Doppler shift affects wireless communications by creating fading in the signal. Fading is unpredictable attenuation that occurs at undesired space and time coordinates. As fading caused by Dopper shift is undesirable, signal processing algorithms attempt to avoid it by estimating it and correcting the waveforms.

## What is Doppler shift?

Doppler shift occurs when the transmitter of a signal is moving in relation to the receiver. The relative movement shifts the frequency of the signal, making it different at the receiver than at the transmitter. In other words, the frequency perceived by the receiver differs from the one that was originally emitted. It’s easy to understand and observe this phenomena with sound waves. A good example is the sound of a race car that passes by you. When the car is getting closer, the sound has a higher pitch. When the car passes you and starts going away, the pitch suddenly becomes lower.

This occurs because the source emits sound waves at a constant frequency but as it moves toward the observer, the distance between the waves in the signal becomes shorter. The waves travel at a speed v and are emitted at a frequency ƒ (cycles/seconds). In our example, the emitter has moved a distance of d towards the receiver between the emission of two succeeding cycles. The cycles thus arrive at the observer at a frequency higher than the emission frequency. The opposite applies when the transmitter is moving away; the distance between each peak (or cycles) increases, and since the wave is moving at the same v speed, the perception of the observer is that the frequency has diminished.
The same effect also applies to electromagnetic waves. The analysis is different because electromagnetic waves do not propagate in a substrate and their speed does not depend of a frame of reference (thus they require a totally different approach for their study). However, the base concept is the same: a frequency shift is caused by the speed of the transmitter in relation to the receiver.

## What is fading and what causes it?

In telecommunications, fading is an important concept related to Doppler shift. Fading is when attenuation appears unpredictably at undesired space and time coordinates. In other words, the signal is lower in amplitude at the receiver, which causes transmission problems. In the case of the Doppler shift effect, fading is due to multipath propagation.

Figure 1: Multi-path propagation

In multipath propagation, the signal reaches the receiver by two or more paths. A potential effect is fading due to destructive interference between phase-shifted signals arriving from different directions. Multipath causes jitter and ghosting in facsimile and television transmissions. This effect can also occur in radar processing and digital radio communications. In GSM, errors are due to intersymbol interference (ISI) (some ways to correct for this include orthogonal frequency division multiplexing (OFDM) and rake receivers).

Some fading also arise when the Doppler shift between two signals are different due to multipath propagation. The relative speed of a moving source is different for different objects located at different places. For example, if the transmitter was moving in Figure 1, it would move with a different speed (different magnitude) towards the wall on which the signal bounces than it would move towards the receiver. The frequency shift of the two signals (the one that goes directly to the receiver and the one that bounces off the wall) would then be different. The difference between the Doppler shifts in signals coming from the same transmitter and using two different paths is called the Doppler spread. In a way similar to the phase-shifted signals that cancel each other by destructive interference, the frequency-shifted signals interfere and create fading.

## How to avoid Doppler spread

To avoid Doppler spread that causes fading, we must predict its effect and correct the signals accordingly. A lot of research is going on in the field of algorithms to enable the prediction and correction of waveforms. Some research activity, aimed at SISO-OFDM and MIMO-OFDM Doppler shift estimation, uses machine-learning algorithms (http://spectrum.library.concordia.ca/976552/). The main idea is to estimate the Doppler spread by using inputs such as emitter velocity and target distance and then correcting the waveform accordingly. Other research looks at obtaining a better knowledge of Doppler shift effects in modern wireless transmission and how to avoid it (http://goo.gl/NNLFxT).

## Research platforms

Nutaq’s PicoSDR2x2 and PicoSDR4x4 are MIMO-enabled platforms with up to four receive and transmit channels, ADCs, DACs, down-converter hardware, and a Virtex-6 FPGA for signal processing. The PicoSDR2x2E even has an embedded Intel quad-core i7 processor for high-level C-based processing and algorithms. This makes the PicoSDR an ideal platform for research in the field of Doppler effect estimation. The INRS (Institut National de la Recherche Scientifique, or National Institute for Scientific Research) based in Montreal, recently bought a platform for research on Doppler effect estimation and are planning to acquire another one.

This blog post introduced Doppler spread and related concepts. It also briefly discussed the research aimed at the estimation and correction of fading caused by it and explained how Nutaq’s research platforms can help facilitate it.