A Carrier Estimation Method for MF-TDMA Signal ... - Semantic Scholar
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JOURNAL OF NETWORKS, VOL. 7, NO. 8, AUGUST 2012
A Carrier Estimation Method for MF-TDMA Signal Monitoring Xi Liu School of Electronics and Information Engineering, Beihang University, Beijing, China Email: [email protected]
Wenquan Feng, Chunsheng Li, Chao Ma School of Electronics and Information Engineering, Beihang University, Beijing, China Email: [email protected], [email protected], [email protected]
Abstract—Based on the need of MF-TDMA signal monitoring, this paper investigates the estimation method for frequency offset and carrier phase. The procedure for timing recovery is introduced, and then an effective algorithm is deduced for estimating carrier frequency and phase. The proposed open-loop algorithm demands no preambles and has a wide capture range. In addition, the overall block diagram of a monitoring receiver, which we designed with the proposed estimation algorithm, is presented.
to establish a monitoring system at NCC, so as to find out anomalies and make adjustment in time.
Index Terms—Carrier phase estimation; Frequency offset estimation; MF-TDMA; VSAT;
I. INTRODUCTION MF-TDMA is a two-dimensional multiple access type which combines frequency division with time division. By frequency hopping, variable rate and virtual circuit technology, flexible MF-TDMA network can be achieved between different terminal stations [1]. Because of its flexibility and extensibility, MF-TDMA satellite communication system has been applied more and more. Key points in MF-TDMA satellite communication system involve timing recovery, capture and synchronization, control of power and frequency, etc. Based on this, this paper discusses on the carrier estimation methods for MF-TDMA signal in VSAT satellite network monitoring. As shown in Fig 1, VSAT satellite communication system is comprised of the network control center (NCC), the satellite transponder and VSAT stations [2]. There are three typical transmission patterns in VSAT satellite network: CDMA, SCPC and TDMA. If multiple carriers coexist in a common transponder band, TDMA transmission turns to be MF-TDMA, which can provide more changeful service and is more flexible. MF-TDMA network is more efficient while the implementation techniques are complex: solar outage, rainfall, or improper operations on VSAT stations will impact the quality of communication. Consequently, it is necessary
© 2012 ACADEMY PUBLISHER doi:10.4304/jnw.7.8.1170-1175
Figure 1. VSAT system configuration
In general, VSAT network is power limited, rather than frequency limited system, in which modulation scheme that has the highest power efficiency should be adopted. Therefore, coherent QPSK or BPSK is selected in most cases. For the digital communication systems with PSK modulation, there are two types of carrier synchronization methods [3]: one is using a feedback closed-loop to track the carrier frequency and phase of the received signal, such as quadratic loop and Costas loop; and the other one is the direct estimation of received carrier using open loop structure. In MF-TDMA systems, carrier parameters may vary as the burst slots come from different VSAT stations, which have caused considerable difficulty for closed-loop carrier recovery. For this reason, the open loop maximum likelihood estimation of carrier parameters is mostly studied at present. The open loop estimation methods can be divided into two groups according to weather the training sequences preamble or not: the DA (data-aided) algorithms and the NDA (non-data-aided) algorithms [4]. For the application fields of MF-TDMA signal monitoring, as it is difficult to be informed of preamble sequences, therefore the NDA algorithms are usually adopted. Based on the premised demand, this paper
JOURNAL OF NETWORKS, VOL. 7, NO. 8, AUGUST 2012
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proposes an open loop carrier estimation method and the corresponding architecture of monitoring receivers [5-6].
We consider performing the monitor at intermediate frequency, thus the architecture of the sampling receiver can be shown as in Fig 5.
II. ARCHITECTURE OF THE MONITORING RECEIVER In this paper, we take QPSK for example and express the received MF-TDMA signal as:
((
r (t ) = ∑ Ak (t ) exp j 2π fk t + ϕk (t ) + θk
)) + n (t )
(1)
in which Ak ( t ) is the amplitude of received signal, f k is the carrier frequency, θ k is the carrier phase deviation,
ϕk ( t ) is the modulated symbol phase taking values in
{ 1 4π ,3 4π ,5 4π , 7 4π }, n ( t ) is the additive white Gaussian noise, and the subscript k represents the ordinal number of the multiple carriers. Fig 2 represents the time-frequency two-dimensional expansion of this MF-TDMA signal as in (1). Spectrogram of this signal and the time-domain envelope of a single channel are shown in Fig 3 and Fig 4.
