11 September 2022

OFDM-48 and some comments about OFDM analysis with SA

tags: ,

I wanted to further investigate the OFDM-48 signal published a few days ago [1], in particular the "mode" of construction of the signal and consequently the correct PSK modulation used in the channels. Signals Analyzer documentation [2] reports that, according to the method of forming the data channels and pilot tones, it is possible to meet at least three modes of OFDM signals, actually there may be more modes but SA OFDM tool considers the most basic ones:

Mode A:
All channels are formed "as is", including pilot tones. In this case, the pilot tone cannot be chosen arbitrarily, and is assigned from a limited number of suitable candidates. A typical representative of this mode is the WINDRM 51-tone signal.

Mode B:
All channels are configured as potential pilot tones, any channel can be assigned as a pilot. A typical representative of this mode is CIS-12.

Mode C:
Mixed formation type, all channels are formed as they are, according to mode A. But the pilot tone (s) is formed in a special way, according to mode B. In this mode, any channel or channels can be assigned to the pilot . A typical representative is 188-110B-39 tone signal.

In general, it should be noted that mode B is typical for CIS signals and mode C for NATO signals, even if the 16-tone 188-110 App.A signal is formed according to mode B. Of course this is a subdivision that comes from analysis and practice, although it's quite confirmed.  Most likely, in hypothesis, the signals of modes A and C are formed using 2^n dimensional FFT/IFFT algorithms, and signals according to the mode B without these restrictions.

To appreciate their differences, I synthesized two distinct OFDM-48 signals (modes A and B) using the OCG (OFDM Calculator - Generator) tool [3] downloaded from the radioscanner.ru site. The synthesis process requires the calculation of the OFDM parameters ("Calculate") which will then used in the synthesis stage ("Synthese"). The input fields of the "Calculate" tag (see figure 2) must be filled with the appropriate values, among them I chosed the Fmin Fmax values according the bandwidth limits of the original signal after its direct translation (figure 1).

Fig. 1 - direct translation of the original recording

After entered the correct values for FFT_size/2, TonesMin/Max and Fmin/max, the "Calculate" stage returns the relative OFDM parameters (figure 2); it should be noted that the values of SymbolRate and DeltaFreq calculated by the tool correspond exactly to those desired, that is to those obtained at the time from the analysis of the "original" signal (respectively: 50 Baud and 62.5 HZ).

Fig. 2 - computing the OFDM-48 parameters

As said, the values returned by the "Calculate" stage must then be entered in the input fields of the "Sythese" tag to build the desired OFDM signal; values FFT_Size/2 and TonesTotal are the same of the Calculate stage. As shown in figure 3, I synthesized the OFDM-48 signals (MakeOFDM button) according to the A and B modes, both using PSK2 modulation and without pilot tone(s).

Fig. 3 - synthesis of the two OFDM-48 signals

So I went on to analyze the two OFDM signals with the GREAT ADVANTAGE of already knowing their main parameters, especially the "formation" mode and the used modulation (PSK2).
To the facts, if the "mode" used in the analysis match the one used during the formation of the OFDM signal then we will get the actual modulation used in the channels. The following figures 4 and 5 show this evidence: the PSK2 constellation (the modulation actually used in channels) appears only when the "modes" of the analysis and the OFDM formation match; otherwise, the DBPSK constellation appears.

Fig. 4 - analysis of the OFDM-48 PSK2 mode-A signal

Fig. 4 - analysis of the OFDM-48 PSK2 mode-B signal

As proof, I synthesized the same OFDM-48 signal but this time with DBPSK modulation (figures 5 and 6).

Fig. 5
 
Fig. 6 - analysis of the OFDM-48 DBPSK mode-A signal

This means that we can obtain the correct values of the baud rate, spacing and number of channels but if we do not know a priori the used modulation we could face a margin of uncertainty about it. The best way to fix such impasse is to isolate a single channel and analyze it as if it were a normal PSK-n signal but with the foresight to use the differential mode (Diff = 1) when studying its constellation (figures 7,8). However, this is not always possible because it depends on the quality of the recording.

Fig. 7 - OFDM-48 PSK2, single channel verification

Fig. 8 - OFDM-48 DBPSK, single channel verification
 

That done, I tried to trace back to the "native" sampling rate (SR) of the original OFDM-48 signal analyzed in the previous post [1].

(the following comments are from "Analysis OFDM with CP in SA versions 6.2.6.5" [4])
It is well known that in OFDM signals there is a concept called "native sampling frequency" (SR) which has to satisfy some principles:
- SR/Br = x
- SR/Sh = y
where Br is the symbol rate (Baud), Sh is the separation between channels (Hz), and x y are positive integers. The SR frequency has to be a multiple of Br, and its relation to the channel spacing is “native”. On the other hand, we speak of “independence” of the SR frequency and “native” and “non-native” SR frequencies, which must certainly have specific values.

Let's explain this. A given recording has been sampled at a particular rate: we speak of "independence" because that sample frequency does not have to correspond to the "native" frequency. This does not influence or affect the obtaining of the parameters of an OFDM signal, indeed if necessary, the value of SR can be resampled/recalculated as necessary. Since the "native" value of the sample rate is a multiple of both Br and Sh, if we calculate the exact values ​​of Br and Sh, we will have the possibility of estimating a set of SR frequencies SR1, SR2, SR3..., SRn that meet the requirements and in which at least one frequency of them will be the “native” one.

Back to the native SR, if its value is not known but the OFDM signal formation values LU and LG are (1), then the following formula can be used:

SR = (LU + LG) * Br

Well, OCG tool also gives the possibilty to get pairs of LU LG (just "Get LU,LG" tag) according the desidered values of the signal such as channels, shift, and Br. We can choose any LU LG pair but it is better to leave the signal as much as possible as it is, ie without "heavy" resampling and using a pair of values as close as possible to the pair found from the analysis of the original signal [1]. In this case I chose the pair LU = 228  LG = 57 (figure 9), therefore:

SR = (228 + 57) * 50 = 14250 Hz

as you see, the resulting SR frequency is almost the same of the one used when recording the signal.

Fig. 9

The analysis of the signal after its resample at 14250 Hz is shown in figure 10. Since it is assumed to be a CIS signal, and they usually use mode B, it can be said that the modulation used is DBPSK, even if mode A & PSK2 remains equally likely.

Fig. 10 - analysis of the resampled OFDM-48 signal

Without using OCG, a trick to obtain one or more "effective" SR frequencies is to multiply the value of the shift by an positive integer n, ie:
SR = Sh * n  
taking into account the bandwidth occupied by the signal, ie the resulting SR value must be equal to twice the  upper boundary (see Nyquist rate [5]). In this case n would be = 228.
 
(1) the relation between the duration of LG (guard interval) in samples and the duration of LU (length of useful information) in samples gives the factor K (or "Magic K", visible in the OFDM analysis results), since K = LG/LU. Defining a consistent value of K is one of the primary goal/task of the analysis of signals OFDM, knowing this factor it is possible to receive all much more precisely and faster. 

 
 

No comments:

Post a Comment

Subscribe to: Post Comments (Atom)