sampling instant. Figure 6: Estimated and simulated BER vs. (optimal) sample time for the EPA LTE FDD downlink. Figure 7: Estimated and simulated BER vs. (optimal) sample time for the exponential LTE FDD downlink. Thereby, the BER values coming out of both the ISI of the EPA channel and the five selected exemplar CFO values, are presented, for 16 QAM modulation type, in Table 7.  
On the first look, the above BER values of the order of 1% seem quite high. However, these pertain to the case when the CP of 4.69 us was not applied, otherwise the entire EPA power delay profile would be contained within the CP span, implying that BER = 0, whereas, for the exponential profile, BER would have taken very small values, closer to zero with \"steeper\" power delay profile. This paves the way to isolation of the impact of CFO alone on BER, once considering the CP applied. Considering CFO as a random variable, which is statistically independent of other BER degrading impairments including ISI (due the EPA delay spread) in this case, we can justifiably consider their related error occurrences as mutually independent, too, and so additive.