Method and apparatus for complementary cumulative distribution driven level convergence for spectrum sensing

A method for use in a digital communications receiver for controlling an input signal level (200) into an analog-to-digital converter (ADC) initially receives a sample sequence (201) where a threshold crossing rate is measured as a percentage samples of an input signal that exceed the threshold (203). The error between the measured threshold crossing rate and a desired reference threshold crossing rate is calculated (205) and an error signal is then utilized in a feedback loop to control the receiver gain such that the error is reduced (207).

FIELD OF THE INVENTION

The present invention relates generally to digital communications systems and more particularly to the control of signal input levels in a digital communications receiver for the purpose of sensing the presence of a plurality of different waveforms.

BACKGROUND

In general, a typical digital communications receiver is designed for use in connection with a particular type of input waveform. When the waveform is received, an analog-to-digital converter (ADC) input signal is maintained at a power level in order to maximize ADC's dynamic range. This ultimately works to minimize quantization noise and clipping induced noise for enhanced receiver performance over a range of input signal levels. In other words, the power level into the ADC is constrained to maximize the signal-to-noise ratio (SNR) of the particular digitized waveform. In that the receiver is designed for one type of input waveform, these types of power level control methods minimize the error in ADC input power relative to some reference power level, which is selected based on apriori knowledge of the input waveform characteristics.

One example of this type arrangement is where the power of a matched filter output is compared to a reference power determined by the signal of interest, the ADC dynamic range, RF front end parameters, etc. The front end gain is adjusted to minimize the difference between the power of the matched filter output and the reference power. This type of matched filter design is based on the known signal waveform such as a pseudo-random noise (PN) sequence, packet preamble, pilot tone, or the like. Often, the reference power is selected according to the peak-to-average characteristic of the waveform to be detected. Accordingly, the reference power for an orthogonal frequency division multiplexing (OFDM) signal will differ from that of a single tone (sine wave) or a direct sequence spread spectrum (DSSS) waveform. Note that for most useful waveforms (excepting a single tone) a certain amount of clipping is typically permissible in order to maximize SNR, where the percentage of clipping is dependent on the input waveform.

Gain control stages as used in the prior art are not adequate for spectrum sensing in cognitive radio applications. In cognitive radio, the signal or waveform input to the ADC is, in general, random and unknown. Also, there may be several superimposed waveforms present on the scanned channel which are then input to the ADC. In this case, the a priori waveform characteristics required to determine an optimal reference power for level control are absent.

Hence, there is a need to provide a means to achieve a desired level of clipping which is acceptable for spectrum sensing in the absence of apriori knowledge of waveform characteristics.

DETAILED DESCRIPTION

Turning now to the drawings,FIG. 1is a block diagram illustrating the complementary cumulative distribution driven level convergence (CCDDLC) control loop system in accordance with an embodiment of the invention. The system100_includes an input signal x(n)103. This is input to a variable gain amplifier105in receiver101. The output of the variable gain amplifier105is directed to an ADC107whose digital sample sequence is sent to a function representing the complementary cumulative distribution function (CCDF), P(x(n))>γ109, where γ is the absolute maximum output value supported by the ADC, known as the clipping level.

The output of the of the CCDF109is represented as the function P(n)111. This is applied to a mathematical subtraction function113with a target CCDF represented by Pr115. The output of the subtraction, P(n)−Pr, provides a signal e(r)117which is provided to a multiplication function119where it is multiplied with a value121representing the loop gain. The output of the multiplication function119is input to a loop filter123which sums the multiplication function119output and the previous value125of the gain control value126. The output is the new gain control value, v(n)126, which is in turn input to a function127which generates the variable gain amplifier's gain value G(n), according to the variable gain amplifier's gain response characteristic where G(n)=10[G_max−av(n)/20] were G_max is the maximum gain in decibels (dB) and ‘a’ is a predetermined constant of proportionality (e.g. dB/bit) used in connection with the control value v(n). Thereafter, G(n) is then used to control the gain of the variable gain amplifier105. Thus, this invention controls an ADC input signal power level to yield a desired probability of clipping without prior consideration of waveform characteristics. Those skilled in the art will recognize that this technique is appropriate for spectrum sensing applications where the use of a waveform dependent, predetermined reference power as a set point is not feasible.

Rather than using ADC input signal power as used in prior art topologies, the system100uses the complementary cumulative distribution function, CCDFX(γ)=P(X>γ), of the input waveform as the comparative statistic. The CCDF at the nthADC sample is estimated as:

Ix(k)=0 for |x(k)|≦γ1 for |x(k)|>γis the indicator function;and γ is the clipping level of the ADC.

As seen inFIG. 1, the CCDF statistic is the input to an exemplary (PI) control loop where Prrepresents the target CCDF, P(n) is the CCDF at sample n, β is the loop gain and G(n) is the programmable gain amplifier gain for a control value, v(n).

For this non-linear system, an idealized linear approximation using perturbation (small signal) analysis can be used to characterize the performance (e.g., convergence time, stability) and obtain qualitative insight.

Let P(n)=CCDFX(γ) at time n,

Assume the CCDF is a function of control value, v(n), and the signal power, Px(n):

P(n)=f(v(n), Px(n)) where this idealized model assumes no delay in the programmable gain amplifier.

