Channel estimation and compensation for preamble-assisted DAPSK transmission in digital mobile radio system

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546 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 50, NO. 2, MARCH 2001

Channel Estimation and Compensation for

Preamble-Assisted DAPSK Transmission in Digital

Mobile Radio System

Der-Zheng Liu, Student Member, IEEE, and Che-Ho Wei, Fellow, IEEE

Abstract—This paper presents a novel channel estimation and compensation technique, combining fading estimation and frequency offset estimation, for preamble-assisted differentially encoded amplitude- and phase-shift keying (DAPSK) transmission in the digital mobile radio system. The received preamble symbols are used to estimate the combined distortions caused by multipath fading and frequency offset. The detected data symbols as well as preamble symbols are used to enhance the accuracy of the estimation process. The combined distortions can be compensated in the data symbols at the same time. The storage-delay time of the estimation process is only several symbols long. A series of computer simulations have been carried out to investigate the bit error rate performances of the preamble-assisted 16-DAPSK sig-nals with uncertain frequency offset in the frequency-nonselective and frequency-selective Rayleigh fading channels.

Index Terms—Channel compensation, channel estimation, dif-ferentially encoded amplitude- and phase-shift keying (DAPSK), fading channel, frequency offset, preamble.

I. INTRODUCTION

R

ECENTLY, there has been growing interest in applying multilevel modulations, such as quadrature amplitude modulation (QAM), differentially encoded phase-shift keying (DPSK), and differentially encoded amplitude- and phase-shift keying (DAPSK), with higher spectral efficiency to the burst-mode high-data-rate digital mobile radio systems [1]–[4]. In mobile environments, the amplitude and phase of received signals are perturbed randomly by both additive white Gaussian noise (AWGN) and multipath fading [5]. Multipath fading, which introduces severely time-varying amplitude and phase distortion to signal waveforms, obstructs the receiver to recover reliable amplitude and phase references for data detection. The irreducible bit error rate (BER) caused by multipath fading inhibits the use of multilevel modulations. However, channel compensation techniques and differential detection techniques have been studied to mitigate multipath fading in the multilevel modulation transmission, respectively [4].

Manuscript received February 1, 1999; revised July 25, 2000. This work was supported by the MTI Center for Networking Research, National Chiao Tung University, Hsinchu, Taiwan, R.O.C., and by the National Science Council of the Republic of China under Grant NSC87-2218-E-009-054. This paper was presented in part at the 10th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’99), Osaka, Japan, September 12–15, 1999.

The authors are with the Department of Electronics Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. (e-mail: dzliu.ee84g@nctu.edu.tw; chwei@cc.nctu.edu.tw).

Publisher Item Identifier S 0018-9545(01)03074-2.

Two types of conventional channel sounding schemes, pilot tone-aided scheme and pilot symbol-aided scheme, can be used to suppress the irreducible BER and enable the multilevel mod-ulations with coherent detection. In a pilot tone-aided scheme, such as transparent tone-in-band (TTIB) [6], [7], the pilot tone provides the receiver with an explicit amplitude and phase refer-ence for data detection. This scheme requires relatively complex signal processing and results in an increased peak-to-average power ratio. In the pilot symbol-aided scheme, the channel dis-tortion can be estimated by the received pilot symbol [8]–[10] and then used to correct the fading effects in the data symbols.

However, in the pilot symbol-aided scheme, the storage-delay time for the process is at least one frame long even by using a simple first-order estimation technique [10], as illustrated in Fig. 2. Furthermore, most previous works on pilot symbol-aided modulation system assumed that the frequency offset produced negligible degradation. If a less accurate oscillator is employed and nontrivial frequency offset is not properly compensated, a significant loss in performance or in throughput rate would result [11]. Consequently, frequency offset estimation is re-quired to relieve the stringent requirements on the oscillator’s accuracy and stability. A frequency offset compensation of pilot symbol-assisted modulation (PSAM) transmission using maximum-likelihood estimators (MLEs) has been investigated by Kuo and Fitz [12] in the frequency-nonselective fading channel. The frequency offset can be estimated from the demodulated pilot symbols. However, the acquisition time is needed at least several frames long.

