References or literature on polar feedback/modulation?

For my thesis, I eventually want to regulate the output power of each element of an array RF power amps (class D/E/F). From what I can tell, this will require a polar feedback/modulation scheme. Despite lots of searching and buying several reference books, I've yet to find any description of this technique beyond a couple paragraphs and a few simple block diagram. I've never seen an actual description of how such a system is designed, specified, or debugged.

Does anyone here have any experience with polar feedback, or know of any resources which are fairly detailed? I'd like to at least have a couple examples to work from before trying it all myself.

Thanks in advance.

If all you are interested in is regulating the output power, why do you think you need polar feedback? You can achieve power control with a simple power sensor.

Most of this work is being done by corporations' research. It will eventually filter out to public.

The primary benefit is to use non linear RF power amps to accomplish high power efficiency linear modulation schemes. Toughest part is having enough characterization of non linear PA and reproducability of the PA to be encompassed by the feedback scheme.

For higher level modulations requiring high linearity and high peak to average power ratios there is often a lot of power consumed in the feedback downconversion scheme that eats up much of the benefit.

Other item of concern is backfeed from other nearby transmitters. For example, cellphones in a convention hall way with two or three other people on their phones within arms length. Good directional coupler helps.

I'm not sure what you mean here. Of course there's some part of the circuit that samples the output power, but you also need a feedback/control loop, and for switchmode amplifiers it has to be polar modulation.
I can definitely see that being an issue for most mobile communication applications where RF power is <1W, but for me I'm looking at >30W so a couple watts of dissipation in the controller isn't a huge deal.
Well this is an expected issue that I assume I'll have to deal with at some point (though it's also an issue with cartesian feedback as well...).

Ok, I simply thought you were looking at controlling the "long Term" average power, not in doing PA linearization work.

There's a fair number of publications on this, and I can dig up some references later. Linear Technology has some receivers that are designed for this


http://cds.linear.com/docs/en/produc...d/2PB_9003.pdf

but I still don't think they are polar Receivers. I haven't seen any publications on Polar Receivers in the past 10 years or so that I've been looking at at this type of stuff. I think all I've seen are IQ receivers for signal linearization. Once you have the signal @ baseband, IQ to polar conversion is pretty straightforward.

I would really appreciate anything.
Right, for the process of down converting and sampling the feedback signals, I can use a more typical I/Q downconversion chain. Once I've sampled that into a DSP that's where the real challenge with polar feedback is. From what I've read, the challenge is getting the phase and envelope information to propagate to the amplifier output with similar bandwidths, which is difficult because the amplifier responds to each one very differently. That's what I can't find any specific info on.

But I'm also on the lookout for off the shelf components to make the RF sampling easier. I'm still not sure what sort of receiver chain I could use for sampling the feedback signal. Part of me really wants to avoid a full analog I/Q downconversion chain (mixers and filters are costly, need power and space, etc) and just directly sample the RF with an ADC and use digital downconversion, but I'm also intimidated by the harsh clock jitter requirements for that approach, and the difficulty of debugging a fully digital process (I'm an analog guy, I need to see things on a scope!).

Any referrals to neat components like that one from linear would be appreciated. Something has a built in mixer (digital or analog), an ADC, and maybe another DDC would be ideal. Fortunately my amp's requirements aren't incredible. My center frequency is just 125MHz, and I only need a control bandwidth of ~1MHz max.

Take another look at that Linear tech link. They have receiver modules that are specifically designed for PA linearization.

Joel Dawson has a book out that's just OK. It's his PhDdissertation with covers, and it does cover PA linearization.

Here are a couple of papers that might help get you some more references.

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 1, JANUARY 2005
A Hybrid Digital/RF Envelope Predistortion Linearization System for Power Amplifiers
Wangmyong Woo, Member, IEEE, Marvin D. Miller, Student Member, IEEE, and J. Stevenson Kenney, Senior Member, IEEE

Radio Frequency Digital-to-Analog Converter
Susan Luschas, Member, IEEE, Richard Schreier, Member, IEEE, and Hae-Seung Lee, Fellow, IEEE

IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 39, NO. 12, DECEMBER 2004

Quad-Band GSM/GPRS/EDGE Polar Loop Transmitter
Tirdad Sowlati, Member, IEEE, Dmitriy Rozenblit, Raja Pullela, Morten Damgaard, Evan McCarthy,
Dongsoo Koh, Member, IEEE, David Ripley, Florinel Balteanu, Member, IEEE, and Ionel Gheorghe, Member, IEEE

You've really hit the crux of the issue, the alignment between amplitude and phase is pretty important, it needs to be done to within a small fraction of a bit to keep your transmit spectral purity. And it's likely to vary across temperature.

There are a lot of publications in JSSC about handset transceiver IC's that are all small signal polar with 0 dBm output power and an external amp, but I haven't seen a lot of higher power amps. Of course, I'm not interested, so I haven't been looking either.

Well that's what they're advertising, but it looks like their receiver modules are just general purpose building blocks for RF chains and don't really have any built-in predistortion functions. Which is fine because I'm not trying predistortion. A couple of their lower end modules might be useful (like the LTM9002) for experimentation though.

One interesting thing linear tech claims is that many of their RF components claim to have very wideband (like two decades) quadrature LO splitters, with very low phase mismatch, but don't rely on dividing the LO frequency. I can't see how they could possibly pull that off, so I'm somewhat skeptical.
Thanks, I will look these up once I'm at work.

