0.14 Mix’n’match receiver design  (Page 6/9)

There are many factors that contribute to the recovery error, including the following:

• Residual interference from adjacent FDM bands (caused by imperfect bandpass filtering before downconversionand imperfect lowpass filtering after downconversion).
• AGC jitter (caused by the deviation in the instantaneous signal from its desired average and scaled by the stepsize in theAGC element).
• Quantization noise in the sampler (caused by coarseness in the magnitudes of thequantizer).
• Round-off noise in filters (caused by wordlength limitations in filter parameters andfilter algebra).
• Residual interference from the doubly upconverted spectrum (caused by imperfect lowpass filtering after downconversion).
• Carrier phase jitter (occurs physically as a system impairment and is caused bythe stepsize in the carrier recovery element).
• Timing jitter (occurs physically as a system impairment and is caused bythe stepsize in the timing recovery element).
• Residual mean squared error left by the equalizer (even an infinitely long linear equalizer cannot removeall recovery error in the presence of simultaneous channel noise and ISI).
• Equalizer parameter jitter (caused by the nonvanishing stepsize in the adaptive equalizer).
• Noise enhancement by the equalizer (caused by ISI that requires large equalizer gains, such as a deep channel nullat frequencies that also include noise).

Because M atlab implements all calculations in floating point arithmetic, the quantization and round-off noise in the simulationsis imperceptible. The project setup presumes that the AGC has no jitter.A well-designed and sufficiently long lowpass filter in the downconverter can effectively removethe interference from outside the user band of interest. The in-band interference from sloppy adjacent FDM signals shouldbe considered part of the in-band channel noise. This leaves carrier phase, timing jitter, imperfections inthe equalizer, tap jitter, and noise gain. All of these are potentially presentin the ${\mathcal{M}}^6$ software-defined digital radio.

In all of the cases in which error is due to the jiggling of the parameters in adaptive elements (in the estimation of thesampling instants, the phase errors, the equalizer taps), the errors are proportional to the stepsize used in the algorithm.Thus, the (asymptotic) recovery error can be made arbitrarily small by reducing the appropriate stepsize.The problem is that, if the stepsize is too small, the element takes longer to converge.If the time to convergence of the element is too long (for instance, longer than the complete message),then the error is increased. Accordingly, there is some optimal stepsize that is large enough to allow rapidconvergence yet small enough to allow acceptable error. An analogous trade-off arises with the choiceof the length of the equalizer. Increasing its length reduces the size of the residual error.But as the length grows, so does the amount of tap jitter.

Such tradeoffs are common in any engineering design task. The next section suggests a method of quantifying thetradeoffs to help make concrete decisions.