In this paper, we consider the DAPSK modulation, which was first proposed in [13] and further studied for application in high-data-rate wireless communications [14]–[19]. The major advantage of DAPSK modulation is its robustness to fast channel variation and simplicity in demodulation, because it allows a simple differential detection without tracking the absolute amplitude and phase of received signals. Several studies in the differential detection of DAPSK have been presented in [20]–[23]. A noncoherent detection scheme for the preamble-assisted DAPSK transmission was presented and analyzed in [23]. This scheme yields an error performance approaching that of the QAM scheme with ideal coherent de-tection within a loss of approximately 1 dB in AWGN channel. Here, we focus on the channel estimation and compensation techniques of a preamble-assisted DAPSK transmission for coherent differential detection. The frame structure of the preamble-assisted DAPSK transmission system is illustrated in Fig. 1. The receiver is assumed to have a priori knowledge of 0018–9545/01$10.00 © 2001 IEEE

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Fig. 1. Frame structure of preamble-assisted DAPSK transmission system.

Fig. 2. Storage-delay time of pilot symbol-aided scheme (K = 1 and L = 6).

Fig. 3. Storage-delay time of preamble-assisted scheme (K = 4 and L = 19).

the preamble sequence, and so is able to extract the preamble symbols from the received signal. The received preamble symbols are used to estimate the combined distortions caused by multipath fading and frequency offset. In the proposed scheme, detected data symbols as well as preamble symbols are used to enhance the accuracy of estimation process. The storage-delay time for the process can be reduced to only several symbols long, as illustrated in Fig. 3. At the same time, signal distortions caused by multipath fading and frequency offset can be compensated in the data symbols. The major dif-ference between our proposed scheme and Chung’s scheme in [23] is that preamble symbols are used in the proposed channel estimation to achieve the coherent differential detection, rather than the noncoherent differential detection of DAPSK signals.

This paper is organized as follows. Section II describes the preamble-assisted DAPSK transceiver and the channel model used in the simulations. The proposed preamble-assisted channel estimation and compensation technique is described

in Section III. The BER performance of the proposed pre-amble-assisted scheme is presented in Section IV and compared with the pilot symbol-aided scheme for coherent detection and the differential detection scheme for noncoherent detection. A brief conclusion is given in Section V.

II. PREAMBLE-ASSISTEDDAPSK SYSTEM ANDCHANNEL MODEL

The preamble-assisted DAPSK transceiver and the equiva-lent-baseband channel model are shown in Fig. 4.

A. Transmitter

In the transmitter, the preamble symbols are packaged and inserted into a frame in front of data symbols for transmission. The transmitter sequentially encodes information bits onto the amplitude ratio and phase difference between two consecutive transmitted symbols. In the preamble-assisted modulation trans-mission, each frame consists of one preamble block of sym-bols followed by one data block of ( ) symbols, as shown in Fig. 1. Note that the preamble-assisted modulation transmis-sion with corresponds to the PSAM transmission.

The -ary DAPSK (MDAPSK) modulation with concentric amplitude rings, each containing phases, where

, can be further described as follows. A sequence of transmitted bits is first grouped and mapped by Gray labeling into one of independent symbol pairs ( ) according to MDAPSK signal constellation, where

(1) (2) For , the th MDAPSK symbols of the th frame is given in the complex form by

(3) where is a fixed ring-ratio and

(4) is the normalized-gain of the MDAPSK symbols, that is, the average transmitted signal power is normalized to unity. and

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548 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 50, NO. 2, MARCH 2001

Fig. 4. Preamble-assisted DAPSK transmission system and channel model.

Fig. 5. A DAPSK encoder.

indicate the amplitude and phase levels of the transmitted symbols and are related to and by

(5) (6)

respectively. Therefore, an MDAPSK encoder can be treated as a combination of an -ary differentially encoded ampli-tude-shift keying ( DASK) encoder and an -ary differen-tially encoded phase-shift keying ( DPSK) encoder, as illus-trated in Fig. 5. Note that MDAPSK modulation with

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B. Channel Model

Here, we consider that the multipath fading channel is fre-quency nonselective and modeled as a Rayleigh fading channel. The Rayleigh fading process was generated according to Jakes’ model [5], where the correlation function of fading process is given as

(7) where is the maximum Doppler shift of the fading signal caused by the mobile motion. The Doppler shift is given by , where is the velocity of the mobile and is the wavelength of the carrier. In general, the normalized maximum Doppler shift is used as the measure for the fading rate, where denotes the symbol duration.

