# Simplify Receiver Characteristic and Performance Tests

Noise is an unwanted signal that affects both transmitter and receiver performance in communications systems. It degrades both the modulation quality of a transmitter and the sensitivity of a receiver. As an R&D engineer, your goal is to eliminate as much noise in electronic devices as possible.

However, to simulate a realistic environment you may need to inject a “noise” signal into your design. The noise signal needs to express simple and traceable mathematical models. The Additive White Gaussian Noise (AWGN) is the most common noise for a receiver performance test. In this post, you will learn about the AWGN and how to correctly and accurately apply AWGN to your desired signal for a receiver performance test.

## What is AWGN and Why Is It Important?

Noise is part of all communications channels. The Shannon-Hartley theorem below tells you the maximum rate at which information can be transmitted over a communication channel with a specified bandwidth within the presence of noise.

C = B * Log2 (1+S/N)

where

C is the channel capacity in bits per second.
B is the signal bandwidth in Hz.
S is the average received power over the bandwidth in watts.
N is the average power of the noise over the bandwidth in watts.

To simulate realistic channel condition in a repeatable manner, you need to add random noise to the wanted signal. AWGN is a mathematical model that is used to simulate the channel between the transmitter and receiver. The model is a linear addition of wideband noise with a constant spectral density and a Gaussian distribution of amplitude. AWGN doesn't apply to fading tests, intermodulation, and interference receiver tests. For example, for LTE Evolved Node B (eNB) receiver tests (3GPP TS 25.141) you need to apply AWGN to the LTE wanted signal for eNB dynamic range test in section 7.3 and all non-multipath receiver performance test cases in clause 8. Figure 1 illustrates a common receiver performance test setup. The first signal generator outputs the wanted signal and the second generator generates the AWGN. Use a hybrid combiner to combine the signals and connect to a device under test. Make sure the isolation between the two signal generators is good enough so that they won’t impact the other unit’s automatic leveling control (ALC) operation.

Figure 1. Measurement system set-up for receiver dynamic range test

The signal generators need AWGN generation capabilities for receiver tests. Figure 2 depicts the bandwidth and power between the carrier (wanted signal) and AWGN. Carrier bandwidth is the occupied bandwidth of the carrier and the noise bandwidth is the flat noise bandwidth. The actual flat noise bandwidth should be slightly wider than the carrier bandwidth (typically 1.6 times of the carrier bandwidth). When you combine the carrier and AWGN signal for receiver tests, the carrier now appears larger because of the added noise power.

When you perform receiver tests, measure the noise power that you observe within carrier bandwidth as shown in yellow in Figure 2. By knowing the noise power value, you can calculate the carrier to noise ratio (C/N). Additionally, most standards use energy per bit over noise power density at the receiver (Eb/No) to characterize their receiver as opposed to C/N. You need to know the carrier’s bit rate in order to do this. Below is the conversion equation for C/N and Eb/No.

(Eb/No) dB = C/N dB - 10 log10 (bit rate/carrier bandwidth)

These additional measurements and calculation make receiver measurements setup more tedious. Luckily, with evolving digital signal processing (DSP) technologies, signal generators can add real-time noise AWGN to the baseband waveforms digitally instead of using two signal generators and a hybrid combiner. This provides an accurate amplitude level for both the carrier and noise signal without additional measurements. You also don’t need to worry about the correction of external accessories. In addition, you can easily select either C/N or Eb/No as the variable controlling the ratio of the carrier power to noise power in the carrier bandwidth as shown in Figure 3.

Figure 3. Setting real-time AWGN on Keysight MXG N5182B

## Fast Setup and Accurate Signal Generation

The receiver measurements for most wireless and wired communication systems require AWGN which helps verify the channel capacity of each system. You can measure receiver characteristics (bit error rate or block error rate) and performance (data throughput) with a traceable and accurate noise signal. A vector signal generator enables you to add AWGN to a carrier in real time. Then, you can easily apply real-time AWGN to the wanted signal using the signal generator’s internal digital signal processing.