The Improvement of Envelope Detector Performance Through the Use of a Nonlinear Transformation

In the design of many digital receiver systems, practical design considerations may dictate the use of envelope detectors and RC integrators. This paper analyzes the improvement which can be gained by the insertion of a nonlinear transformation between the envelope detector and the RC integrator. The characteristic curve of the optimum nonlinear transformation is determined and is found to yield an improvement of approximately 2.5 dB over the range of operating conditions analyzed. The form of the optimum transformation is
y=\frac{K_{0}}{K_{2} + I_{0}\frac{x}{\sigma\sqrt{2_{\gamma}} + K_{1}
where K
0
and K
1
are arbitrary constants and K
2
depends on the input signal-to-noise ratio γ and where σ
²
is the noise power at the input to the envelope detector. The performance of a suboptimum nonlinear transformation composed of a two-level quantizer (e.g., Schmitt circuit) is also analyzed and is found to yield a 1.5 dB improvement when adjusted to give the best performance. The best performance is achieved over a wide range of operating conditions when the threshold of the two-level quantizer is adjusted so that noise alone would cause a quantizer output of "one" 15 per cent of the time and "zero" 85 per cent of the time.