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how to assume the single bit quantizer's gain

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finfoun

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We all know the single bit quantizer's effective gain is determined by it's input 'y'(see Schreier's book <Understanding Delta-Sigma Data Converters> Page28 formula 2.5) .But when we design the NTF and STF of SD modulator with single bit quantizer,how to assume the gain of quantizer's gain?Because the gain actually has something to do with the modulator's input signal,we can not predict it preciselly before we could simulate the modulator.
But interestingly when the modulator have been designed with assuming the gain of quantizer to be 1,the gain calculated by simulation seems to track the desired value. Could anyone tell me why?Thanks very much!!
 

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