higher than 256 QAM?

[TimS.]

Hello,

I was just wondering if it is possible to do higher than 256 QAM with the PXI-5671 VSG? I noticed that the provided example stops at 256 but I added an entry for 512 and it didn't throw any errors. I haven't done a closed loop modulate/demodulate circuit yet to verify if it was properly generated but I thought I would ask here first.

Also, my DSP knowledge is a bit rusty so if anyone could provide an overview of how the QAM M-ary level corresponds to required bit rates, bandwidth, etc. that would help me out greatly.

Thanks,

Tim S.

[Matt_A]

Hello Tim S.,

If you examine the MT RFSG Generate QAM.vi example (which is the example I assume you are referring to), you will note that the QAM M-ary control is wired to the Modulation Toolkit VI to generate the QAM system parameters (MT Generate QAM System Parameters.vi). This VI creates the system parameters for the QAM modulation scheme in software and does not directly interact with the PXI-5671, so there is no dependence on the device for the number of constellations in your modulation scheme. However, the MT Generate QAM System Parameters.vi function is only built to accept powers of 2 from 4 to 256 for the M-QAM parameter.

In regards to your question about constellations versus bit rates and bandwidth, I would direct you to an example program which demonstrates some key concepts about this topic. The RF Simulation Demo: QAM Symbol Mapping example discusses how to convert number of constellations to bits. It states:

"the number of bits that can be represented by a symbol has a logarithmic relationship to the M-ary.  For example, we know that 2 bits can be represented by each symbol in 4-QAM.  While this makes sense intuitively, it is actually defined by the equation shown below:

Bits per Symbol = log₂ (M)

Thus, using the equation above, each symbol in 256-QAM can be used to represent an 8-bit digital pattern (log₂ (256) = 8).  Because the M-ary of a QAM modulation schem affects the number of bits per symbol, it has a significant affect on the actual data transmission rate."

We can make the association between bit rate and symbol rate by looking at the number of bits per symbol of our modulation scheme. Suppose, as discussed above, we were using a 256-ary QAM scheme in which each symbol represents an 8-bit digital pattern. If we wish to transmit data with a bit rate of 1 MB/sec, then we would need a symbol rate of 1 MSymbol/sec. We can determine this value through the following calculation:

(1 MB/sec * 8 bits/B) / 8 bits/Symbol = 1,000,000 Symbols/sec

or, generally:

bit rate / bits per Symbol = Symbol rate

I hope this was the kind of information you were looking for. If you have any other questions or if you would like further explanation on any of these topics feel free to post back to the forum and let us know.

[TimS.]

Hi Matt A.,

First off, thank you for that very informative reply. It was indeed what I was looking for and it was very helpful.

Second, besides going higher than 256 QAM I am also trying to determine the maximum data rate I could accomplish using the PXI-5671 generator. There are many variables which affect it though so I guess it would be a trial and error test. The PXI-567 can do 100MSamples/sec, with 20MHz bandwidth, and the software default resampling is 16 samples/symbol but it can be varied. I was wondering if anyone has determined a mathematical equation that incorporates QAM Symbol Rate (based on the equations you stated), IQ samples/symbol, and PXI-5671 Sample rate as well as taking into account any effects of aliasing or oversampling? I think that would be the only way to figure out the maximum data transfer rate of the PXI-5671 hardware.

-T.S.

[Matt_A]

Hello Tim S.,

As you stated, there are multiple factors that go into determining the maximum data rate. Using the following parameters, I was able to determine an estimate of the theoretical maximum bit rate for the NI PXI-5671:

Symbol Rate: 20 Msymbols/sec (limited by bandwidth of upconverter)
Digital Modulation Scheme: 256-ary QAM (highest number of symbols allowed by Modulation Toolkit)

From these settings, I derived the following equations:

For QAM each symbol represents n bits where 2^n=number of symbols (M-ary), therefore for 256-ary QAM, each symbol represents 8 bits (2^8=256).

So, at a maximum symbol rate of 20 Msymbols/sec we have a data rate of:

20 Msymbols/sec * 8 bits/symbol = 160 Mbits/sec or 20 MB/sec

Again, I want to reiterate that this is the theoretical limit on the bit rate. Several factors could limit rate, including environment, channel impairments and receiver performance can all affect the maximum realistic rate you can obtain. I would also note that with a symbol rate of 20 Msymbol/sec you would be looking at 4-5 samples per symbol since the maximum IQ rate of the card is 100 MS/sec. I would be very weary of the ability to represent 256 distinct constellations (for 256-ary QAM) with only 4-5 samples. That being said, I think a more important question to ask would be what rate you need to attain and what your channel is going to look like. Is there a reason you are specifically only interested in the maximum data rate?

[TimS.]

Hi Matt A,

No there is no reason that I'm specifically interested in maximum data rate only. It was more of a curiousity. I also may have a future requirement for a high data transmission rate 256-QAM signal and I just wanted to get some background on the basic equations and variables involved. You have been great in explaining those to me.

I agree that being able to generate and receive a 256-QAM constellation with only 4-5 samples/symbol is pretty unlikely. The environment in which I would be doing this in would most likely be a noisy RF environment with many different antennas and possible interferance. Not that I know what antennas I'm using yet but the channel bandwidth of them will most likely be my biggest limitation in acheiving a very high data transmission rate. If the requirement for it ever pops up I will probably just to do a study on Bit-Error-Rate vs. data rate in order to figure out my real world limitation.

Thanks,

Tim S.

[Matt_A]

Hello Tim S.,

I'm glad I could help with the bit rate vs. symbol rate analysis. The only reason I was careful to ask about maximum bit rate is that I wanted to be sure that it was clear that this is a theoretical maximum and not necessarily practical. It sounds like you've got your application pretty well thought out, and I agree that performance analysis (like bit error rate) is probably the best way to determine the practical limitations of your test configuration. Good luck with your development and feel free to let us know if you have any other questions.