In the last blog post, we generated the main beam pattern and calculated the size and location of the antenna’s sidelobes. We saw something like this:
The problem is that those sidelobes point the antenna in different directions. For a transmitter, it means we will radiate energy to undesired locations. And for a receive array, it means that our receive signal will be sensitive to noise and interference that is coming from those angles. So the question is: How do we get rid of those sidelobes?
The most common answer to this question is something called “tapering.” It is fairly easy to implement but it has significant tradeoffs that you’ll see.
Before we get into that, let me explain where this “tapering” concept comes from. Consider an ordinary square wave signal in the time domain. This is called a boxcar, or rectangular, waveform. And in antenna terms, we’d call it “uniform illumination”. The Fourier transform of that square wave is a sin(x)/x function. And then in power terms, we get this thing that looks very similar to the gain pattern that we measured with Phaser: we see a main lobe and a bunch of sidelobes.
Note that the first sidelobe is -13dB down from the peak lobe. To get rid of these sidelobes in the frequency domain, a common solution is to “window” the time domain signal such that it smoothly starts and ends at zero amplitude. Common windows are Hanning, Blackman, Hann, Hamming, etc.
Windowing is done for the frequency domain, but it’s largely the same in the spatial domain of our phased array antenna. If we have a uniformly illuminated antenna pattern, then we will get sidelobes. But if we window that antenna pattern, then we reduce the sidelobes. In antenna terms windowing is “tapering” the power at each element down from the center toward the edge of the antenna.
Here’s an example comparing uniform weighting (that’s what we did above--so every element has the same amplitude) vs a Hamming-weighted amplitude taper:
Let’s Experiment with Tapering
That’s very interesting, but it is even more interesting if we can experience the effect of tapering directly. So let’s do that now! If you have a Phaser board, then open the file called “tapering.py” at this GitHub site.
It’s the same as the previous file we used (“beamsteer.py”), but instead of a uniform gain for each of the 8 elements, we now have the option to put in different gains. You can see that these gains are just amplitude percentages that follow a windowing function:
Here’s the impact if I select a Hamming taper:
So the sidelobes went down: they are now 25 dB below the main lobe’s peak, instead of only 13 dB down. But...that main lobe got a lot wider. And the peak gain was also reduced. Both results are not good – the whole reason that we make an array of thousands of antenna elements is to have a narrow beam and high gain. So we helped one problem, but we did so at the expense of other key metrics. It’s a true engineer’s dilemma. Just for fun, try other amplitude weights and see if you can generate your own taper that has some better optimization of sidelobes.
Hopefully, this blog provided you with a hands-on introduction to sidelobe reduction using amplitude tapering. How to optimize the reduction of sidelobes while preserving beamwidth and gain is a huge field of study. And many other sidelobe suppression schemes are used—with some being wildly complicated! But this amplitude tapering is the most straightforward, and probably the most widely used. For more information, you can check out this article series:
It’s also where I grabbed the windowing explanations above—many thanks to my co-authors Pete Delos and Bob Broughton for their great insights into these topics. And if you want to see hands-on demonstrations of tapering, or any of these other blog concepts, in action, then check out the videos posted here:
In the next blog, we’ll explore another very interesting concept: grating lobes. It is a bit of a weird topic, but it’s a big deal in phased array antenna design. We’ll use the Phaser kit, and a bit of programming, to create and see real antenna grating lobes. It’s pretty cool, and we’ll walk through it all in the next post.