Kok Chen, W7AY
w7ay (at) arrl (dot) net
January 14, 2013
We study the effects of transmit filtering on an Amateur RTTY signal (Frequency Shift Keying, with data rate of 45.45 baud and FSK shift of 170 Hz).
Specifically, we show (i) the practical limit of how narrow an RTTY transmit filter can be constructed, and (ii) some representative plots of the amount of energy overlap there is between the Mark and Space signals for various filters. The former determines the extent we can help avoid causing interference to an adjacent RTTY station, and the latter can help determine the limit of how narrow a transmit filter can be made when used in conjunction with an AFSK transmitter that has high intermodulation distortion.
Prior works with RTTY transmit filtering include a study of what a transmit filter does to a Matched Filter waveform [reference 1] and a study of interference from unfiltered RTTY signals during busy RTTY activity [reference 2].
In section 2, we show how a transmit filter affects the error rates from a demodulator that uses a Raised Cosine filter.
When an RTTY signal is filtered, the Mark and Space carriers will overlap temporally. When this overlapping signal is passed through a practical AFSK transmitter, the transmitter's intermodulation distortion (IMD) will cause the spectrum of the filtered signal to widen. In section 3, we will discuss the dependency of the overlap energy on the transmit filter bandwidth. This information can be used to estimate the spectrum widening when the transmit IMD characteristics are known.
2. Transmit Filtering
When demodulated with an optimal Raised Cosine data filter, the transmitted RTTY signal need not include any keying sidebands that reaches beyond the response of the receiver's Raised Cosine filter. A Raised Cosine (β=1) data filter for an Amateur RTTY signal has a -6 dB point at 22.725 Hz and falls to zero beyond 45.45 Hz.
As a result, when used with a 170 Hz FSK shift, this receiving filter will not respond to anything that extends beyond a 261 Hz passband.
This implies that an ideal distortion free, ripple free, brick wall transmit filter needs only be 261 Hz wide. However, the skirt of a practical filter does not have infinite slope, and the filter top is not completely flat, so a practical filter will need to be somewhat wider than 261 Hz.
Additionally, if the filtering is performed with anything other than a linear phase filter, we will also need to take group delay into account. Filter group delay is not within the scope of this discussion, since we shall assume that digital signal processing (DSP) techniques are available in the transmitter, or in the software that generates the AFSK signal for the transmitter.
We shall use a Blackman windowed bandpass filter for our purpose. The reason for choosing a Blackman window is that while the filter skirt is relatively shallow (compared to the Hann window, for example) down to about -20 dB, the skirts fall very steeply beyond that. This will help keep the transmit signal from adversely affecting a nearby signal that is more than 50 dB weaker (about 8 "S" units).
Figure 2.1 shows the frequency response of a Blackman windowed bandpass filter whose -6 dB bandwidth is 280 Hz wide (we will see later why we choose 280 Hz). The FIR filter has 8192 taps with a sampling rate of 48000 samples/sec.
Figure 2.1: Blackman Windowed Bandpass Filter with bandwidth of 280 Hz
Notice that the response of the filter falls below -100 dB beyond a 400 Hz bandpass.
Figure 2.2 shows a plot of the Character Error Rate for 20000 characters from a bandpass filtered RTTY signal in additive white Gaussian noise (AWGN).
An unpublished experimental RTTY modem that has a built-in Channel Simulator is used to generate data for the plot. The automatic threshold corrector (ATC) of the demodulator is turned off since there is no selective fading. The error rate is plotted against the bandwidth of the filter that is shown in Figure 2.1 (but for different cutoff frequencies).
Figure 2.2: Character Error Rate vs Transmit Filter Bandwidth
The SNR of the RTTY signal is -7 dB (in a 3 kHz noise bandwidth). The asymptotic error rate on the right of Figure 2.2 is about 0.42%. Although the plot in Figure 2.2 stops on the left at 190 Hz, the error for a 180 Hz filter was measured to be 2.4% (6 times more than the error rate for the wider filters, and represents a SNR loss of almost one decibel). The error rate rises very steeply below 190 Hz.
The theoretical Cramér-Rao bound [reference 3] for a 45.45 baud RTTY at this SNR has a character error rate of about 0.40% (VE3NEA's "theory" curve [reference 4] shows the bound drawn as a blue curve in his AWGN plot).
From this, we propose that a properly centered Blackman windowed transmit bandpass filter that is 270 to 280 Hz wide, and has the number of taps described above will not cause additional decoding errors.
