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I have chosen the preamble to be 48 bits (16 bits for carrier recovery+16 bits for timing recovery+ 16 bits for AGC of 30dB + 16 bits for phase ambiguity) As channel is gaussian and there is no much frequency offset i was thinking number of bits would be ok? but i am seeing sometimes they is timing error? I choose the preamble length based on some sample application? Is there any criteria to choose the preamble properly? Does it depend on snr, data rate ...

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  • $\begingroup$ Any specific reason for not using all the 48 bits for all of these 3 tasks. The algorithms for each of these task could perform better with access to all 48 bits $\endgroup$ – Dsp guy sam Jun 4 at 15:25
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Timing recovery is implemented as a control loop (measure the timing error and adjust the sample offset) and therefore would have an acquisition time depending on the control loop parameters (loop BW). A reasonable estimate for acquisition time assuming the start of acquisition is in the linear capture range of the loop is the first order 10% to 90% rise time estimate of $t_r = 0.35/BW$ where $t_r$ is the estimated rise time from 10% to 90% and $BW$ is the loop BW in Hz. This is accurate for a first order loop and a reasonable estimate whenever there is a dominant pole as that would set the settling time.

If the Initial state is not within the linear operating range of the loop or if there is lower SNR, this can take much longer. The best approach is to model this in a time domain simulation and observe the timing error versus time with step response testing to evaluate convergence time/ behavior and validate that the loop BW is as predicted from a more detailed control loop model from which these parameters can be computed and help identify issues such as capture range and non-linear behavior. A simulation can also help identify issues related the SNR as well as noise enhancement in the loop. For this purpose the preamble would be treated as infinitely long until it is certain the loop can work in the desired length in all conditions (will this loop operate with carrier offsets or will that be addressed before timing recovery, etc)

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  • $\begingroup$ So acquisition time depends only on the loop bandwidth ( not on symbol rate). This time should be calculated into bits to arrive the number of bits for timing recovery? Based on this we can arrive what offset can my timing have with respect to the transmitter. Similarly is there any criteria for carrier recovery? How the SNR degrades the signal? It will have effect only on the carrier recovery and timing recovery?Can AGC help with the degraded SNR? -Steve $\endgroup$ – Steve Jun 4 at 11:59
  • $\begingroup$ @Steve This post may help you further: dsp.stackexchange.com/questions/31170/… $\endgroup$ – Dan Boschen Jun 4 at 12:01
  • $\begingroup$ @Steve They discourage a lot of back and forth discussion here; your questions are numerous and more detailed than we can go through in a simple Q&A but I hope the answer and the above link is helpful to you. $\endgroup$ – Dan Boschen Jun 4 at 12:04
  • $\begingroup$ It was a great in depth analysis. Basically I should choose my loop bandwidth for carrier recovery and timing recovery to be between R/100 and R/20( R symbol rate) But in carrier recovery I am using the loop for carrier freq and phase but in timing recovery I am using the loop for symbol freq and phase. But may be in timing I will be using << R/20. My question is How do I choose how many bits for carrier and timing recovery preamble? $\endgroup$ – Steve Jun 5 at 11:16
  • $\begingroup$ @Steve usually the number of bits is set in the waveform packet design so I assume you are designing your own custom packet? A design parameter is the loop BW for each which sets the acquisition time and will be a trade with noise performance and capture range (consider dynamic loops with wide BW for acquisition to get wider capture range and then narrow for tracking for lower noise). To answer your question design based on those criteria and then the preamble must be longer than the acquisition time since it uses the preamble to acquire. $\endgroup$ – Dan Boschen Jun 5 at 12:18

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