Interference filter

The interference filter is an optional processing step that can be applied to the raw (I,Q) samples from the FIR filter chips.

The filter can remove strong but sporadic interfering signals that are occasionally received from nearby man-made sources. The technique relies on the statistics of such interference being noticeably different from that of weather.

For each range bin at which (I,Q) data are available, the interference filter algorithm uses the received power (in dB) from the 3 most recent pulses. This 3-pulse algorithm is only intended to remove interference that arrives on isolated pulses, and for which there are at least 2 clear pulses in between. Interference that tends to arrive in bursts are not rejected.

P_{n - 2}, P_{n - 1}, a n d P_{n}

where:

P_{n} = {10 \log}_{10} (I_{n}^{2} + Q_{n}^{2})

If the 3 pulse powers have the property that:

| P_{n - 1} - P_{n - 2} | < C_{1} a n d | P_{n - 1} - P_{n - 2} | > C_{2}

(Alg. 1)¹

then (I_n, Q_n) is replaced by (I_n-1, Q_n-1). Here C₁ and C₂ are constants that can be tuned by the user to match the type of interference that is anticipated, and the error rates that can be tolerated. For some environments, it is possible that good results can be obtained with C₁ = C₂; but RVP10 does not force that restriction.

Two variations on the fundamental algorithm are also defined. The CFGINTF command allows you to choose algorithms to use, and to tune the 2 threshold constants. You may also do this from the Mp setup menu. See Configure interference filter (CFGINTF) and Mp — processing options.

| P_{n - 1} - P_{n - 2} | < C_{1} a n d | P_{n} - P_{n - 1} | > C_{2}

(Alg. 2)

| P_{n - 1} - P_{n - 2} | < C_{1} a n d | P_{n} - L i n A v g (P_{n - 1}, P_{n - 2}) | > C_{2}

(Alg. 3)

Where LinAvg() denotes the decibel value of the linear average of the two decibel powers. The Alg.2 and Alg.3 algorithms also include the receiver noise level(s) as part of their decision criteria. When power levels are compared in the algorithms, any power that is less than the noise level is first set equal to that noise level. This makes the filters more robust and properly tunable, so that interference is more successfully rejected on top of blank receiver noise.

Optimum values for C₁ and C₂ vary from site to site, but some guidance can be obtained using numerical simulations. The results shown below were obtained when the algorithms were applied to realistic weather time series having a spectrum width = 0.1 (Nyquist), SNR = +10 dB, and an intermittent additive interference signal that was 16 dB stronger than the weather. The interference arrived in isolated single pulses with a probability of 2%.

The algorithm performance is summarized in the first 3 columns of the following table, for which C₁ and C₂ have the common value shown. The fourth column also uses Algorithm #3, but with the value of C₁ raised by 2 dB. The Missed rate is defined as the percentage of interference points that manage to get through the filtering process without being removed. The False (false alarm) rate is the percentage of non- interference points that are incorrectly modified when they should have been left alone.

Algorithm results for +16 dB interference
`C1,C2`	`Alg.1 Missed/False`		`Alg.2 Missed/False`		`Alg.3 Missed/False`		`Alg.3, C1+=2 dB` `Missed/False`
`6.0dB`	`17.8%`	`10.91%`	`17.8%`	`4.06%`	`17.8%`	`3.48%`	`10.3%`	`4.15%`
`8.0dB`	`10.5%`	`6.57%`	`10.5%`	`2.42%`	`10.4%`	`1.71%`	`6.1%`	`1.92%`
`9.0dB`	`8.5%`	`5.09%`	`8.5%`	`1.81%`	`8.3%`	`1.16%`	`5.4%`	`1.28%`
`10.0dB`	`7.3%`	`4.01%`	`7.3%`	`1.42%`	`7.5%`	`0.79%`	`5.4%`	`0.85%`
`11.0dB`	`8.9%`	`3.14%`	`8.9%`	`1.06%`	`8.3%`	`0.51%`	`6.5%`	`0.54%`
`12.0dB`	`11.6%`	`2.53%`	`11.6%`	`0.85%`	`11.3%`	`0.33%`	`9.9%`	`0.35%`
`13.0dB`	`17.0%`	`2.07%`	`17.0%`	`0.67%`	`16.3%`	`0.22%`	`15.3%`	`0.23%`
`14.0dB`	`23.5%`	`1.70%`	`23.5%`	`0.54%`	`22.4%`	`0.14%`	`21.6%`	`0.15%`
`16.0dB`	`39.2%`	`1.21%`	`39.2%`	`0.35%`	`39.6%`	`0.06%`	`38.9%`	`0.06%`
`20.0dB`	`67.3%`	`0.65%`	`67.3%`	`0.14%`	`72.5%`	`0.01%`	`72.4%`	`0.01%`

A false alarm in actual precipitation echo affects the values of moments calculated at the gate of the false alarm. For example, the measured power and estimates of reflectivity, subsequently, become slightly lower. The following table maps the rates of false alarms to mean relative changes of reflectivity (in dB).