The equivalent-baseband signal at the receiver is given by

(8)

where is the pulse-shaping filter and denotes the av-erage received signal-to-noise ratio (SNR) per symbol. Thus the average SNR per bit is given by

(9) is a complex Gaussian process whose real and imaginary components have the same power spectral density (PSD) with . represents the combined distortion introduced into the desired signal in the fading channel. and are frequency offset in radian and residual phase error introduced during demodulation, respectively.

C. Receiver

We assume that the pulse-shaping filter in the trans-mitter has a square-root raised-cosine (SRRC) shape with a rolloff factor ; and that the matched filter

at the receiver has similar SRRC shape. The demodulated signal after the matched filter is given by

(10) where the symbol denotes the time convolution process.

Assuming that the maximum Doppler shift due to mobile motion is far smaller than the symbol rate 1 , i.e., the fading rate is small, then the intersymbol interference (ISI) caused by the filtering process can be neglected. Therefore, the demodu-lated signal after the matched filter can be simplified as

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where is a raised-cosine Nyquist pulse

with and is a filtered Gaussian

process.

The demodulated signal after the matched filter is sampled and digitized through the analog-to-digital converter (ADC) driven by the sampling instants provided by symbol timing recovery. We have that

(12) where denotes the sampling timing error. The on-time sam-ples of the th frame

(13) are used for the detector and decoder.

Assuming that the baseband received signal is sampled in synchronism, i.e., , the sampled signal at time

is given by

(14) where

noise term;

combined distortion due to multi-path fading;

and normalized frequency offset in ra-dian and residual phase error, re-spectively.

To reduce the performance degradation by channel distortions caused by multipath fading and frequency offset, channel esti-mation and compensation described in Section III are adopted in front of the DAPSK decoder.

D. DAPSK Demodulation

The DAPSK decoder is a combination of an amplitude-level decoder and a phase-level decoder, as illustrated in Fig. 6. The amplitude and phase level of the compensated symbols ob-tained through the envelope-level detector and phase-level de-tector are given by

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Arg (16)

respectively. The change of amplitude and phase levels between two consecutive compensated symbols can be computed as

(17) (18) respectively. The differentially detected symbol pairs of MDAPSK signals are obtained by comparing with the decision thresholds and then taking modulo-operations as

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550 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 50, NO. 2, MARCH 2001

Fig. 6. A DAPSK decoder combined with an amplitude-level decoder and a phase-level decoder.

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respectively, where denotes the roundoff operation. The re-ceived bit sequence is mapped by Gray labeling from the differ-entially detected symbol pairs according to the MDAPSK signal constellation, where

(21) (22) The th detected MDAPSK symbol of the th frame in com-plex form is given by

(23) where the ring ratio and normalized gain are the same as that in the DAPSK encoder

(24) (25) indicate the amplitude and phase levels of the detected MDAPSK symbol , which are related to the differentially detected symbol pairs , respectively.

In the absence of AWGN and with the optimal channel com-pensation, the compensated symbols are very close to the trans-mitted symbols, i.e., . Therefore, the amplitude and phase levels of the compensated MDAPSK symbols are given by

(26)

(27) and then the amplitude and phase levels of the detected MDAPSK symbols are obtained as

(28) (29) respectively.

III. CHANNELESTIMATION ANDCOMPENSATION Since the preamble symbols are known at the receiver, in the absence of AWGN, the channel distortions in the preamble block, for , can be obtained by

(30)

where is the th preamble symbol of the th frame. The estimate of normalized frequency offset (in radian) due to the Doppler shift and the mismatch of local oscillator (LO) in the receiver can be obtained by

Arg Arg (31)

However, in the presence of AWGN, the estimates of channel distortions in the preamble block, for , are calculated as

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Fig. 7. Proposed channel estimation and compensation scheme.

