9 Continuous Carrier Operation
9.4 Physical Layer
9.4.5 Spectrum Spreading
9.4.5.1 Return link continuous carrier code synchronization
Frame/code acquisition in the continuous mode return link is the first operation to be performed, i.e. before carrier and timing estimation. In fact, in the presence of direct sequence spread spectrum it is difficult to perform parameter estimation with sufficient accuracy before code acquisition. In the following, results on the code synchronization performances are shown taking into account the following assumptions:
• Symbol Rate (information symbol rate after coding & modulation) = 1 Msps.
• Spreading factor (SF) = 1, 2, 3, 4, 8.
• Chip rate = Symbol Rate * SF.
• Modulation: QPSK.
• Framing:
- Short FEC frame (16 200 coded symbols).
- Data payload length: 16 200/2 = 8 100 QPSK symbols.
- Unique Word length: 26 symbols, DVB pattern.
- Pilot: 11 fields of 36 symbols each.
- Frame Length = SF × (8100 + 11 × 36 + 26 + 64) = SF × 8 586 [chips].
• Operating points:
- Es/N0 = 0,7 dB, r = 1/2; Es/N0 = -1 dB, r = 1/3.
- Ec/N0 = Es/N0 - 10 log10(SF).
• Propagation conditions:
- LOS AWGN.
- Frequency uncertainty = 3,0 kHz (oscillator mismatch + Doppler).
• Timing recovery:
- No timing recovery prior to frame synchronization.
- Two hypotheses per chip are considered, worst case fractional timing delay of 0,25 Tc.
- Timing frequency error = 100 ppm.
• Phase recovery:
- Phase noise: the same as for the FL scenario.
9.4.5.1.1 Phase noise sensitivity assessment
In figure 37, it can be seen that the spectrum spreading technique is insensitive to phase noise, which is therefore neglected in the analysis hereafter.
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Pfa Pmd
SF = 1, EsN0 = 0.7, Delta = 0.25 - phase noise
SF = 2, EsN0 = 0.7, Delta = 0.25 - phase noise
SF = 1, EsN0 = 0.7, Delta = 0.25
SF = 2, EsN0 = 0.7, EcN0 = -2.3, Delta = 0.25
Figure 37: Performance evaluation in the presence of phase noise
9.4.5.1.2 ROC performance in AWGN
In figure 38, analytical and simulated ROCs are presented in AWGN with Es/N0 = 0,7 dB and chip time misalignment δ = 0,25, in the exemplary scenarios with SF = 1, 2, 8. Notably, the analytical curves well validate the simulation results. This conclusion is further extendable to all possible SF values, allowing in the following to consider only simulation results. By comparing the different SF, it clearly emerges that the introduction of DS spreading improves ROC performance because the interference introduced by the unknown information data (self-noise) during the Start of Frame (SoF) search procedure is attenuated in this case.
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SF = 1, EsN0 = 0.7, Delta = 0.25 SF = 1, EsN0 = 0.7, Delta = 0.25, Analytical SF = 2, EsN0 = 0.7, EcN0 = -2.3, Delta = 0.25 SF = 2, EsN0 = 0.7, EcN0 = -2.3, Delta = 0.25, Analytical SF = 8, EsN0 = 0.7, EcN0 = -8.3, Delta = 0.25 SF = 8, EsN0 = 0.7, EcN0 = -8.3, Delta = 0.25, Analytical
Figure 38: Simulated and analytical ROC performance at Es/N0 = 0,7 dB, with non ideal sampling (δ = 0,25) considering spreading factors SF = 1, 2, 8
By considering all possible SF values, the simulated ROC curves at Es/N0 = 0,7 dB reported in figure 39 are obtained, where the same considerations with increasing SF still hold. Similarly, the performance at Es/N0 = -1 dB are reported in figure 40.
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SF = 1, Es N0 = 0.7, Delta = 0.25
SF = 2, Es N0 = 0.7, EcN0 = -2.3, Delta = 0.25 SF = 3, Es N0 = 0.7, EcN0 = -4.1, Delta = 0.25 SF = 4, Es N0 = 0.7, EcN0 = -5.3, Delta = 0.25 SF = 8, Es N0 = 0.7, EcN0 = -8.3, Delta = 0.25 SF = 16, EsN0 = 0.7, EcN0 = -11.3, Delta = 0.25
Figure 39: Simulated ROC performance at Es/N0 = 0,7 dB, with non ideal sampling (δ = 0,25) considering spreading factors SF = 1, 2, 3, 4, 8, 16
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Pmd
SF = 1, EsN0 = -1, Delta = 0.25 SF = 2, EsN0 = -1, EcN0 = -4, Delta = 0.25 SF = 3, EsN0 = -1, EcN0 = -5.8, Delta = 0.25 SF = 4, EsN0 = -1, EcN0 = -7, Delta = 0.25 SF = 8, EsN0 = -1, EcN0 = -10, Delta = 0.25 SF = 16, Es N0 = -1, EcN0 = -13, Delta = 0.25
Figure 40: Simulated ROC performance at Es/N0 = -1 dB, with non ideal sampling (δ = 0,25) considering spreading factors SF = 1, 2, 3, 4, 8, 16
9.4.5.1.3 Mean Acquisition Time performance in AWGN
In figure 41 and figure 42, the Mean Acquisition Time (MAT) is reported vs. the false alarm probability, considering a single dwell serial search procedure [i.12], with two hypotheses per symbol to contrast the chip timing uncertainty. In particular, the worst case condition for the sampling error is assumed, considering a symbol/chip timing misalignment δ = 0,25. The procedure terminates when the correct alignment has been detected. In case of false alarms, the procedure restarts after a penalty time Tp = 2 TF (non-absorbing false alarm), being TF the frame duration.
