Hello,

I will try ro provide answers to your question if I understand your question correctly. The signal processing is as following:  the output of the Gardner loop  should be used only to select the value of the group delay of the fractionnal-time Farrow interpolator (that is applied to the output of the matched filter) at the oversampled rate. Once this has been done, to extract the symbols, you simply have to downsample the signal available at the output of Farrow interpolator and to apply the decision operator once per symbol period.

Have you done this ?

Pascal.

Hi Pascal,

Thanks for your reply.

My algorithm sequence is:

1. Sampling IF input using ADC (It provides 24 samples per symbol)

2. Quadrature Mixer

3. LPF on both in-phase and quadrature arms (Its output consists 24 samples /symbol)

4. Matched filter on both in-phase and quadrature arms (Its output consists 24 samples /symbol). Since I am using rectangular pulses to generate modulation signal a rectangular window is used as matched filter coefficients.

5. Down sampling to get 2 samples per symbol.

Why I am down sampling 24 samples per symbol into 2 samples per symbol is, my actual system has 2 paths from where I am going to receive input to the demodulator:

The above mentioned 5 points providing 2 samples/symbol data, on this data I have to perform demodulation.

It also receives these 2 samples/symbol data from a external module and I have to perform demodulation on it.

This 2 samples/symbol data is fed to symbol synchronization block which consists Gardner symbol synchronizer and Farrow filter.

I am using Gardner algorithm output (mu) as delay input to the Cubic Farrow fractional interpolator and it is providing me the fractionally interpolated output samples. Output of Farrow interpolator also contains 2 sample/symbol.

Currently, as you mentioned in your replay I am taking 2 samples for each symbol period and finding absolute maximum of these 2 samples to pick corresponding Farrow interpolator output as an optimum symbol sample. My question is, is this correct approach? or do I need to follow any other method to get optimum symbol sample?

On these optimum symbol samples I have to perform DBPSK/DQPSK differential decoding. Can you provide some information on this differential decoding?

I have a question about your Farrow interpolator: What are the possible values for the fractionnal group delays. Are they in the range [0;0.5 Ts] or in the range [-0.5 Ts;+0.5 Ts]  where Ts is the symbol period ?

If I understand well your problem, I think that you sould not select the sample corresponding to the absolute maximum of the 2 samples available at the output of the Farrow interpolator because the optimal choice has been previously done  when selecting he fractional delay of the Farrow interpolator. Instead of the selecting the absolute maximum, try to use always the same sample (for example the first one).

Once you have done the decisions on the symbols (at a symbol rate), you  shoud apply a symbol-to-binary conversion, and then multiplex the 2 binary streams (I and Q) into a single one. To perform the differential decoding on this binary stream, you can find (Matlab Excahnge) Matlab files such as diff_enc.m (for the encoder) and diff_dec.m (for the decoder).

Hi Pascal,

Yes, you are right. My fractional group delay value is not within the limit of -Ts/2 to +Ts/2. In simulation I am seeing the fractional delay value of +/-3 and some times it is going to infinity. I have to debug it. Do you have any suggestions on fractional group delay value (Mu) and how to keep it in within the limit?

My symbol synchronization/Symbol Timing Recovery (STR) algorithm is as follows:

Output of Matched filter (2 samples/symbol) are fed to Farrow interpolator. Output of Farrow interpolator is fed to Gardner algorithm and the same is used as recovered samples.

Using Gardner algorithm I am calculating the Mu for each Ts period. The following formula is used to calculate the Mu.

err = [y(n-2) - y(n)] * y(n-1)

Mu(n) = Mu(n-1) + (err * alpha)

Where,

• y are the Gardner algorithm input samples coming from the output of Farrow filter.
• Mu is fractional group delay value.
• alpha is the loop filter gain.

Finally this is Mu is passed to Farrow interpolator.

Pascal, I have some doubt on picking up the optimum samples from Farrow output. As you said if we pick same sample from the Farrow output, is it possible to get the optimum sample every time, even there is any arbitrary initial delay in input samples?

Actually I did not find above mentioned encoder and decoder files on Matlab Central/ File Exchange. I will try to search for it. Mean while can I get some elaborated information regarding the thing "multiplex the 2 binary streams into a single one" explained in your reply.

Thanks for your valuable time spending for me.