## Introduction to beamforming

It is a property of signals to interfere with each other when they share the same frequencies, the same (or almost the same) propagation direction, and the same polarization. Signals can cancel out with destructive interference and sometimes (partially or totally) add up with constructive interference. Beamformers use this property to create spatial filtering devices that can aim the transmission or reception of signals in a specific direction.

The word “beamformer” suggests that beams are created and that beamforming only aims its transmission at one target. However, this is not always the case as selective reception can also be called beamforming. That being said, in order to simplify our explanations, we will consider only the directional emission of waveforms.

At its heart, beamforming involves the installation of many antennas (an array). For matters of simplicity, we’ll consider a purely sinusoidal wave, but the following ideas also apply to non-sinusoidal waves as they may be decomposed in a sum of sinusoids by Fourier analysis. If there is no phase difference between the signal emitted at each antenna and if the emitting frequency and amplitude are all equal, the electromagnetic waves will sum up to give twice the amplitude at some points in space where the distance travelled by each wave front will be equal or different by exactly one cycle (2π radians). It will also sum up at other points in space where the distance travelled is such that the value of both signals is of the same sign at a given time and will cancel out partially at some points where the values differ in sign. It will completely cancel out where the distance causes a phase-shift of half a period (π radians) between the signals. From this, a radiation pattern such as the one shown in Figure 1 can be traced. Figure 1 shows the field strength as a function of the direction relative to the emitting antenna.

Figure 1: Example of a radiation pattern (Wikipedia)

Now, if we introduce a known phase shift between the signal emitted at each antenna without changing any other parameters (e.g. frequency), we will obtain a different radiation pattern. We can thus control the radiation pattern by modifying the phase shift between different antennas. A 4-element antenna array is shown in Figure 2. This array introduces an equal phase shift between its antennas. Antenna 1 has 0 phase-shift, antenna 2 has 1.5λ phase shift, antenna 3 has a 3λ phase shift and antenna 4 has a 4.5λ phase-shift, where λ is the wavelength of the emitted signal. All the elements on the array are distanced by λ/2. By combining these two parameters (distance and phase-shift), one can find the radiation pattern of the array.

Figure 2: 4-element 1.5λ separated by λ/2 distances

An approximate radiation pattern of the antenna array (neglecting the side lobes that would normally occur) is shown in Figure 3. We can see that it represents a “beam” as the emission is highly directional.

Figure 3: Approximate radiation pattern of a beamforming antenna array

Hence, beamforming requires highly controllable phase shifts. If we are trying to have two antennas radiate perfectly in phase and we get a phase noise of 1.5λ, we may have a very random and unreliable radiation pattern. In the subsequent parts of this blog post, we’ll go over some common error sources and explain some techniques to avoid them.

## Why use beamforming?

Now that we’ve explained beamforming, what are its applications? As we said previously, we can use beamforming techniques in both transmission and reception. In transmission, beamforming has applications in cellular telecommunications and is used in some cellular phone standards. In these applications, the available spectrum is often very limited. Beamforming techniques can be used so that communication to the devices of multiple customers can be achieved on the same frequencies. Normally, interference would occur but if beamforming is used, it is possible to steer the beams in a way the signals will not interfere. In the same way, beamforming techniques may be used in reception to eliminate interfering signals by performing spatial filtering. If the listener knows the direction of the signal’s source, the reception may be tuned so that it rejects signals coming from other directions.

Beamforming techniques can also increase the total distance when using the same radiated energy, as the energy will be concentrated towards a determined direction instead of being radiated in random directions (where the energy would simply be lost). Many other applications of beamforming are used in other fields, including radar, sonar, seismology, radio astronomy, acoustics, and biomedicine.

## What affects beamforming?

Jitter, clock skew, phase noise and channel crosstalk are phenomena that arise in digital systems and may affect beamforming applications. They reduce the reliability of the system’s equipment in terms of signal phase and frequency. In this part of the blog post, I will talk about these phenomena and how Nutaq designs its products to minimize their effects.

### Phase noise

“In signal processing, Phase noise is the frequency domain representation of rapid, short-term, random fluctuations in the phase of a waveform, caused by time domain instabilities (“jitter”). Generally speaking, radio frequency engineers speak of the phase noise of an oscillator, whereas digital system engineers work with the jitter of a clock.”

Wikipedia

Noise on a channel may be seen as a phase vector (phasor). It has a magnitude and a phase just like any other signal, but both are random and may only be represented using a probabilistic approach. The amplitude of the noise will affect the amplitude of the channel’s signal. The phase of the noise will change the phase and/or frequency of the channel’s signal.

Consider the following noise free signal:

v(t) = Acos(2πf0t).

Phase noise is added to this signal by adding a stochastic process represented by φ to the signal as follows:

(t) = Acos(2πf0t + φ(t)).

Wikipedia

If we add a function of the variable t in the argument of the cosine function representing the signal, we may affect both phase and/or frequency. For a better understanding of phase noise, refer to the Wikipedia article and its sources.

The point here is to underline this phenomenon as something that can affect applications like beamforming and to point out that Nutaq’s acquisition cards provide a solution to this problem. The clock oscillator used on Nutaq’s MI125 acquisition board is a CCHD-575 from Crystek. Its typical phase jitter is 82 fSec RMS at 100 MHz and its phase noise floor is just -168 dBc/Hz (which is very low). This enables Nutaq’s MI125 to be used in highly demanding applications like beamforming that require ultra-low phase noise.

### Clock skew

Digital signals are sampled at a rate determined by the circuit clock’s frequency. Clock skew is a quantity used to characterize the delay between the time a clock signal is received by two separate registers. If the clock is not received by all the registers at the same time, there may be a phase shift in the transmitted or received signal that was not in the original signal. Nutaq’s clock tree uses the ICS8535 fanout buffer to minimize clock skew and deliver high performance in highly demanding applications.

### Crosstalk

Channels are not perfectly isolated; a signal from one channel may be partially transmitted to another. This can affect the phase, frequency, or amplitude of the signals. For example, if the phase is changed by some random value on one channel, then (following what was said in the previous sections), the radiation pattern may be modified by the crosstalk.

Because crosstalk is an undesirable phenomenon, Nutaq designs its products in ways to minimize its effects. Nutaq performs testing that measures the crosstalk between adjacent channels and between the more distant ones (i.e. channels 1 and 16). For the MI125, adjacent channels have a typical crosstalk of 64 dBFS and more distanced channels have a typical crosstalk of 86 dBFS.

Nutaq’s products are conceived with precision in mind and offer features like Edge Rate Contact™ breakout SMA cables. The cables, available with the MI125 acquisition board, have a known length, thus ensuring a very high accuracy when uses in the most demanding applications like beamforming.

## Conclusion

In this post, we introduced beamforming and we discussed phenomena that occurs which may affect the reliability of beamforming systems. We also listed the specifications that make Nutaq’s boards ideal for use in beamforming applications.