Phase and frequency estimation for PSK packets: bounds and algorithms

Cowley, William G.

doi:10.1109/26.476092

Cited by 66 publications

(42 citation statements)

References 4 publications

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“…At high SNR, the value of F B and F Q is equivalent to one; so, the same bound applies for both the BPSK and QPSK signals [43]. The value of F B and F Q differs at low SNR and is obtained from the results presented in [43]. In [44], the authors extended the study presented in [43] and derived the CRLB for 8PSK signal with random phase.…”

Section: Comparison To Crlbmentioning

confidence: 77%

Section: Comparison To Crlbmentioning

confidence: 99%

“…The CRLB derived in [43,44] uses a likelihood function on a known signal in the presence of additive white noise for the digitally phase modulated signal.…”

Section: Comparison To Crlbmentioning

confidence: 99%

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Efficient phase estimation for the classification of digitally phase modulated signals using the cross-WVD: a performance evaluation and comparison with the S-transform

Mei

Sha’ameri

Boashash

2012

EURASIP J. Adv. Signal Process.

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This article presents a novel algorithm based on the cross-Wigner-Ville Distribution (XWVD) for optimum phase estimation within the class of phase shift keying signals. The proposed method is a special case of the general class of cross time-frequency distributions, which can represent the phase information for digitally phase modulated signals, unlike the quadratic time-frequency distributions. An adaptive window kernel is proposed where the window is adjusted using the localized lag autocorrelation function to remove most of the undesirable duplicated terms. The method is compared with the S-transform, a hybrid between the short-time Fourier transform and wavelet transform that has the property of preserving the phase of the signals as well as other key signal characteristics. The peak of the time-frequency representation is used as an estimator of the instantaneous information bearing phase. It is shown that the adaptive windowed XWVD (AW-XWVD) is an optimum phase estimator as it meets the Cramer-Rao Lower Bound (CRLB) at signal-to-noise ratio (SNR) of 5 dB for both binary phase shift keying and quadrature phase shift keying. The 8 phase shift keying signal requires a higher threshold of about 7 dB. In contrast, the S-transform never meets the CRLB for all range of SNR and its performance depends greatly on the signal's frequency. On the average, the difference in the phase estimate error between the Stransform estimate and the CRLB is approximately 20 dB. In terms of symbol error rate, the AW-XWVD outperforms the S-transform and it has a performance comparable to the conventional detector. Thus, the AW-XWVD is the preferred phase estimator as it clearly outperforms the S-transform.

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Section: Comparison To Crlbmentioning

confidence: 77%

Section: Comparison To Crlbmentioning

confidence: 99%

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Efficient phase estimation for the classification of digitally phase modulated signals using the cross-WVD: a performance evaluation and comparison with the S-transform

Mei

Sha’ameri

Boashash

2012

EURASIP J. Adv. Signal Process.

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“…T HE true Cramér-Rao lower bounds (CRLBs) for joint frequency and phase estimation from unknown data symbols (blind operation) of modulated signals have been presented in [1]- [4]. The CRLBs for modulated signals can be expressed as the CRLBs of a carrier wave (CW) divided by a function of modulation and noise power, i.e., CRLB CRLB , assuming that the CW and the modulated signal have average unity power.…”

Section: Introductionmentioning

confidence: 99%

Carrier-phase and frequency-estimation bounds for transmissions with embedded reference symbols

Rice

2006

IEEE Trans. Commun.

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Abstract-The true Cramér-Rao lower bound (CRLB) for the joint estimation of carrier phase and frequency is derived for transmission bursts with interleaved reference and phase-shift keying/quadrature amplitude modulated data symbols. Results are presented for the special cases of midamble, and preamble and postamble, pilot-symbol insertion. The derivation reveals that the CRLB is a function of the location of the reference symbols in the burst, the number of reference symbols, the number of data symbols, the signal-to-noise ratio and the data-modulation scheme. By distributing the reference symbols symmetrically about the center of the burst and analyzing relative to the middle of the signal vector, the joint frequency and phase estimation can be decoupled, and the optimal phase estimation is achieved. In the decoupled case, the phase CRLB is independent of the location of reference symbols in the burst. In a symmetrical burst, the use of a preamble and postamble is found to provide a lower frequency-estimation CRLB than that with a midamble. It appears that the frequency CRLB is reduced as the reference symbols are symmetrically distributed closer to the ends of the burst.

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“…In [2], the CRB's for estimating the frequency offset and the carrier phase have been computed for BPSK and QPSK, assuming the timing to be known; different constellations yield different expressions for the CRB's.…”

Section: Introductionmentioning

confidence: 99%

Low-SNR limit of the Cramer-Rao bound for estimating the carrier phase and frequency of a PAM, PSK, or QAM waveform

Steendam

Moeneclaey

2001

IEEE Commun. Lett.

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Abstract-In this letter we consider the Cramer-Rao bound (CRB) for the estimation of the time delay of a noisy linearly modulated signal with random data symbols and random carrier phase. Because of the presence of the nuisance parameters (i.e., data symbols and carrier phase), a closed-form expression of this CRB is very hard to obtain for arbitrary PSK, QAM or PAM constellations and a band-limited transmit pulse. Instead, here we derive a simple expression for the limit of the CRB at low signal-to-noise ratio (SNR), which is a relevant benchmark for timing recovery algorithms operating at small 0 .

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Phase and frequency estimation for PSK packets: bounds and algorithms

Cited by 66 publications

References 4 publications

Efficient phase estimation for the classification of digitally phase modulated signals using the cross-WVD: a performance evaluation and comparison with the S-transform

Efficient phase estimation for the classification of digitally phase modulated signals using the cross-WVD: a performance evaluation and comparison with the S-transform

Carrier-phase and frequency-estimation bounds for transmissions with embedded reference symbols

Low-SNR limit of the Cramer-Rao bound for estimating the carrier phase and frequency of a PAM, PSK, or QAM waveform

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