Impact of false alarms on reflectivity estimates
`Alg.1` `False` `Bias` `(dB)`		`Alg.2` `False` `Bias` `(dB)`		`Alg.3` `False` `Bias` `(dB)`		`Alg.3, +2 dB False` `Bias` `(dB)`
`10.91%`	. .	`4.06%`	. .	`3.48%`	. .	`4.15%`	. .
`6.57%`	. .	`2.42%`	. .	`1.71%`		`1.92%`	. .
`5.09%`	. .	`1.81%`	. .	`1.16%`	. .	`1.28%`	. .
`4.01%`	. .	`1.42%`	. .	`0.79%`	. .	`0.85%`	. .
`3.14%`	. .	`1.06%`	. .	`0.51%`	. .	`0.54%`	. .
`2.53%`	. .	`0.85%`	. .	`0.33%`	. .	`0.35%`	. .
`2.07%`	. .	`0.67%`	. .	`0.22%`	. .	`0.23%`	. .
`1.70%`	. .	`0.54%`	. .	`0.14%`	. .	`0.15%`	. .
`1.21%`	. .	`0.35%`	. .	`0.06%`	. .	`0.06%`	. .
`0.65%`	. .	`0.14%`	. .	`0.01%`	. .	`0.01%`	. .

It is important to minimize both types of errors. If too much interference is missed, then the filter does not do an adequate job of cleaning up the received signal. If the false alarm rate is too high, then background damage is done at all times and the overall signal quality (especially sub-clutter visibility) may be compromised. Try to keep the false alarm rate fairly low, perhaps below 1%; and let the missed percentage fall where it may.

The following table shows the results obtained if the interference dominates by 26 dB. To summarize the numerical results in the table:

The Missed rates of Alg.1 and Alg.2 are identical, but the False rate of Alg.1 is much higher. Alg.1 does not perform as well for additive interference, but it is included in the suite for historical reasons.
The Missed error rate for Alg.3 is nearly identical to that of Alg.2, but Alg.3 has a significantly lower false alarm rate. This is because of the somewhat improved statistics that result when the linear mean of P_n-2 and P_n-1 is used in the second comparison, rather than just P_n-1 alone. We recommend that Alg.3 generally be chosen in preference to the other two.
Alg.3 can be further tuned by allowing the two constants to differ. For example, by raising C₁ slightly above C₂ (fourth column), we can trade off a decrease in the Missed rate for an increase in the False rate. Lowering C₁ would have the opposite effect.

Optimum tuning depends on the type of interference you are trying to remove. In the previous example, where the interfering signal is only 16 dB stronger than the weather, there was a close trade-off between the Missed and False error rates.

Algorithm results for +26 dB interference
`C1,C2`	`Alg.1 Missed/False`		`Alg.2 Missed/False`		`Alg.3 Missed/False`		`Alg.3, C2+=5 dB` `Missed/False`
`6.0dB`	`17.8%`	`10.75%`	`17.8%`	`3.95%`	`17.8%`	`3.44%`	`17.8%`	`0.34%`
`8.0dB`	`9.9%`	`6.48%`	`9.9%`	`2.31%`	`9.9%`	`1.68%`	`9.9%`	`0.15%`
`9.0dB`	`7.4%`	`4.99%`	`7.4%`	`1.75%`	`7.4%`	`1.14%`	`7.4%`	`0.10%`
`10.0dB`	`5.9%`	`3.91%`	`5.9%`	`1.36%`	`5.9%`	`0.76%`	`5.9%`	`0.06%`
`11.0dB`	`4.8%`	`3.06%`	`4.8%`	`1.06%`	`4.8%`	`0.50%`	`4.8%`	`0.04%`
`12.0dB`	`3.2%`	`2.37%`	`3.2%`	`0.83%`	`3.2%`	`0.33%`	`3.2%`	`0.03%`
`13.0dB`	`2.6%`	`1.83%`	`2.6%`	`0.62%`	`2.6%`	`0.20%`	`2.8%`	`0.01%`
`14.0dB`	`1.9%`	`1.45%`	`1.9%`	`0.50%`	`1.9%`	`0.12%`	`2.6%`	`0.01%`
`16.0dB`	`1.3%`	`0.90%`	`1.3%`	`0.30%`	`1.3%`	`0.05%`	`5.8%`	`0.00%`
`20.0dB`	`3.1%`	`0.39%`	`3.1%`	`0.12%`	`2.0%`	`0.01%`	`31.5%`	`0.00%`

Note that we can re-tune the constants and operate with C₁= 13dB and C₂= 18dB (fourth column); which yields a low 2.8% Missed rate, and an extremely low 0.01% false alarm rate. Since the false alarm rate is (approximately) independent of the interference power, these filter settings would leave "clean" weather virtually untouched. That is, we would have a safe filter that only removes fairly strong interference. You could leave such a filter running at all times without too much worry about side effects.

¹ The JMA internal specification for Interference Filter algorithm for use on Chitose airport Doppler weather radar is the basis for Alg.1