## Some Facts About FDK (Wanjina)

### Fact #1 - FDK is NOT the same as DFCW or VFSKCW:

Please don't confuse FDK with DFCW / VFSKCW. The DFCW mode was one (I called it VFSKCW) that I abandoned in favour of FDK a long time ago and which later was brought to practical fruition by Rik Strobbe. DFCW is a simple and effective way of encoding the dots and dashes of CW in a more efficient way. FDK is NOT DFCW and is a completely different mode.

In fact, in an effort to counter the confusion I have re-named FDK as Wanjina. This is a Koori word for the Spirit People who travelled across the seas in long boats to watch over them.

### Fact #2 - You Do NOT Need a Linear Amplifier to Transmit FDK (Wanjina):

For minimum bandwidth it IS best to use Linear Amplifiers. The principle of FDK (Wanjina) is to transmit two tones simultaneously separated by a small frequency difference. This small frequency difference encodes the character. Each character has a unique frequency difference assigned to it. The waveform looks identical to that of the two-tone test waveform. Under linear conditions the spectrum space occupied is about 7Hz for the 60 second burst FDK mode.

However, by using the same method that is commonly used for BPSK/WOLF the bandwidth is about 30Hz for products less than 20dB down. This method uses an XOR gate to phase-switch the carrier at a rate which is half the frequency difference. Here you don't have to use a Linear Amplifier. Considering all the resistance to advanced modes from various sections (especially from those parts where they are crammed into 1600Hz of spectrum space) it would be advisable to only use this mode either for QRP experiments or in the LowFer US band. If you currently transmit WOLF or BPSK then you can transmit FDK (Wanjina).

### Fact #3 - FDK (Wanjina) is a NOT a Complicated Mode:

Actually I believe that the simplicity of the method causes people to have difficulty understanding it. If you understand QRSS which is standard, but slow CW, or DFCW / VFSKCW where the dots and dashes of ordinary Morse Code are represented by two different but fixed frequencies sent sequentially, then you are 90% of the way to understanding FDK (Wanjina). Watching QRSS on, say, Argo, shows lines across the screen which can be visually decoded into dots and dashes by the actual duration of the lines. DFCW / VFSKCW compresses the time needed to send information by representing the dots and dashes not as different durations (1:3), but as two distinct frequencies slightly different in frequency. Each frequency (assuming no drift) does not change. Watching DFCW / VFSKCW shows "dots" which have no gaps (except for letter and word spaces) but are slightly different in frequency.

If you watch FDK you would see two lines at the same time on the screen. The difference between the two lines is what encodes the character, The duration of each pair is 60 seconds and as each character is sent the frequency spacing between the two tones changes for each different character. You could actually roughly guess what character is being transmitted by looking visually at the space between the tones. Certainly you could guess it within a range of 5 characters. However, as the step in difference is of the order of 0.1Hz and there are about 49 of them spaced across the screen, electronic identification is needed for accurate decoding.

### Fact #4 - FDK (Wanjina) Does Not Suffer from a Big Power Deficit Compared to Other Modes:

To get to the truth of this, more than a simplistic analysis is needed. In particular, it needs to be taken into account what governs the output power characteristics of the intended transmitter and put this against the S/N implications of each. One could classify this into several categories:

**Rules Limited**- the Tx is limited by the maximum allowable input power (US Lowfer).**Dissipation Limited**- the Tx is limited to a maximum power level by overheating of components.**Peak Limited**- the Tx is limited to a maximum peak power.

Let's take the first case where we are limited to an input power and apply it to the situation for a number of modes - QRSS, DFCW and FDK (Wanjina) where we are attempting to transmit a message of seven characters plus word space in 8 minutes - say "WANJINA".

**Rules Limited (e.g. US LowFer regulations):**

Firstly, looking at receiver bandwidth needed :-

- QRSS - needs 73 units in 480 seconds (8 minutes) - gives 6.6 second dots. Needs FFT equal to or shorter than about 3.3 seconds to resolve visually - equals operating BW of about 0.3Hz.
- DFCW - needs 24 units in 480 seconds - gives 20 second dots. Needs FFT equal or shorter than about 10 seconds to resolve visually - equals operating BW of about 0.1Hz.
- FDK (Wanjina) - needs 8 units in 480 seconds - gives 60 second dots. Can use FFT equal to or shorter than about 60 seconds to resolve (not resolved visually) - equals operating BW of about 0.0165Hz.

Taking FDK (Wanjina) as a base then we can see that DFCW is 7.8dB down on FDK and QRSS is 12.6dB down on FDK in terms of S/N gain from the respective required receiver bandwidth.

Secondly, looking at power out when limited to, say, 1W input :-

- QRSS - 1W input - assume 100% eff. = 1W for the single carrier.
- DFCW - 1W input - assume 100% eff. = 1W for the single carrier.
- FDK (Wanjina) - 1W input - assume 100% eff. = 0.5W for each of the two tones.