Okay, this paper was quite interesting. One thing I realized while reading is that the approach taken to these feedback and linearization schemes is impacted by the type of modulation scheme used. For example, the above paper is dealing with EDGE, which only covers an output power range of 17dB. This is nice for polar modulation, since it avoids severe issues that arise when output power must be controlled very close to zero. But in my application, I have to synthesize shaped RF pulses whose envelope must pass through zero with good fidelity. Naturally this is something that you would want to avoid when developing a modulation scheme, but unfortunately I'm stuck with my requirements. So are there any common modulation schemes that also have to deal with the issue of needing to modulate the envelope down to zero? If so, looking for literature on those would probably be most helpful to me.

Also in the Quad-Band Polar Loop paper, I came across one very interesting line:
I believe that by "spectral requirements" they are talking about the level of the spectral mask. But why would loop bandwidth mismatch affect the resulting EVM and spectral mask differently?

Bummer!
Sounds like you're going to have to do some original research.

Wait a minute: Isn't that exactly what's expected of grad students working on theses?

Hopefully after you publish your thesis we will have such a resource.

Of course, but "original" doesn't mean I need to start from absolute scratch!
Right, but I have to at least convince my advisor that this approach is worthwhile and feasible, which is the main reason I'm looking for literature to review.

There's been plenty of work at lower powers for handsets. Asbeck at UC San Diego comes to mind, as does Green Mountain Radio Research. Earl McCune is also an author you should look up. I've also seen purpose build linearization IC's advertised, but I'm don't recall the vendor name.

Going through Zero for your modulation is going to make things difficult. Typically, modulation signals are defined in IQ space. Doing a Rectangular to Polar transformation is a very nonlinear transformation on the signal. What happens to the magnitude and phase signals it pretty ugly. The clean, well defined bandwidths become very smeared out, and you'll need to figure out what the required modulation bandwidth is for magnitude and phase. In the specific case I was working on, phase was about 3x the IQ bandwidth, and amplitude was about 2x the IQ bandwidth.

These were calculated by using Matlab to generate IQ signals, doing a R->P transformation, and then filtering the Mag/Phase signals, and re-combining them, and figuring out the resulting mask/EVM degradation. Lot's of assumptions were made.

Delay between magnitude and phase is a little tricky to manage, because the signal flow paths are different. A rule of thumb we came up with was that the delay's needed to match to about 1/10 of a bitwidth for the reconstructed signal to not be degraded too much.

If you're starting with a different signal, you're going to have to take a stab at getting the modulation bandwidths and such right, so you can figure out the delay constraints and the linearization bandwidths you'll need to support.

I'm not expecting to find a magic IC that does most of the work for me, finding good building blocks (vector modulators, RF sampling ADCs, quadrature downconverters, FPGAs, etc) is what I'm after. Is there a favorite family of FPGAs for RF chain control or software radio applications?

Right, that's certainly a hurdle. Inevitably, I will have to choose a minimum envelope power inside of which I will either deactivate the phase feedback loop, or shut off the RF power completely, since obviously getting a robust phase measurement isn't practical at very low power.

As far as I can tell, there are two things about my application that set it apart from most communication schemes: First is that the output must cross through zero. The second is that I'm dealing with an array of elements which are mutually coupled. I need to be able to null out the interference from adjacent elements, which is strictly something that open loop predistortion cannot achieve, it requires feedback. And it will likely require significant modifications to the typical polar feedback schemes in which envelope and phase paths are handled separately.

One thing occurred to me while thinking over the differences between polar and cartesian feedback schemes. Suppose you want to traverse the output power 180 degrees about the origin (say from +1 to -1). A polar feedback scheme would try to accomplish this by just modulating phase from 0 to pi, while keeping envelope constant. So the output power would trace a path along the unit circle from start to finish. Contrast this with a cartesian feedback scheme, which would first just modulate the I component from +1 to -1, so the output power would trace a path directly from +1 to -1 along the I axis. Is one better than the other in any respect (control simplicity, output spectrum, etc)? Because in principle there's no reason that a polar modulation scheme couldn't follow the same trajectory as the cartesian one (modulate envelope from 1 to 0, switch phase from 0 to pi, then modulate envelope from 0 to 1), but making a polar modulation system follow that trajectory would require a different feedback technique. I'm wondering if that's an approach worth taking for my application...

I think you choice is Altera and Xilinx. More than that, it's probably dependent on who you can get samples from.Big FPGA's are godawful expensive, there's a lot of silicon there. I was pointing out that it's been reduced to a magic IC as an example of the general state of the technology. It might be worth looking at, just to see what's on the market and what it can do.




So the output power trajectory is really independent of the feedback approach. You can represent each point on that in either IQ or RTheta, and the actual path taken is driven by the modulation bandwidth and filtering requirements for spectral splatter. In the specific example you give, you could use either feedback control method to take either path. A Polar transmitter approach requires control of both the phase and the amplitude of the signal, so you could go through (0,0) with a polar approach as well.

Whether you use IQ or polar feedback control is really driven by the Transmitter architecture. If you're using a IQ based transmitter, then IQ control is the way to go. If you've got a large signal polar transmitter (Wideband Phase modulator with a AM modulation stage after it) then you should use polar modulation. You had mentioned earlier that you were using a class D/E switch mode amplifier, which can be used for Amplitude modulation. But you could also use it simply as a gain stage, and use an IQ modulator to generate the input.