The instantaneous estimate of normalized frequency offset in radian at the th symbol of the th frame is calculated as

Arg (33)

In the proposed channel estimation, the detected data symbols as well as the preamble symbols are used to enhance the accu-racy of estimation process. In the data block, the previous es-timates of channel distortions and normalized frequency offset are used to estimate the current channel distortion and normal-ized frequency offset. There exists a phase rotation be-tween and , caused by frequency offset. Therefore, the estimates of channel distortions on the data symbols, for

, are calculated as

(34)

where is the window size of a moving average filter. The choice of a suitable window size of the moving average filter is a tradeoff between the accuracy of estimation process and the complexity in implementation. The estimate of normalized frequency offset is updated recursively through an exponentially weighted (EW) filter, for , and given by

(35) where is the forgetting factor, . The choice of the forgetting factor of the EW filter is a tradeoff between

conver-gence speed and mean square error (MSE) in steady state. The estimates of channel distortions are used to correct the data sym-bols, and the compensated symsym-bols, for , are obtained as

(36)

The compensated symbols are then fed into the detector and de-coder to produce the detected symbol and the binary data at the output. The proposed channel estimation and compensation scheme is illustrated in Fig. 7.

IV. COMPUTERSIMULATIONS

A series of computer simulations have been carried out to investigate the BER performances of the preamble-assisted 16-DAPSK signals not only in the frequency-nonselective but also in the frequency-selective fading channels.

The frequency-selective fading channel is modeled as a two-ray Rayleigh fading channel [24] with the time delay between the main path and the delayed path. Each of the transmission paths introduces uncorrelated Rayleigh fading distortion to the corresponding transmitted signal. The main-path-to-delayed-path power ratio is defined as SDR , where and are the signal power of the main path and delayed path, respectively. When SDR dB, the signal powers of the main path and delayed path are equal. The normalized delay between the signals from the main path and delayed path is defined as . However, this channel model becomes frequency nonselective when

SDR dB or .

Moreover, the signal-to-noise ratio is defined as SNR . The normalized frequency offset

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552 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 50, NO. 2, MARCH 2001

Fig. 8. BER performance versus window sizeW of moving average filter in frequency-nonselective fading environments (SDR = 1 dB and f T = 0:001).

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Fig. 10. BER performance versus normalized frequency offset1fT in frequency-nonselective fading environments (SDR = 1 dB, SNR = 30 dB, and

f = 0:001).

of frequency offset. The normalized maximum Doppler shift, or the fading rate, is defined as , and in the absence of the fading distortion.

Furthermore, the parameters of the simulation system are de-scribed as follows. In the proposed preamble-assisted scheme and the noncoherent differential detection scheme, the frame length and the preamble length . In the pilot symbol-aided scheme, , and . A symbol rate of k symbols per second are used throughout the simulations. The signal constellation of 16-DAPSK modulation contains two concentric amplitude rings, each containing eight phases, i.e., , . The ring ratio of 16-DAPSK signals equals to 2.0. Therefore, the normalized gain is . The rolloff factor of the SRRC filter equals 0.5. The forgetting factor of the EW filter in frequency offset estimation is 0.5.

A. Frequency-Nonselective Fading Channels

Fig. 8 shows that the BER performance versus the window size of the moving average filter in frequency-nonselective fading environments (SDR dB and ). The dashed lines show the BER performance in the absence of fre-quency offset ( ). The solid lines show the BER per-formance with a frequency offset ( ). From the sim-ulation results, the suitable window size of the moving average filter is chosen as for the accuracy of estimation process and the complexity in implementation.

The BER performance versus the SNR per symbol in fre-quency-nonselective fading environments (SDR dB and

) is shown in Fig. 9. The dashed lines show the BER performances of the schemes referred to in [10], where “DD-16DPSK” and “DD-16DAPSK” denote the BER perfor-mances of 16-DPSK and 16-DAPSK signals with noncoherent differential detection and “PSA-16PSK” and “PSA-16QAM” denote the BER performances of 16-PSK and 16-QAM sig-nals with the pilot symbol-aided technique for fading compensa-tion, respectively. The lines marked with “PA-16DAPSK” show the BER performances of 16-DAPSK signals with the proposed preamble-assisted channel compensation, where “Optimal” de-notes that the receiver has the knowledge of frequency offset and fading effect, so there is no estimation error. We can see that the proposed preamble-assisted scheme outperforms the other schemes even with a frequency offset ( ).

