Understand noise power ratio for modern wireless applications

The concept of noise power ratio (NPR) has been around since the early days of frequency division multiplexed (FDM) telephone systems. The NPR is simply a measure of the "quietness" of an unused channel in a multi-channel system when there is random activity on the others. Noise and intermodulation distortion products fall into the unused channel causing less than ideal performance. Originally used to check 4-kHz wide voice channels in FDM links, the same concept is useful today in characterizing multi-channel wideband communication systems, but there are some important differences in the modern measurement techniques.

History of NPR
Noise power ratio testing has been used since the early days of frequency division multiplexed (FDM) communication systems. In a typical FDM system, 4-kHz wide voice channels are "stacked" in frequency bins for transmission over coaxial, microwave, or satellite equipment. The number of channels depends on the system. A group is composed of 12 voice channels and occupies a bandwidth of 48 kHz. Similarly, a supergroup has 60 channels and occupies a bandwidth of 240 kHz, and a mastergroup has 300 channels and occupies a bandwidth of approximately 1.3 MHz. Supergroups and mastergroups are often combined to make up even higher capacity systems. For instance, an 1800-channel system occupies a bandwidth of approximately 8 MHz .

At the receiving end of the transmission link, the FDM data is demultiplexed and converted back to 4-kHz individual voiceband channels. The FDM signal is therefore composed of many individual voice channels and passes through amplifiers, repeaters, channel banks, etc., which add noise and distortion to the signal.

Early studies at Bell Telephone Labs (Reference 1) led to the conclusion that the composite signal in an FDM system having more than approximately 100 channels can be approximated by Gaussian noise having a bandwidth equal to the bandwidth of the combined FDM signal. For instance, a 1800-channel FDM signal is approximated by Gaussian noise with a bandwidth of 8.2 MHz.

The "quality" of an individual voice channel is then measured by first assuming that there are random "talkers" on all channels except the specific 4-kHz channel under test. An individual 4-kHz channel can therefore be measured for "quietness" using a narrow-band notch (bandstop) filter and a specially tuned receiver which measures the noise power inside the 4-kHz notch as shown in Figure 1A.

1. Noise Power Ratio (NPR) Measurements.

Noise Power Ratio (NPR) measurements are straightforward in an analog transmission system (Figure 1A). With the notch filter out, the rms noise power of the signal inside the notch is measured by the narrowband receiver. The notch filter is then switched in, and the residual noise inside the notch is measured.

The ratio of these two readings expressed in dB is the NPR. Several notch frequencies across the noise bandwidth (low, midband, and high) are tested to characterize the system adequately. Details of early NPR test equipment and the measurements can be found in Reference 4. NPR measurements on ADCs are made in a similar manner, except the analog receiver is replaced by a buffer memory and an FFT processor which performs the calculations as shown in Figure 1B. There are some cases where the combined FDM signal is converted to digital with an analog to digital converter (ADC), transmitted, and then converted back to analog using a digital to analog converter (DAC) at the receiver. In this case, the analog method shown in Figure 1A is used in performing the NPR test.