800 MHz receiver criteria as harm claim thresholds

Bob Pavlak at the FCC prompted me to read the 800 MHz “unacceptable interference” rules in the context of an interference limits approach (root post).

The 2004 Report & Order (pdf) introduced the concept of unacceptable interference, “a term of art adopted for the limited purposes of this proceeding … that defines a bright-line test for interference protection that takes into account, among other factors, the strength of the desired signal and the characteristics of the receiver being employed” (Report & Order, footnote 8). While this sounds like a receiver performance requirement, I think it actually amounts to an interference limit or harm claim threshold. In fact, if it is reformulated as a harm claim threshold, it becomes more powerful because it does not enshrine a particular set of receiver performance parameters in the rules, leaving manufacturers and system operator with more flexibility.

The 2004 Report & Order defined minimum receiver performance criteria for non-cellular (e.g. public safety) 800 MHz licensees to be entitled to full protection against unacceptable interference from cellular systems. While receiver performance requirements were only given for voice transceivers, leaving the criteria for non-voice equipment extremely vague (“the value reasonably designated by the manufacturer”), this was an important exercise in setting the limits on the harm claims that receiving systems could make.

The 47 CFR 22.970 rules that implemented the Order state that unacceptable interference will be deemed to occur for a mobile voice transceiver if the following conditions are met:

1. A median desired signal of −104 dBm or higher (47 CFR 22.970 (a) (1) (i) (A))
2. The Carrier to Noise plus Interference ratio, aka C/(I+N), of the receiver section is less than 20 dB (47 CFR 22.970 (a) (1) (ii) (B))
3. The device has 75 dB intermodulation rejection ratio; 75 dB adjacent channel rejection ratio; −116 dBm reference sensitivity (47 CFR 22.970 (b) (1))

I believe this formulation can be converted into a harm claim threshold, i.e. the maximum undesired signal level, call it U, that a system has to tolerate before being able to claim interference. 

First, the C/(I+N) condition #2 can be written in logarithmic terms as C – (I + N) < 20, or

I + N > C – 20              (1)

Now, as the rule states, C/(I+N) is measured in the receiver section, i.e. after filtering. If U is the power at the receiver input and there’s 75 dB adjacent channel rejection per condition #3, the undesired signal after filtering is U – 75. In other words,

I + N = U – 75             (2)

Substituting I+N from eq. (2) into eq. (1) gives U – 75 > C – 20, or

U > C + 55            (3)

In other words, unacceptable interference will be deemed to occur for a mobile voice transceiver if

• The median desired C signal is −104 dBm or higher
• The undesired signal U is greater than the desired signal C + 55 dB

This amounts to a harm claim threshold, albeit one defined in terms of the desired signal power C as experienced from place to place, rather than as a uniform field strength value across a license area as I would be inclined to do.

For example, at C = -104 dBm, the harm claim threshold is -124 dBm + 75 dB = -49 dBm. Converting to field strength at 800 MHz and assuming a 0 dBi gain antenna, this is 86 dB(μV/m).

So to the extent my logic is sound, the harm claim formulation U > C + 55 is equivalent to the list of conditions for unacceptable interference in Part 22.970. However, it’s more powerful since it implies but does not require the specific C/(I+N) and receiver performance criteria in the rules.

For example, let’s say an operator chooses a system design that delivers adequate performance with C/(I+N) of 15 dB rather than 20 dB; perhaps it’s more tolerant of noise because of a more robust modulation, better error correction if it were a digital system. Then 5 dB less adjacent channel rejection is required; 70 dB would be sufficient, rather than 75 dB. In other words: the system designer could have made different trade-offs than the ones baked into the rules.

An indefinite number of parameter combinations would work, not just the one enshrined in the rules.

It’s easily seen by cranking the arithmetic above, but substituting the variable “SINR” for 20 dB C/(I+N) and “ACS” for the 75 dB adjacent channel rejection ratio. The equations become

I + N > C – SINR              (1')
I + N = U – ACS               (2')
U > C + ACS – SINR        (3')

Comparing (3) and (3') we can see that the rules imply that ACS – SINR = 55. This is true for ACS=20 and SINR=75 (Part 22.970), but also for ACS=15 and SINR=70, etc.