The filter can probably be tightened further, but as seen in Figure 2.1, even a 280 Hz Blackman window provides better than 100 dB of keying sideband suppression beyond 400 Hz (200 Hz on each side of the center of the RTTY signal). If channelized, we can comfortably fit RTTY stations 400 Hz apart when such a filter is used, with 100 dB worth of isolation between stations. The interchannel isolation is actually about 10 dB better since the first RTTY keying sideband is about 9 dB lower than the carrier power. The centers of an S2 station and an S9+50 dB station can be as close as 400 Hz apart and the S2 station can still be copied.
A less precise filter (fewer taps per sampling rate, for example) will need to be a bit wider since the flat top of the Blackman filter will not extend as wide. Similarly, some other window shapes may also need other adjustments. Windows should be chosen, in any case, to ensure that the filter does not appreciably widen even down to the -80 dB level.
3. Mark/Space Overlap
Intermodulation distortion is a somewhat unpredictable quantity between different transmitters. However, for a moderately well behaved transmitter, each decibel of increase in power tends to increase the 3rd order intermodulation components by about 2 dB. Conversely, reducing the output by a factor of just 1 dB can reduce the 3rd order intermodulation by 2 dB.
The following figures show the Mark/Space eye pattern of a filtered RTTY signal (the red curve is the Mark signal and blue curve is the Space signal). Each 4 horizontal divisions is equal to one bit period.
The curves are constructed using two separate OOK tones, one at the Mark frequency and one at the Space frequency, and their individual detected responses are plotted. This is done so that the detector that is used to measure each tone can have a bandwidth that is wide enough to capture the true rise and fall times of the filtered RTTY signal. The detector that produces the above curves has a rise time of approximately 0.05 msec (a 45.45 baud signal has a bit period of 22 msec).
Notice that the ringing is not the typical filter ringing that is commonly seen from a narrow band filter. This is because the Mark signal is not centered in the transmit band pass filter; one set of its keying sidebands is heavily attenuated by the filter while the other set of keying sideband has an additional distance of 170 Hz before they are cut off. The Space signal is likewise offset on the other side of the center of the bandpass filter, with the complementary set of keying sidebands more attenuated than the other.
The worst case IMD (maximum power) should occur when the two components cross at half the maximum level. Due to the complementary nature of the waveforms, the overlap at other points in the waveform are always lower.
The amount of IMD that is seen at the output therefore depends heavily on how long the waveforms "linger" near the halfway point. As seen in the above 3 plots, the amount of time spent near the halfway point is inversely proportional to the filter bandwidth (i.e., the rise time of a pulse is roughly inversely proportional to the filter bandwidth).
One would therefore expect a 300 Hz filter to have produce twice the overlap of a 600 Hz filter. Since each dB of overlap power can amount to 2 dB of IMD, one might expect the 300 Hz filter to produce between 3 and 6 more dB of IMD than a 600 Hz filter.
By measuring the IMD that is produced by a given filter through a transmitter, then using the 3 to 6 dB IMD for each halving of the filter bandwidth, we can roughly guess how narrow we can construct a final transmit filter. These are rough guidelines based upon a "well behaved" transmitter." The actually IMD will need to be carefully measured when the bandwidth of the filter is chosen.
4. Conclusion and Observations
It is shown that we can indeed implement practical transmit RTTY filters that do not cause additional decoding errors, and at the same time are useful even when channel spacings of the RTTY signals are very small, and when the dynamic range of signals is very large (100 dB).
Please note that the transmit filter that is used in Section 2 is a symmetrical FIR filter and the passband is perfectly centered on the RTTY signal. This means that the filtering will maintain the original Mark/Space balance, and equally important, the filter is linear phase.
Arbitrary transmit filters (for example, analog crystal filters) will not have a symmetric passband and will additionally have group delays. To replicate the results in section 2, the filter must satisfy both of these conditions. If the filter is not implemented numerically in DSP (digital signal processing), it should be designed so that the frequency response is flat within a fraction of a decibel up to 280 Hz and have minimal group delay between the Mark position and the Space position. An analog filter will probably need to be at least 400 Hz to satisfy the conditions. An analog filter may also not have the 100 dB ultimate rejection of the digital filter that is shown in Section 2.
- Kok Chen, W7AY, FSK Sidebands, http://www.w7ay.net/site/Technical/RTTY
- Andy Flowers, K0SM, RTTY Spectrum
- Cramér-Rao bound, Wikipedia, http://en.wikipedia.org/wiki/Cramér–Rao_bound
- Alex Shovkoplyas, VE3NEA, RTTY Software