LabVIEW Communications System Design Suite
IQ sample rate intuition in USRP transmitter
Hi Ferdoon,
I think the simplest way to describe this is with a picture:
This picture represents the bandwidth of the baseband signal. The symbol fs is the IQ Sample Rate. There are several meanings to bandwidth; you are familiar with the one used in data communication but for RF signals the bandwidth refers to the width of the box above. As the picture implies, your bandwidth is 0.8 times the IQ rate. Since I and Q are used to describe the baseband signal before it has been mixed with the carrier signal (or after it is downsampled by the receiver) the IQ bandwidth is essentially the baseband bandwidth. The bandwidth dictates the signals you can transmit or receive. Lets say you have a 10 MHz sinewave signal and you want to transmit that signal on a 2 GHz Carrier Signal. If your transmission bandwidth is 5 MHz then you will be unable to send the 10 MHz signal. In this case, you need to define a IQ rate, of at least 12.5 MHz in order to output your 10 MHz signal. I think the east way to think about it is your sample rate. If you have 1000 samples, you can output those samples at a rate of once a second, 1000 times a second, 1 million times a second, and so on.
This is a super rudimentary description, but I hope it helps.
Cheers,
Michael
Hi Ferdoon,
This is a good question that is often confused. I want to focus on your original question for the sake of completeness: "what is the definition of IQ sample rate in LabVIEW Communications?"
For the sake of understanding, let's talk about it on the RX side first. A USRP, as a receiver, is basically just taking a RF signal, mixing it down to baseband, and digitizing it. Like with any digitizer, the faster you sample, the more bandwidth you get. Looking at Nyquist's theorem, we need to sample at least 2x faster than the highest frequency we care to measure. So, if we want a bandwidth of 50 MHz, we need to sample at least at 100 MHz. Make sense so far?
So, how does a USRP handle this? Well, there are several quirks that come into play with a SDR. Let's take a closer look at how a USRP RIO works:
In a very simple world, a USRP RIO would mix a signal to baseband, digitize using a ADC, and send the sample to the host. That's not how a USRP RIO works, however! There are several things to take into account. First, a USRP RIO, like most direct-conversion SDRs, takes both in-phase (I) and samples out of phase by 90 degrees, or quadrature (Q) samples. This is where the term "IQ" comes from. There are a whole pile of reasons this is done, many of which I don't understand. But the important thing is that this effectively means that the signal is being sampled twice as fast. That's why the term "IQ rate" is used, rather than "sampling rate". An IQ rate of 100 MS/s is roughly equivalent to a sample rate of 200 MS/s.
But what sets that IQ rate? The obvious answer is that this is set by the sample rate of the two ADCs--one for the I path, and one for the Q path. However, this is not true. The ADCs actually run at a fixed rate--roughly 120 MS/s for the 40 MHz USRPs, and 200 MS/s for the 120 and 160 MHz USRPs. When you set the IQ rate, you are actually setting the rate of the factional decimators in the FPGA. In other words, if you set the IQ rate to 12 MS/s, the fractional decimator will keep 1 out of every 10 samples. This has pretty much the same effect as simply lowering the sample rate of those ADCs.
So, in short, the IQ rate is neither the sample rate nor the Bandwidth, although it is closely related to both. It's the resulting sample rate of the I and Q components of the signal after some DSP has occurred. But roughly, you can calculate the bandwidth by looking at the IQ rate.
Now for a few additional comments:
Another user mentioned that the bandwidth is .8 times the IQ rate. This is a rule of thumb, not a hard and fast law of physics. I have a shaky understanding on the details of this, but I'll do my best: As part of the decimation process, filters are applied in the FPGA that can have an ugly roll-off that cuts into your usable bandwidth. If you have an IQ rate of 10 MS/s, you'll still get 10 MHz of BW, but the edges will have some serious attenuation. Therefore, it's a good idea to oversample by a factor of 1.25 to push the filter roll-off past the edges of the band. This is actually why the max Bandwidth on the USRP 2944/2954 is 160 MHz-- .8*200 MS/s = 160.
You mentioned doing this for transmit, rather than receive. In that case, the situation is the same, but reversed. Instead of downsampling, a fractional interpolator is used to up-sample the signal.
You mentioned symbol rate, rather than sampling rate or IQ rate. I'm also shaky in this area, but I understand symbol rate to be different than IQ rate (and bandwidth), although related. IQ rate is closer to bit rate, rather than symbol rate, since each symbol can be multiple bits. In other words, symbol rate is derived from the IQ rate, based on how many bits are used per symbol.