Fig. 10 shows that the BER performance versus the nor-malized frequency offset in frequency-nonselective fading environments (SDR dB, SNR dB, and ). From the simulation results, we can see the improvement in the suppression of frequency offset for the proposed preamble-assisted channel compensation. Since frequency offset contributes a continuous phase rotation in signal waveforms, the BER performances of PSA-16PSK and PSA-16QAM signals are degraded severely with the increase of frequency offset ( ). However, frequency offset contributes a constant phase rotation (2 ) for DPSK and DAPSK signals after differential detection, the BER perfor-mance of noncoherent differential detection is degraded rapidly when the normalized frequency offset is close to the boundary,

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554 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 50, NO. 2, MARCH 2001

Fig. 11. BER performance versus normalized maximum Doppler shiftf T in frequency-nonselective fading environments (SDR = 1 dB and SNR = 30 dB). 1/2 , where is equal to the possible phase number of

signals. The boundaries for DD-16DPSK and DD-16DAPSK signals are 1/32 and 1/16, respectively. A theoretical boundary of the normalized frequency offset for the proposed scheme is (1 2, where is the rolloff factor of the matched filter. In the simulations, , so the boundary for PA-16DAPSK signals is 0.25.

Fig. 11 shows that the BER performance versus the fading rate in frequency-nonselective fading environments (SDR dB and SNR dB). Since the “Optimal” scheme is optimal only for the channel estimation process, the noise term still exists. The signal energy varies rapidly with the increase of fading rate. Thus, the BER performance of the PA-16DAPSK signal in the “Optimal” scheme is dominated by the noise. Furthermore, the error of channel estimation in-creases with the fading rate. Therefore, the BER performances of PA-16DAPSK signals with are degraded severely by the estimation error and the noise with the increase of the fading rate.

B. Frequency-Selective Fading Channels

Several simulations have been finished to show the BER performance in the frequency-selective fading environments (SDR dB and ). Fig. 12 shows the BER performance versus the main-path-to-delayed-path power ratio SDR in frequency-selective fading environments (SNR dB and ) with the normalized delay of 0.125. Fig. 13 shows that the BER performances versus the nor-malized delay between the main path and delayed path in

frequency-selective fading environments with the equal-power

assumption (SNR dB, SDR dB, and ).

From the simulation results, we observe that the BER perfor-mance is degraded with the increase of the normalized delay and the decrease of the main-path-to-delayed-path power ratio SDR. However, the performance of the PA-16DAPSK signal is the best among the signals under test.

V. CONCLUSION

In this paper, a novel channel estimation and compensation technique, combining the fading estimation and frequency offset estimation, is investigated for a preamble-assisted DAPSK transmission system in mobile environments. The received preamble symbols are used to estimate the combined distortions caused by multipath fading and frequency offset. The detected data symbols as well as the preamble symbols are used to enhance the accuracy of estimation process. A moving average filter with a suitable window size is employed in the channel estimation process.

Several simulations have been completed to show the im-provement in the suppression of frequency offset. Computer simulation results show that the tolerance of frequency offset for 16-DAPSK signals can be increased from 0.0625 to 0.25 by the proposed channel compensation technique. From the computer-simulation results in the frequency-nonselective fading environ-ments (SDR dB), we observe that the error of the channel estimation is increased and the BER performance is degraded with the increase of the fading rate . In the

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frequency-se-Fig. 12. BER performance versus main-path-to-delay-path power ratio SDR in frequency-selective fading environments (SNR= 30 dB and f T = 0:001) with normalized delayT =T = 0:125.

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556 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 50, NO. 2, MARCH 2001

lective fading environments (SDR dB and ), the BER performance is degraded with the increase of the nor-malized delay and the decrease of the main-path-to-de-layed-path power ratio SDR. However, the performance of the PA-16DAPSK signal is the best among the signals under test.

ACKNOWLEDGMENT

The authors are grateful to the editor and the anonymous re-viewers for their helpful comments and suggestions.

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Der-Zheng Liu (S’96) received the B.S. degree in

electrical engineering from National Cheng Kung University, Tainan, Taiwan, R.O.C., in 1993 and the M.S. degree in electronics engineering from National Chiao Tung University, Hsinchu, Taiwan, in 1995, respectively, where he is currently pursuing the Ph.D. degree.

His research interests include digital signal processing, wireless communications, and related circuits design.

