# BPSK using carriers other than sinusoidal wave

I am currently a student in communications & electronics engineering undergrad working on a small project employing Direct sequence spread spectrum. For simplicity and since I am using TTL level gates I have used XOR gates as mixers. After spreading the data with the PN CODE, using a second XOR gate with square wave (2MHz toggling between logic high 5V and logic low 0v) carrier which in principle should give BPSK signal.

The thing is my professors who are evaluating the project refuses this concept claiming that the carrier must be sinusoidal in order to generate BPSK signal. They even claim square wave doesn’t have a phase and therefore cannot be switched 0 and 180 degrees!

Now are they correct in their saying?, and if not how to convince them otherwise since all text books seem to explain BPSK using sinusoids as it’s easier for calculation.

If someone has seen a book that explains this in detail please mention it!

Attached below is the circuit and description taken from ARRL spread spectrum source book.

## 1 Answer

### Preface

I'd agree with your professor here: The output of this (really a bit old-timey) circuit is chips of a DSSS signal, with a chiprate of 2Mchip/s and a spreading factor of 1000: The PN sequence generator runs at 2 MHz, and gets kind-of-mixed with a 2 MHz square wave. It's arguable whether there is a 2 MHz carrier or whether this is more like a Manchester system.

The following answer will go into a few "side tracks" here and there. This is intentional – I do a little "concluding, you need to…" list below, and I think it's going to be very helpful for you to understand what is happening to solve the problems your professor (and physics) has with your approach!

So, don't be scared by the wall of text, take it one paragraph at a time.

### What's wrong with the approach

The article is a little confusing (especially to an undergrad!) in its usuage of the word "carrier": the thing you have in your schematic, I'd call a "chip clock", not a "carrier". If you mentally replace all the occurrences of the word "carrier" in this article with "chip clock", I think it becomes easier to understand!

I'd understand this is a baseband signal, where the spread signal is toggled with the 2 MHz clock; "putting it to an antenna" might only work, because the (approximately) rectangular waves produced by this system have such steep edges that you get harmonics at every odd multiple of 2 MHz. Sure, an amplifier/antenna system might be designed just so that it selects one of these harmonics, but the text doesn't mention that, so I'd conclude: this is not a BPSK-DSSS system.

(In the rest of the article, he describes that he also transmits the carrier separately, which of course doesn't happen in a real DSSS system. An actual receiver would have to reconstruct the carrier from the received signal first. So, as you can see, this is just "half" a receiver, and you only have a schematic of "half" a transmitter – the RF part is missing.)

Looking closely: because they alternate between 0 and some logical high, they are not BPSK chips, either, but OOK chips.

So, at the very least, you'd need to take the output of U8C, and remove the average from it, to convert it from an OOK-signal to a bipodal signal. You might then call it BPSK-modulated chips and you'd want to do that before mixing up, as otherwise you'd get something like DSSS with an unsupressed carrier – that's not something you want.

Then you still need to mix this 2 MHz wide signal up to a carrier that's >> 2 MHz. Not hard to produce such a carrier – you can, as briefly mentioned above, just isolate one of the higher harmonics of your 2 MHz clock (output of U3A), for example the 9th harmonic at 18 MHz.

You could do the average-removal after your mixing, but sadly, your baseband signal has the same sharp harmonics, but due to the spread-spectrum nature of that signal, they are going to be hard to remove from intermodulation products. So, if you want your transmitter to be legal, you'll have to apply a better pulse shape than the rectangle that you currently have. Luckily, that shape doesn't have to be very pretty for an undergrad project – so just remember that pulse-shaping is used to limit the bandwidth of a signal to the channel bandwidth, and choose the kind of electronic thing that limits bandwidths to frequencies below a specific cut-off frequency.

You can then mix the two – and using a chopper mixer is exactly as valid as using any other other mixer, but don't forget that you're not aiming for OOK, but BPSK!

### What to do about it

So, to not spoil your project with doing your work for you, concluding, you need to find a solution to the following technical challenges:

• remove the average from your 2 Mchip/s signal
• isolate the 9th harmonic (or some other) from your 2 MHz square wave to get a carrier that is much higher in frequency than your signal is wide (which is what we usually teach in undergrad wireless communicatiosn), and sinusoidal
• pulse-shape your average-removed 2 Mchip/s with the mentioned system that only lets through signal up to a cut-off frequency.
• mix the result of these two

### What to think about it

As a general remark: Things will get nicer, more intuitive in your studies. Old ARRL literature really isn't that good, mathematically, on most things digital, and for some reason you have been given a very old article.

Also, and I don't mean that negatively, ARRL literature like that targets amateurs in radio, and you're educated as a professional: there's probably a rift between what you've been taught at uni and how things are displayed in the article!
And honestly, in the 1970s/1980s, from which the technology in this article is, things were much harder than they are today. (This is an American ham/amateur radio text from the early 1990s, so the technology being used being 20 years old at the point of publication is kind of (sad but) "usual". DSSS only became legal, and even then, just under technically "stupid" constraints, to use somewhen in the mid-1980s. So, there was not yet "established" ways of talking about these things among hams, which is probably the reason that terminology is a bit different than I, as someone educated in the 2000s/2010s have, would have used. The rest of the book chapter you have at hand does have very advanced things inside – the whole synchronization on the receiver side, you'll find, is the actual hard part about DSSS, together with equalization. The Chapters 9 and the appendices are way more theoretical than your article, and that's rare in amateur "mass" literature: it highlights how much research went into DSSS in amateur radio circles back then. 34 years later, this is already very mature technology.)

You could do all the things on your schematic in a single microcontroller that costs less than a sandwich, in software. Generally, the progress in technology allows communications engineers to implement systems like BPSK-DSSS in a much more "textbook" way, so like you've learned it in the lecture or the literature of why DSSS works, because we're no longer restricted to logic elements to generate binary signals (most of the time, we can just use a DAC with many more levels than just 2!).

So, enjoy the fact that you can use this undergrad project to learn the theory right now that you'll be able to use later on; very little radio equipment design these days will require you to design logic level circuits! It's great that you get to experience what a harmonic of a square wave is right now. My guess is that your professor wants you to research exactly that, which is why they let you work on this with logic level elements. Do that! You really want to explain in your report for this project why you could just use a harmonic as carrier, you'll want to go into how the spectra of your signals look at different points (after all, this is a spread spectrum project, so you should probably draw a couple spectra! I think especially the spectrum of your "CA" signal and the signal after extracting the 9th harmonic is something you should show, explain. After all, you've gotten criticized for the shape of your "carrier", so that's important to put right!), and I'm very happy that you say you spoke to your professor and they rejected your approach; that's a harsh thing to experience, but it also tells you that technical rejection can be a good thing when you can communicate about it.

• Thanks for the detailed explanation! It will definitely be helpful 👍 Apr 20 at 14:21