Passive Switched Capacitor RF Front Ends for Spectrum Sensing in Cognitive Radios

Table 1

Summary of variables in LTI model.

Variable	Description	Expression
𝐱	Input (16 samples)	𝑥(𝑖),∀𝑖=[0,15],𝑖∈ℤ
𝐧𝐬	Sampler noise	𝜎^2𝑛𝑠,𝑖=2𝑘T/𝐶; 𝐶= capacitance per copy
𝐅	Ideal FFT	1𝐒16^4𝐒3𝐒2𝐒1 (see the appendix)
Δ𝐅	Linear FFT error	See Section 6
𝐅^′	FFT approximation	𝐅+𝚫𝐅
𝐍^′𝐩	Processing noise at 𝑜/𝑝	See Section 6
𝐍𝐪	Quantization noise at ADC 𝑖/𝑝	See Section 6
𝐇	Correction matrix	𝐅(𝐅^′)^−𝟏; see Section 6 and [25]
𝐘^′	Digitized 𝑜/𝑝	(𝐅+Δ𝐅)(𝐱+𝐧𝐬)+𝐍^′𝐩+𝐍𝐪; see Section 6
𝐙^′	Digitized and corrected 𝑜/𝑝	𝐇𝐘^′=𝐗+𝐍𝐬+𝐍𝐩+𝐇𝐍𝐪; see Section 6