Che-Ho Wei (S’73–M’76–SM’87–F’96) received

the B.S. and M.S. degrees in electronic engineering from National Chiao Tung University (NCTU), Hsinchu, Taiwan, R.O.C., in 1968 and 1970, respec-tively, and the Ph.D. degree in electrical engineering from the University of Washington, Seattle, in 1976. From 1976 to 1979, he was an Associate Professor at NCTU, where he is now a Professor and Vice Pres-ident of the university. During 1979 to 1982, he was the Engineering Manager of Wang Industrial Com-pany in Taipei. He was the Chairman of the Depart-ment of Electronics Engineering of NCTU from 1982 to 1986 and Director of Institute of Electronics from 1984 to 1989. He was on leave at the Ministry of Education and served as the Director of the Advisory Office from September 1990 to July 1992. He was Dean of Research of NCTU from August 1993 to July 1995 and Dean of the College of Electrical Engineering and Computer Sci-ence from August 1995 to July 1998. His research interests include digital com-munications and signal processing, and related circuit design.

Dr. Wei was the Founding Chairman of the Taipei Chapter of the IEEE Cir-cuits and Systems Society and IEEE Communication Society. He was a member of the Board of Governors, IEEE Circuits and Systems Society, from 1992 to 1994. He received the Distinguished Research Award from the National Science Council, R.O.C., in 1990 to 1996. He received the Distinguished Engineering Professor Award from the Chinese Institute of Engineers in 1995. He received the Academic Achievement Award from the Ministry of Education, R.O.C., in 2000. He received the IEEE Third Millennium Medal and IEEE Circuits and Systems Society Golden Jubilee Medal, 2000.

數據

Fig. 1. Frame structure of preamble-assisted DAPSK transmission system.
Fig. 1. Frame structure of preamble-assisted DAPSK transmission system. p.2
Fig. 2. Storage-delay time of pilot symbol-aided scheme ( K = 1 and L = 6).
Fig. 2. Storage-delay time of pilot symbol-aided scheme ( K = 1 and L = 6). p.2
Fig. 3. Storage-delay time of preamble-assisted scheme ( K = 4 and L = 19).
Fig. 3. Storage-delay time of preamble-assisted scheme ( K = 4 and L = 19). p.2
Fig. 4. Preamble-assisted DAPSK transmission system and channel model.
Fig. 4. Preamble-assisted DAPSK transmission system and channel model. p.3
Fig. 5. A DAPSK encoder.
Fig. 5. A DAPSK encoder. p.3
Fig. 6. A DAPSK decoder combined with an amplitude-level decoder and a phase-level decoder.
Fig. 6. A DAPSK decoder combined with an amplitude-level decoder and a phase-level decoder. p.5
Fig. 7. Proposed channel estimation and compensation scheme.
Fig. 7. Proposed channel estimation and compensation scheme. p.6
Fig. 8. BER performance versus window size W of moving average filter in frequency-nonselective fading environments (SDR = 1 dB and f T = 0:001).
Fig. 8. BER performance versus window size W of moving average filter in frequency-nonselective fading environments (SDR = 1 dB and f T = 0:001). p.7
Fig. 9. BER performance versus SNR in frequency-nonselective fading environments (SDR = 1 dB and f T = 0:001).
Fig. 9. BER performance versus SNR in frequency-nonselective fading environments (SDR = 1 dB and f T = 0:001). p.7
Fig. 10. BER performance versus normalized frequency offset 1fT in frequency-nonselective fading environments (SDR = 1 dB, SNR = 30 dB, and
Fig. 10. BER performance versus normalized frequency offset 1fT in frequency-nonselective fading environments (SDR = 1 dB, SNR = 30 dB, and p.8
Fig. 11. BER performance versus normalized maximum Doppler shift f T in frequency-nonselective fading environments (SDR = 1 dB and SNR = 30 dB)
Fig. 11. BER performance versus normalized maximum Doppler shift f T in frequency-nonselective fading environments (SDR = 1 dB and SNR = 30 dB) p.9
Fig. 12. BER performance versus main-path-to-delay-path power ratio SDR in frequency-selective fading environments (SNR = 30 dB and f T = 0:001) with normalized delay T =T = 0:125.
Fig. 12. BER performance versus main-path-to-delay-path power ratio SDR in frequency-selective fading environments (SNR = 30 dB and f T = 0:001) with normalized delay T =T = 0:125. p.10
Fig. 13. BER performance versus normalized delay T =T in frequency-selective fading environments (SDR = 0 dB, SNR = 30 dB, and f T = 0:001).
Fig. 13. BER performance versus normalized delay T =T in frequency-selective fading environments (SDR = 0 dB, SNR = 30 dB, and f T = 0:001). p.10

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