A question that has remained unanswered is: "Which digital mode is the best for weak-signal VHF communications?" In this note, I would like to compare CW, Hellschrieber, WSJT, PSK31, and RTTY. These are very common modes with soundcard software available for all of them. It would be interesting to see how they compare theoretically. That is found below.
I would like to reference everything to the noise in a 2.5 kHz bandwidth. This technique is used by K1JT in his analysis of WSJT -JT44. This puts everything relative to a voice bandwidth. Then the noise in a 1 kHz bandwidth is 4 dB less, and in a 250 Hz bandwidth 10 dB less. Then we can talk about a Signal to Noise Ratio (SNR) based on the average transmitted power and another based on peak transmitted power. This will help in sizing up PA specs for the particular application. As a reference SSB needs about a 6 dB SNR(det) to work with phonetics. Since it also needs the full 2.5 kHz bandwidth, the SNR(ave) is about 6 dB and about 10 dB for SNR(pk) with audio processing.
A very common mode, available on almost every radio, is CW. We have to specify a few parameters so we know what we are comparing. Let's consider one of the better cases, On-Off keyed CCW at 12 wpm or 60 characters per minute or 1 character per second. Here we run at 10 baud, with a peak to average ratio in transmit power of 3 dB. Let's assume a criterion of "acceptable copy" to be 7 distinguishable characters, that is, a 6-letter callsign and a space. This varies from 40 to 100 bits depending on the call. Let's say that a bit error ratio of one in a hundred is acceptable, so BER=0.01. The noise bandwidth for a machine decoded OOK CW signal is 10 Hz. To get the BER requires a SNR(det) of about 9 dB. Now 10 Hz is 24 dB below 2.5 kHz, so SNR(ave) must be -15 dB. With 3 dB peak to average transmitter power, SNR(pk) must be -12 dB.
Normal Feld-Hell is another OOK system like CW. It sends a 7x7 dot-matrix representation of a character, bottom to top,column by column, left to right, with the first and last columns white space. Since it is usually set up as "keyed-on carrier means black and keyed-off carrier means White, the duty cycle is about 25% and peak to average is about 6 dB. The time to send a column is about 61 msec so a character of 7 columns takes 0.4 seconds, yielding 2.5 characters per second or 150 characters per minute, which is 25 wpm. It needs about 250 Hz bandwidth to pass a transmission. Now since this is a "fuzzy" mode, the human eye-brain combination can recognize the characters with only a peak SNR(det) of 3 dB or average SNR(det) of -3 dB. The 2.5 kHz bandwidth is 10 dB more than the 250 Hz noise bandwidth needed, So SNR(ave) is -13 dB. SNR(pk) is -7 dB.
Here I am going to look at the JT44 mode. The JT44 mode is basically a single-tone FSK-type system. It uses a 43 letter alphabet, where each letter is assigned a tone frequency about 11 hz from its neighbors, occupying about 500 Hz in total. A synchronizing tone frequency is returned to about half the time on a pseudo random basis. All tones are then in the 1270 Hz to 1755 Hz range, able to go right into the mic jack of an SSB transmitter. The message is about 22 characters long and is repeated 3 times in about a 30 second transmission. The three copies are averaged, which is worth 1.5 dB. Since the characters are sent three times, the thruput is only about 44 characters per minute or 7 wpm or 0.7 characters per second. The transmit time is about 25 seconds out of 30 seconds available, consisting of 66 data intervals and 69 synchronizing tone intervals, each of about 0.19 seconds duration. So the transmission is at 5 baud and needs 5 Hz of bandwidth for each tone. Noise can be estimated in 2.5 kHz as 2500/5 = 500 or 27 dB. If 6.5 dB SNR(det) is needed to run adequately error free, then including the 1.5 dB improvement, I expect SNR(ave)=SNR(pk)=-22 dB relative to noise in 2.5 kHz. This agrees with the WSJT write-up.
PSK31 uses BPSK modulation at 31 baud to produce a speed of about 30 wpm. This is only rough since the system uses a variable length coding scheme for the letters so thruput depends on content. The filter need only be 30 Hz wide to pass the BPSK modulated carrier. This is about 800 times narrower than a 2.5 kHz bandwidth, or 19 dB. Peaks are about 3 dB above average power with the shaping selected. If 7 dB is needed for SNR(det), then SNR(ave)=-12 dB and SNR(pk) is about -9 dB.
Standard RTTY is 60 wpm, about 6 characters per second. Usually 7 bits are sent per character: one start bit, 5 data bits, and 1, 1.5, or 2 stop bits. The baud rate is about 45 baud. Usually 2-level FSK is used with 170 Hz shift. That also means RTTY will have filters of about 50 Hz bandwidth each. The signal is constant level too. The SNR(det) is about 8 dB. 2500/50 is also about 50 or 17 dB. So SNR(ave)=SNR(pk)= -9 dB which is really not too shabby.
SNR relative to noise in a 2.5 kHz SSB bandwidth is summarized as follows:
MODE BW THRUPUT SNR(ave) SNR(pk) SNR(ave) at 1 char/sec **** ** ******* ******** ******* ********************** SSB 2500 Hz 250 wpm +6 dB +10 dB N/A but -8 dB CCW 10 Hz 12 wpm -15 dB -12 dB -15 dB (12 wpm = 1 c/s) Hell 250 Hz 25 wpm -13 dB -7 dB -17 dB WSJT 5 Hz 7 wpm -22 dB -22 dB -20 dB PSK31 30 Hz 30 wpm -12 dB -9 dB -17 dB RTTY 50 Hz 60 wpm -9 dB -9 dB -17 dB Note: WSJT gives performance very close to the Shannon limit for 12 wpm (7 wpm thru).
The last column tabulates the relative efficiencies of the modes. As can be seen, at the same number of characters per second, the signal-to-noise performance is relatively similar. WSJT is the best performer here. It has the smallest alphabet and can average or integrate several repetitions of the same message to improve the performance in noise.
For VHF it seems that WSJT might be the best alternative for working a weak station in a distant grid, since it has the best absolute sensitivity, mostly due to its low thruput, that is, slow speed. Frequency stability and accuracy are often only fair at VHF. WSJT wins again here. With its synchronizing tone being transmitted about half the time, WSJT can be mistuned by several hundred Hertz and still be properly demodulated. PSK31 and CCW cannot afford even 10 Hz of mistuning and probably are inappropriate for VHF. RTTY can be mistuned 50 Hz and it can still work. Feld-Hell can probably work mistuned by 50 Hz. As a point of fact, many VHF rigs tune in 100 Hz steps for SSB and can't get closer than 50 Hz to a target frequency.
A variation of WSJT may be appropriate here for general keyboard to keyboard contacts. Use the same alphabet and tone assignments with the same synchronizing tone, but add an alternate synchronizing tone pitch and diddle at idle. This allows the receiving station to sort of lock in the DF and DT, but this could be almost instantaneous and would require only a few seconds. One could resynchronize every thirty seconds too. If you do not repeat the message, average, or integrate, the thruput is about 12 wpm. Performance would be about 4 dB better than CCW and 3 dB worse than present.
John Matz KB9II