Therefore FDK is 3dB down on both QRSS and DFCW in terms of putting power into the receiver for the needed tone(s).

So the score card now is :-

- FDK = 0dB
- DFCW = -7.8dB + 3dB = -4.8dB
- QRSS = -12.6db + 3dB = -9.6dB

So, FDK is 4.8dB better than DFCW and 9.6dB better than QRSS in terms of Rules Limited operation.

**Dissipation Limited:**

Looking at receiver bandwidth needed the same factors apply as in the Rules Limited case above :-

Taking FDK (Wanjina) as a base then DFCW is 7.8dB down on FDK and QRSS is 12.6dB down on FDK in terms of S/N gain from the respective required receiver bandwidth.

Now looking at power out when limited to, say, 1W input * average*
and taking into account the duty cycle :-

- QRSS - 1W input - assume 100% eff. and approx. 48% duty cycle = 2.1W for the single carrier.
- DFCW - 1W input - assume 100% eff. and approx. 63% duty cycle= 1.6W for the single carrier.
- FDK (Wanjina) - 1W input - assume 100% eff. and approx. 100% duty cycle= 0.5W for each of the two tones.

Therefore FDK is 6.2dB down on QRSS and 5.1dB down on DFCW in terms of putting power into the receiver for the needed tone(s).

So the score card in this case is :-

- FDK = 0dB
- DFCW = -7.8dB + 5.1dB = -2.7dB
- QRSS = -12.6db + 6.2dB = -6.4dB

So, FDK is 2.7dB better than DFCW and 6.4dB better than QRSS in the Dissipation Limited case.

**Peak Limited:**

Looking at receiver bandwidth needed the same factors apply as in the Rules Limited and Dissipation Limited cases above :-

Taking FDK (Wanjina) as a base then DFCW is 7.8dB down on FDK and QRSS is 12.6dB down on FDK in terms of S/N gain from the respective required receiver bandwidth.

Now looking at power out when limited to, say, 1W input * peak*
:-

- QRSS - 1W peak - assume 100% eff. = 1W for the single carrier.
- DFCW - 1W peak - assume 100% eff. = 1W for the single carrier.
- FDK (Wanjina) - 1W peak - assume 100% eff. = 0.25W for each of the two tones.

Therefore FDK is 6dB down on both QRSS and DFCW in terms of putting power into the receiver for the needed tone(s).

So the score card in this case is :-

- FDK = 0dB
- DFCW = -7.8dB + 6dB = -1.8dB
- QRSS = -12.6db + 6dB = -6.6dB

So, FDK is 1.8dB better than DFCW and 6.6dB better than QRSS in the Peak Limited case.

** NOTE #1:** This is for the linear case. For the non-linear
case we can claw back 2.08dB, so the score card is :-

- FDK = 0dB
- DFCW = -7.8dB + 6dB - 2.08dB = -3.88dB
- QRSS = -12.6db + 6dB - 2.08dB = -8.68dB

So, FDK is 3.88dB better than DFCW and 8.68dB better than QRSS in the Peak Limited case using non-linear mode (XOR gate 180degrees phase-switching).

### Fact #5 - The 3dB Penalty of FDK Can Be Eliminated by a Single Tone System:

It has been suggested by several that the basic 3dB deficit over single-tone systems caused by the transmission of two tones simultaneously could be overcome by sending the tones sequentially. Unfortunately, I don't think this is the case. In the 60 seconds, one tone would be sent for 30 seconds and then the second tone would have to be sent for the remaining 30 seconds. This means you have half the length of FFT record for each tone and therefore twice the operating bandwidth, resulting in a 3dB loss in S/N. So 3dB gain in power is offset by 3dB loss in S/N due to wider bandwidth. In addition it would necessitate some kind of time synchronisation (i.e. is this tone the last one of a pair or the first one in the next ?). Of course, time synchronisation will improve all methods (QRSS, DFCW / VFSKCW and FDK), but is not in the realm of the basic factors looked at here.

The best way of overcoming the 3dB deficit is to use Piccolo Mk1. I re-invented this over three years ago (1998) and called it AFK. It has then been re-re-invented by several others under the name of PUA-43 and PGP-1 (or something like that). Piccolo was invented in 1957 by some English boffin. In Piccolo the character is encoded in an absolute frequency. It requires high standards for both accuracy and stability. In fact FDK was my attempt to relax the requirement on accuracy (but still requiring a high standard of stability).

** NOTE:** Piccolo MK1 is very suitable for VLF (especially
below 9kHz) as both accuracy and stability can more easily be satisfied.

### Fact #6 - Required Tx and Rx Stability:

FDK DOES require a higher level of stability over the 60 second epochs than QRSS and DFCW / VFSKCW.