Spurious signals created by the presence of multiple carriers in a given bandwidth are a limiting factor in determining a signal channel's dynamic range. These spurious outputs due to system nonlinearities are the result of mixing of fundamental and harmonics of each of the signals (i.e., intermodulation interference). The easiest form of intermodulation interference to measure is two-tone, third-order intermodulation. This only requires the presence of two carriers at equal power levels closely spaced in frequency. The results of this measurement is used to determine the third-order intermodulation intercept point, a theoretical level used to calculate third-order intermodulation levels at any total power level significantly lower than the intercept point. When more than two signals are present in a single communications channel, the dominant interference is due to carrier-triple-beat (CTB) interference, which is the mixing of the fundamental of three carriers producing an interference signal in the same frequency band as the desired carriers. What follows is a review of the types of interference generated by multiple carriers and how to estimate their levels.

Third-Order Intercept Point
The third-order intercept point (Fig. 1) can be used to calculate carrier triple-beat interference for N carriers. In the limit as the number N gets large, multiple carriers exhibit a noise-like characteristic and can be described as the noise spectral density in a given resolution bandwidth. This suggests a practical alternative to measuring channel interference when a large number of carriers are active. Instead of loading the channel with signal sources, the communication channel is loaded with Gaussian noise covering the entire effective bandwidth. The interference is measured by placing a stopband filter in a similar resolution bandwidth and noting the resulting noise level in the stopband with respect to the noise in the passband. The factor is called the noise power ratio (NPR), a measure of communication-channel performance developed many years ago by the telephone companies and being resurrected today by satellite-communications systems to test the viability of multiple-carrier transmissions through a common satellite transponder.

If the total output power is kept constant, the relationship between the two-tone third-order intermodulation interference and the CTB interference for N signals is predictable. Since the results of NPR tests are similar to that of a system with a large number of carriers, these results can be extended to predict the NPR performance of a given system.

The following analysis assumes that all interference is caused by third-order intermodulation, which is usually dominant with higher-order intermodulation having secondary and tertiary effects. Therefore, the results presented are in general a good first-order approximation and should only be used as a convenient tool rather than a exact analytical result.

For system bandwidths less than an octave, even-order intermodulation products are out of band. Odd-order intermodulation products fall in-band, with sidebands close to the carrier. The level of interference is related to the system nonlinearity which can be defined by the theoretical intercept points for each higher-order nonlinearity (e.g., third-order intermodulation is defined by a third-order intercept point, fifth-order nonlinearity is defined by a fifth-order intercept point, etc.).

For simple (nonlinearized) systems, the third-order nonlinearity is usually the most prominent. In-band third-order distortion is the mixing of a fundamental of one signal and the second harmonic of another signal. The presence of more than two carriers in a nonlinear channel creates a spurious response, consisting of the mixing of three fundamental carriers, i.e., CTB. These spurious CTB signals fall in-band at a level 6 dB higher than two-tone, intermodulation products because there are no second harmonics involved in the production of the interference signal. The level of CTB interference is further enhanced by multiple CTB signals occurring in the same frequency band. Figure 2 shows three fundamental signals and the resultant carrier triple beats. The interference signals each down −30 dBc, are products of the three carriers at frequencies, W1, W2, and W3.

Third-order intermodulation interference is caused when two signals are present in the same non-linear communications channel. Measurement of this interference at a carrier signal level below the system compression levels gives the design engineer the ability to calculate the third-order intercept point. This, in turn, allows a prediction of intermodulation interference at any level below the system compression levels. This information can also be used to calculate the worst-case CTB performance for any number (N) of signals in the channel.

The relationship between third-order intercept point, carrier level, and third-order intermodulation interference (Fig. 3) is as follows:

dBc3rd = −2(I_3rd − Carrier)

where:

dBc3rd = the third-order intermodulation level with respect to a single carrier (dBc),
Carrier = the single carrier output level (dBm), and
I_3rd = the third-order intercept point (dBm).

The total output power, P_tot (in dBm), assuming both carriers have equal levels, can be written as:

P_tot = Carrier + 10log(2) = Carrier + 3 dB

Conversely, the individual carrier power is:

Carrier = P_tot − 3 dB

Solving for the third-order intermodulation interference (dBc3rd) in terms of total output power yields:

dBc3rd = −2(I_3rd − P_tot + 3 dB)
    = −2(I_3rd − P_tot) − 6 dB

The third-order intercept point in terms of total power and third-order intermodulation is:

I_3rd = P_tot − 3 dB − (dBc3rd/2)

For convenience, Table 1 offers interference level (dBc) versus total power below the third-order Intercept point for two tones.

The carrier-triple-beat (CTB) interference level for three carriers (CTB₃) is similar to two-tone intermodulation except that a factor of 6 dB is added to account for the fact that no second-harmonic content is needed to create the in-band interference:

CTB₃ = −2(I_3rd − Carrier ) + 6 dB