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
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MAT [s]
SF = 1, EsN0 = 0.7, Delta = 0.25
SF = 2, EsN0 = 0.7, EcN0 = -2.3, Delta = 0.25 SF = 3, EsN0 = 0.7, EcN0 = -4.1, Delta = 0.25 SF = 4, EsN0 = 0.7, EcN0 = -5.3, Delta = 0.25 SF = 8, EsN0 = 0.7, EcN0 = -8.3, Delta = 0.25 SF = 16, EsN0 = 0.7, EcN0 = -11.3, Delta = 0.25
Figure 41: Mean Acquisition Time performance in AWGN at Es/N0 = 0,7 dB, with non ideal sampling (δ = 0,25) considering spreading factors SF = 1, 2, 3, 4, 8, 16
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
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MAT [s]
SF = 1, EsN0 = -1, Delta = 0.25 SF = 2, EsN0 = -1, EcN0 = -4, Delta = 0.25 SF = 3, EsN0 = -1, EcN0 = -5.8, Delta = 0.25 SF = 4, EsN0 = -1, EcN0 = -7, Delta = 0.25 SF = 8, EsN0 = -1, EcN0 = -10, Delta = 0.25 SF = 16, EsN0 = -1, EcN0 = -13, Delta = 0.25
Figure 42: Mean Acquisition Time performance in AWGN at Es/N0 = -1 dB, with non ideal sampling (δ = 0,25) considering spreading factors SF = 1, 2, 3, 4, 8, 16
The MAT performance confirms the results shown by ROC, i.e. performance improves by increasing the spreading factor. The best performance is achieved in correspondence of the minimum points of the MAT curves, which are summarized in table 16. In any case, the worst case performance, which is 15 ms for SF =1 and Es/N0 = -1 dB appears to be satisfactory.
Table 16: Minimum MAT in AWGN at Es/N0 = 0,7 and -1 dB, with non ideal sampling (δ = 0,25) considering spreading factors SF = 1, 2, 3, 4, 8, 16
Es/N0 (dB) SF Ec/N0 (dB) Pfa Pmd MAT (s)
0,7
1 0,7 1,9E-05 0,34 0,0082
2 -2,3 1,7E-06 0,24 0,0054
3 -4,1 8,0E-07 0,17 0,0049
4 -5,3 6,0E-07 0,16 0,0049
8 -8,3 2,0E-07 0,12 0,0047
16 -11,3 5,0E-07 0,06 0,0055
-1
1 -1,0 1,4E-05 0,64 0,0150
2 -4,0 3,7E-06 0,50 0,0090
3 -5,8 8,0E-07 0,48 0,0075
4 -7,0 1,0E-06 0,46 0,0075
8 -10,0 4,0E-07 0,44 0,0071
16 -13,0 2,0E-07 0,38 0,0064
Finally, figure 43 shows the performance in terms of MAT for a smaller signal to noise ratio, Es/N0 = -3dB, and SF = 2. The resulting MAT equal to 0.024s confirms that the requirements are largely satisfied, also in a scenario like this.
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
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MAT [s]
SF = 2, EsN0 = -3, EcN0 = -6, Delta = 0.25
Figure 43: MAT in AWGN at Es/N0 =-3dB with SF = 2 and non ideal sampling
9.4.5.1.4 Performance in Rice Fading Channels
To conclude the performance analysis, in figure 44 and figure 45 ROC and MAT are respectively reported in the presence of Rice fading channel with Rice factor K = 17,4 dB and Es/N0 = 0 dB. The reported results are obtained adopting a semi-analytical approach that is valid for a channel coherence time larger than the SoF duration, but shorter than the frame duration. The proposed approach allows to achieve code/frame synchronization on average in 5 ms for SF = 4 and 10 ms for SF = 1.
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Rice ROC - cold start - SF=4
Rice ROC - cold start - SF=1
Figure 44: ROC performance in the presence of Rice fading channel, K = 17,4, Es/N0 = 0 dB
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050
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Mean Acquisition Time [s]
Rice MAT - Tp=2TF - SF=4
Rice MAT - Tp=2TF - SF=1
Figure 45: MAT performance in the presence of Rice fading channel, K = 17,4, Es/N0 = 0 dB.
Two values of penalty time are considered for comparison