METHOD OF PERFORMING PEAK REDUCTION AND CLIPPING MITIGATION

• US 20130177089A1
• Filed: 01/09/2012
• Published: 07/11/2013
• Est. Priority Date: 01/09/2012
• Status: Active Grant

• Current Assignee: King Fahd University of Petroleum & Minerals (Government of Saudi Arabia)
• Original Assignee: King Fahd University of Petroleum & Minerals (Government of Saudi Arabia)
• Inventors: AL-SAFADI, EBRAHIM BASIL, AL-NAFFOURI, TAREO Y.
• Granted Patent: US 8,804,862 B2
• Time in Patent Office: Days
• US Class Current: 375/260
• CPC Class Codes: H04L 27/2618 Reduction thereof using auxiliary subcarriers
• CPC Class Codes: H04L 27/2624 by soft clipping

Abstract

The method of performing peak reduction and clipping mitigation provides a compressive sensing algorithm at the receiver of a peak-reducing sparse clipper applied to an OFDM signal at the transmitter. By exploiting the sparsity of the OFDM signal in the time domain relative to a pre-defined clipping threshold, the method depends on partially observing the frequency content of extremely simple sparse clippers to recover the locations, magnitudes, and phases of the clipped coefficients of the peak-reduced signal.

Claims

1. A computer-implemented method of performing peak reduction and clipping mitigation, comprising the steps of:

receiving a transmitted OFDM signal modulating a plurality of data symbols, the OFDM signal being clipped by a clipping signal c to lower the transmitted signal'"'"'s peak-to-average power ratio, the clipping signal c being sparse in time;

compressively sensing a peak-reduced portion of the received OFDM signal by utilizing an l₁ minimization scheme, an output of the compressively sensing step providing an estimate of the clipping signal c at the receiver;

feeding through a remaining, non-peak reduced portion of the received OFDM signal;

least squares estimating the remaining, non-peak reduced portion of the received OFDM signal, thereby providing a least squares estimated portion of the remaining, non-peak-reduced portion of the received OFDM signal;

combining the least squares estimated portion of the received OFDM signal with the estimate of the clipping signal c, thereby resulting in a combined estimate of the transmitted OFDM signal; and

transforming the combined estimate of the transmitted OFDM signal, thereby recovering undistorted coefficients of the transmitted OFDM signal;

whereby, the data symbols in the transmitted OFDM signal are accurately recovered.

2. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 1, further comprising the step of augmenting the phase of the received OFDM signal during the compressively sensing step to aid in accurate recovery of the OFDM transmitted data symbols.

3. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 2, wherein said phase augmentation step further comprises the step of rotating the phase with respect to an angle of individual complex coefficients of a received complex vector associated with the received OFDM signal.

4. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 3, wherein said received complex vector is a sparse vector, said compressive sensing step estimating a pattern of sparsity therefrom.

5. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 4, further comprising the step of automatically clipping high peaks of the received OFDM signal at an initial receiving stage by reducing an absolute value of the high peaks to an algorithmically determined lower level.

6. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 4, wherein said phase augmentation step further comprises the step of recovering locations, magnitudes, and phases of said distorted coefficients of the automatically clipped received OFDM signal.

7. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 6, further comprising the steps of:

merging information about the phases with respect to the feedthrough OFDM estimation step into the compressive sensing step such that;

8. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 7, further comprising a sense-then-rotate step using the relation:

{ĉ

^StR(i)}<sub>i∈

Ic</sub>={|ĉ

^NoPA(i)|w<sup>jθ

{circumflex over (x)}(</sup>i)}<sub>i∈

Î

c</sub>.

9. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 7, further comprising a rotate-then-sense step using the relation:

ĉ

^RtS=arg<sub>|c|∈

RN</sub> min {∥

y′

−

Ψ

{circumflex over (Θ

)}_x|c|∥

₂²+λ

∥

c∥

₁}.

10. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 5, wherein the peak-reducing signal is formulated based on a threshold level crossing of the received OFDM signal.

11. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 10, wherein the clipping signal c comprises a peak-reducing homogeneous clipper signal based on the relation:

12. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 5, wherein the clipping signal c comprises suppressing the transmitted OFDM signal by at least one fixed value ζ

, the clipping signal having the attribute of Digital Magnitude Clipping (DMC), the method further comprising the step of providing a probability density function (PDF) in which a nonzero portion of the coefficients of the compressively sensed portion of the received OFDM signal uses the relation;

f(c^dm(i))=(1−

G_|x|(γ

))δ

(|c|−

ζ

)+G_|x|(γ

)δ

(|c|).

13. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 1, further comprising the step of externally weighing said l₁ minimization, the l₁ minimization using the relation:

ĉ

=arg min∥

y′

−

ψ

c∥

₂²+λ

∥

w^Tc∥

₁,

where w is a weighting vector imposed on the l₁ penalty term based on prior information available during said compressive sensing step.

14. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 13, further comprising the step of defining a weighting vector w^ps based on {circumflex over (x)} for inducing a clipping location.

15. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 1, wherein a Bayesian estimation of the sparse clipping signal is performed, the Bayesian estimation comprising the steps of:

performing a linear minimum mean-square error (LMMSE) estimate of amplitudes ν

_c of the received OFDM signal conditioned on a support estimate Î

_c^cs, wherein the amplitudes estimate uses the relation;

{circumflex over (ν

)}_c^LMMSE|Iccs)=σ

<sub>ν

c</sub>²{circumflex over (Φ

)}^H(σ

<sub>ν

c</sub>²{circumflex over (Φ

)}{circumflex over (Φ

)}^H+σ

_z²I_m)<sup>−

1</sup>(y′

−

Î

E<sub>ν

c</sub>);

defining an operator J^I as a Hamming vector of length N and Hamming weight |I| with active coefficients according to a support set I;

marginal izing on all such possible vectors to obtain the relation;

ĉ

^MMSE=E[c|y′

]=Σ

E[c|y′

,J_i]P(y′

|J_i); and

truncating the ĉ

^MMSE=E[c|y′

] relation to a formulation using the relation;

16. The computer-implemented method of performing peak reduction and clipping mitigation according to claim 15, further comprising performing the estimate using a greedy Fast Bayesian Matching Pursuit algorithm.