Method and apparatus for reduced power consumption ADC conversion
View Patent ↗A method for conversion of signals between analog and digital characterised by; applying a non-linear transfer function to an input signal, such that the relation between the quantisation levels of the converter and the input signal vary as a non-linear function of the magnitude of the input signal. The non-linear transfer function is related to the probability density function of the input signal so that larger quantisation bins of the converter correspond to less probable values of the input signal.
1. A method for analog to digital conversion (ADC) comprising:
applying a non-linear transfer function to an input signal such that the relation between the quantisation levels of the converter and the input signal vary as a non-linear function of the magnitude of the input signal,
the non-linear transfer function being related to an at least approximate measurement of probability density function ‘p(x)’ of said input signal so that larger quantisation bins of the converter correspond to less probable values of the input signal,
wherein an application of the non-linear transfer function to the input signal includes iteratively updating the relation between the non-linear transfer function and the measurement of probability density by updating quantisation levels.
2. A method according to claim 1 for analog to digital conversion in a programmable non-linear analog to digital converter, wherein the iterative relation can be ongoing, periodically re-started or used once during an initialisation period.
3. A method for analog to digital conversion (ADC) comprising:
applying a non-linear transfer function to an input signal such that the relation between the quantisation levels of the converter and the input signal vary as a non-linear function of the magnitude of the input signal,
the non-linear transfer function being related to an at least approximate measurement of probability density function ‘p(x)’ of said input signal so that larger quantisation bins of the converter correspond to less probable values of the input signal,
wherein an application of the non-linear transfer function to the input signal includes iteratively updating the relation between the non-linear transfer function and the measurement of probability density by updating quantisation levels,
wherein the non-linear transfer function is applied by predefining quantisation levels according to an optimisation process utilising said non-linear transfer function, and wherein for analog to digital conversion in a programmable non-linear analog to digital converter, the optimisation process for predefining quantisation levels reduces a global mean squared quantisation error determined by a cost function for the process, J, being a function of input value probability density function p(x) and the quantisation error for a given quantisation level a i of corresponding quantisation bin {b i ,b i+1 }, N quantisation levels {right arrow over (a)}=(a 0 , . . . , a N−1 ) T so being updated to reduce the global cost J tot , said global cost being a sum of J over N selected quantisation bins, N quantisation levels {right arrow over (a)}=(a 0 , . . . , a N−1 ) T being taken to define the ADC or DAC quantisation arrangement when global cost J tot is below a given threshold.
4. A method according to claim 3 wherein a Gaussian function with variance σ g 2 is used as approximation for the input value probability density function.
5. A method according to claim 4 wherein cost function J for a single quantisation bin is substantially equal to
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6. A method for analog to digital conversion (ADC) comprising:
applying a non-linear transfer function to an input signal such that the relation between the quantisation levels of the converter and the input signal vary as a non-linear function of the magnitude of the input signal,
the non-linear transfer function being related to an at least approximate measurement of probability density function ‘p(x)’ of said input signal so that larger quantisation bins of the converter correspond to less probable values of the input signal,
wherein an application of the non-linear transfer function to the input signal includes iteratively updating the relation between the non-linear transfer function and the measurement of probability density by updating quantisation levels, and
wherein for programmable non-linear ADCs, quantisation levels are updated according to the output of an iterative gradient descent process utilising a cost function J, being a function of input value probability density function p(x) and the quantisation error for a given quantisation level a i of corresponding quantisation bin {b i ,b i+1 }, the calculation of the gradient of cost function J utilising at least first-order terms of a Taylor series expansion of exponential and error functions about the current quantisation level values.
7. A method according to claim 6 wherein values for terms of Taylor series expansions are provided by a look-up table.
8. A method according to claim 6 wherein values for terms of Taylor series expansions are provided by an approximation function.
9. A method according to claim 6 wherein a Gaussian function with variance σ g 2 is used for the input value probability density function.
10. A method according to claim 9 wherein the first bounded quantisation level at iteration step k, a 0 {k} , is updated as
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all terms as defined herein.
11. A method according to claim 6 wherein convergence of the iterative gradient descent process is only sought once during an initialisation phase.
12. A method according to claim 1 wherein the output of the converter is linearised by application of a nonlinear transfer function being substantially the inverse of the non-linear transfer function applied to the input signal.
13. Apparatus for analog to digital conversion comprising:
a non-linear transfer function module for applying a non-linear transfer function to an input signal such that the relation between the quantisation levels of the converter and the input signal vary as a non-linear function of the magnitude of the input signal,
the non-linear transfer function module being responsive to an at least approximate measurement of probability density function ‘p(x)’ of said input signal so as to relate thereto the non-linear transfer function so that larger quantisation bins of the converter correspond to less probable values of the input signal,
wherein the non-linear transfer function module, is operative, for an application of the non-linear transfer function to the input signal, to iteratively update the relation between the non-linear transfer function and the measurement of probability density by updating quantisation levels.
14. Apparatus according to claim 13 comprising a communication system.
15. Apparatus according to claim 13 comprising a communication system where signals with high Peak-To-Average-Power Ratio (PAPR) amplitudes occur.
16. Apparatus according to claim 13 comprising a communication system utilising a multi-carrier modulation scheme.
17. Apparatus according to claim 13 comprising a communication system utilising orthogonal frequency division multiplexing.
18. Apparatus according to claim 13 comprising a mobile station.