Statistical description of non-coherent automatic gain control

Abstract

In many systems the Automatic Gain Control (AGC) is an important system function prior to Analog-to-Digital Conversion (ADC), for instance. This paper analyses the tracking performance of noncoherent AGC's. The gain fluctuation is described by stochastic differential equations. For typical operational cases the physical probability density functions of the AGC gain variation are compared with different approximation techniques, i.e. the Fokker-Planck (F-P) approach and the assumption of Gausaian distributions; the limitations of the approximation methods are emphasised. Problem StatementIn digital systems the Analog-to-Digital Conversion (ADC) is one of the key functions. As an example from telecommunications, the IF sampling configuration has become an interesting receiver design alternative which allows for significantly simplified hardware and eliminates DC offset problems often imposed by unballanced mixers in quadrature channel receivers. ADC with low precision, i.e. small number of bits, can be applied to bulk procesaing of fast signals, e.g. in applications. where integration is involved over many samples at some stage after conversion.In many systems the input power to the ADC circuit is maintained constant by a wideband non-coherent Automatic Gain Control (AGC). Particularly in coded systems (with low Eb/N.) any variation of the input loading can impose significant degradations of the effective coding gain. In these systems precise gain control is essential; this requirement goes along with the need for proper choice of the operating point and precision of the ADC device. Trade-offs are often required for the conflicting requirements of fast AGC response and of precise AGC tracking.The m signal amplitude at the AGC output depends on the AGC tracking performance and on the distribution of the AGC control signal which determines the gain of the amplifier stages along the receiver IF chain. In order to quantify the degradrations due to quantization and saturation effect8 [8], [lo] imposed by the ADC and to select properly the ADC operating characteristics, the probability Both orthors om with the 133 density function (pdf) must be known for the rma amplitude variation at the AGC output. AGC System AnalysisThe input signal R ( f ) to the AGC is assumed to be R(t) = r n c o s ( w , t + m(t)) + n(f) (1) with wc = 2xfc for the radian frequency; m(t) represents a baseband phase modulating process and P is the signal power. The additive Gaussian bandpass noise n(f) has spectral density No and is of bandwidth (2B,) Q: fc. The signal-tonoise power ratio is defined by (2) P P N No.(2&) . a = -= Z(t) t m AGC Loop -Detector Filter Figure 1: Model of Non-Coherent AGC Loop.The non-coherent AGC in Fig. 1 controls the amplifier stage according to an exponential gain characteristic such that the output power is maintained constant, i.e.The gain Go can be calibrated that for z = 0 the AGC output power equals a desired value for a given total input power. It is straightforward to obtain from Fig. 1 the AGC detector output si...

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