If the equilibrium values of v(n), Px(n) and P(n) is vST, PxST, and PST=Pr, respectively; and the deviation from steady state is:
{circumflex over (v)}(n)=v(n)−vST(n)
{circumflex over (P)}x(n)=Px(n)−PxST(n)
{circumflex over (P)}(n)=P(n)−Pr(n)
Then

P^⁡(n)=∂f⁡(vST,PxST)∂v⁢v^⁡(n)+∂f⁡(vST,PxST)∂Px⁢P^x=K1⁢v^⁡(n)+K2⁢P^x⁡(n)⁢(n)(Eq.⁢1)v^⁡(n)=β⁢P^⁡(n)+v^⁡(n-1)=β⁡[K1⁢v^⁡(n)+K2⁢P^x⁡(n)]+v^⁡(n-1)(Eq.⁢2)
or, taking the Z transform,

Also from (Eq. 2)

It is shown below that K1≦0. Then, given the pole

1[1-K1⁢β],
the loop is stable for β>0.

Also for a step deviation from equilibrium on input signal power, the deviation from the CCDF equilibrium point is

P^step⁡(z)⁢=11-z-1⁢K2⁡[1-z-1][1-K1⁢β]-z-1=K2[1-K1⁢β]⁢11-1[1-K1⁢β]⁢z-1⁢⁢so(Eq.⁢4)p^step⁡(n)=K2⁡(1[1-K1⁢β])n+1(Eq.⁢5)
which illustrates that the CCDF converges to 0 when β>0, K1≦0.

limz->1⁢(z-1)⁢P^step⁡(z)=limz->1⁢(z-1)⁢K2[1-K1⁢β]-z-1=0(Eq.⁢6)
confirming convergence for a step input change in input signal power.

Finally, the number of samples required for {circumflex over (p)}step(n) to go from 0.95 to 0.05, relative to maximum deviation due to a step change in input signal power (i.e., the response time) is:

In general, the exact pole location and hence the response time are difficult to determine analytically due to the dependence on

K1=∂f⁡(vST,PxST)∂v.
The slope of the CCDF vs. control value, v, curves can be examined empirically.

Insight, can be obtained by examining the case of a sinusoidal input signal
x(n)=Acos(2πfonTs)
where fo<Fs/2 is the waveform frequency, Ts=1/Fs is the sample time duration.

A clipping event occurs when the output of the variable gain amp exceeds the ADC maximum input level, i.e.,
Gx(n)=GAcos(2πfonTs)>γ
where
G(dB)=G_MAX−sv
or

The CCDF is given by

Note, the max function is required to cover the case of

γG⁢⁢A=1.
For G such that

γG⁢⁢A≥1,
no clipping occurs and the CCDF=0

Determination of K1, requires taking the partial derivative of CCDF(v,A) with respect to v. However, CCDF(v,A) is a non-linear function of v, with dis-continuities due to the ceil( ) function. However, a linear approximation to CCDF(v,A) can provide a qualitative and fairly accurate quantitative result for K1. The partial derivative of

The response time (at a given control value v) is given as

FIG. 2is a flow chart diagram illustrating high level steps in the complementary cumulative distribution driven level convergence method in accordance with an embodiment of the invention. The convergence method200includes receiving a sample sequence x(n)201, where the complementary cumulative distribution function CCDF(n)=P[x(n)≧γ] is calculated203. The error e(n)=CCDF(n)−target CCDF is calculated205and the finally a gain control value v(n)=fnc[e(n), e(n−1), . . . e(n−N))] is determined207for applications with a particular amplifier stage and/or device. Thus, the function can be a scaling function, a linear combination function of e(n), e(n−1), . . . such as a filter; a non-linear function, or any combination thereof.

FIG. 3is a flowchart diagram illustrating a detailed description of the complementary cumulative distribution driven level convergence method in accordance with an embodiment of the invention. As seen inFIG. 3, the convergence method300includes the steps of receiving a clip indicator I(n)301. Those skilled in the art will recognize that the clip indicator is a “clip” or sample of the input waveform into a device such as an ADC. Once a signal is received indicating that the analog-to-digital converter (ADC) input has clipped, then a binary signal from the ADC is generated by a comparison between the ADC sample output, x(n), and the clip level. The CCDF can be calculated by adding the most recent clip indicator value, I(n), to the CCDF accumulator303and subtracting the oldest clip indicator, I(n−D)305, where the CCDF is calculated over D clip indicator samples. That is

C⁢⁢C⁢⁢D⁢⁢F⁡(n)=1D⁢∑k=0D-1⁢I⁡(n-k)=1D⁡[C⁢⁢C⁢⁢D⁢⁢F⁡(n-1)+I⁡(n)-I⁡(n-D)]
Thereafter, the difference between CCDF(n) and target CCDF e(n) is calculated309as well as a calculation for the error power (Pe)311where

Pe⁡(n)=1K⁢∑Kk=0⁢e⁡(n-k)2
Finally, the gain control, v(n), is calculated using a first function (fnc1)315where v(n)=fnc1[e(n), e(n−1), . . . , e(n−N))], if the error power is greater than a threshold313, otherwise a second function (fnc2)317where v(n)=fnc2[e(n), e(n−1), . . . e(n−N))], is used. An example first and second function is a first and second error multiplier119selected according to the error power. The first and second functions are associated with locked and unlocked states, respectively. When the error power exceeds a threshold, the first function associated with the unlocked state is used to cause quicker convergence to the correct gain control value315. Once the error is below a threshold, the second function associated with the locked state is used to reduce the variation of the gain control about the correct value316.