Figure 5. System diagram of monitoring receiver
First, the receiver quantizes the IF multi-carrier signal by using band-pass sampling, and the local NCO is set to the center frequency of one of the MF-TDMA carriers. After the quadrature down-conversion, the sampling rate is reduced to integer multiples of the symbol rate to facilitate further processing. Then, after the matched filter, we get the complex samples of the baseband TDMA signal. For MF-TDMA signal monitoring system, the top priority is to obtain measurement indices (such as slot power, frequency offset, EVM, etc.) of each channel. If there is any anomalous value, the monitoring system should give an alarm timely. In this paper, we focus on the carrier estimation method of the baseband samples. III. ALGORITHM DESCRIPTION In traditional receivers, feedback loops are commonly used for carrier synchronization, in which the hang-up effect may limit the capture range and slowdown the process of carrier acquisition. Accordingly this article proposes using open-loop estimation method in monitoring receiver, and puts forwards corresponding algorithm suitable for MF-TDMA burst communication.
Figure 2. Sketch map of time-frequency expansion -14
x 10
3.5 3
PSD(W /Hz)
2.5 2 1.5 1 0.5 0 55
60
65
70 Frequency(MHz)
75
80
Power Envelope
Figure 3. Spectrogram of MF-TDMA signal
85
A. Timing recovery Monitoring system receives burst signals from different VSAT stations, so separate estimation for each burst slot is needed. The purpose of timing recovery is to figure out the optimal sampling time, so as to gain the maximum receiving signal-to-noise ratio (SNR) during demodulation. In this paper, Gardner’s timing-error detection algorithm is applied for optimal sampling-points verdict. Pivotal ideas of Gardner’s algorithm are listed as follows: take sample points, of which any adjacent two are half a symbol cycle apart, into account, and use their amplitudes and polarity changes to calculate the timing error [11]. The specific algorithm is u(r ) = I (r − 1 / 2)[I (r ) − I (r − 1)] +Q(r − 1 / 2)[Q(r ) − y(r − 1)]
(2)
Symbols
Figure 4. Time-domain envelope of a single channel
© 2012 ACADEMY PUBLISHER
where I and Q represent the inphase and quadrature samples, and the index r is used to designate the number of symbols: r represents the current sample point, r-1 represents the sample point of the last symbol, and use r-
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1/2 to denote the sample lying midway between the rth and the (r-1)th sample. Therefore, the error calculation only requires to sample the baseband signal at the 2 times of the symbol rate. Gardner’s algorithm is independent from carrier estimation, as a result, the timing recovery can be performed before or after the carrier synchronization. In the monitoring receiver as we described in Fig 5, modified open-loop timing recovery method is adopted for the convenience of processing. We first reduce the sampling frequency, after the quadrature down-converter, to Q times of the symbol rate (Q is an even integer greater than 2). After the matched filter, use (2) to calculate timing error of the Q columns sampled data. And finally, we pick the column which has the minimum variance as the optimal samples. A necessary consideration is that, during one frame period, there are time slots when no data burst but only exists noise, and it is meaningless to calculate timing error at such idle slots. Also, timing error of burst data slots may differ, as they came from different VSAT stations. In order to improve the accuracy of the timing recovery, we use a module called “Slot Extraction” to extract data slots from the energy envelop of modulated carriers. Then, timing error is calculated for each data slot separately. B. Carrier esitimation For non data-aided (NDA) carrier estimation, the Viterbi & Viterbi algorithm, as in [8], is a classic openloop nonlinear phase estimation algorithm, and has been widely used. Generally, the process of V&V estimation can be divided into three steps: first, the modulation is removed by a nonlinear transformation; then, average the phase in the estimation interval; at the final, equivocation of estimated carrier phase should be eliminated. Consider that the MF-TDMA signal being monitored in VSAT network is relayed transparently by the geosynchronous satellite, the dynamic range of carrier frequency is small enough that the Doppler shift can be neglected. Therefore, dominated carrier frequency offset comes from the deviation of frequency standard on different VSAT equipments. Due to the need of average process on estimated phase, the V&V algorithm requires the normalized frequency offset to meet: ΔfTs ≤ 0.05 , in which Δf is the carrier frequency offset, and Ts is the period of one symbol. When the frequency offset Δf exceeds a certain limit, the performance of V&V’s estimation algorithm will descend obviously. For this reason, we consider to evaluate the frequency offset and try to make corresponding compensation before the phase estimation [9-10]. The structural model of the carrier estimation method proposed in this paper is shown as in Fig 6.
JOURNAL OF NETWORKS, VOL. 7, NO. 8, AUGUST 2012
Δof
Figure 6. Structural model of the carrier estimation
For the facility of analyzing, we assume that the timing of samples has been accurately recovered after the matched filter, and the complex baseband samples can be expressed as in (3). ri = x i + j ⋅ yi
((
(
))
)
= exp j 2πΔf ⋅ iTs + ϕi 2π M + θ0 + ni
in
which ϕi ( 2π M )
represents
the
M-ary
(3)
PSK
modulated ui data, θ 0 is the initial phase, and ni represents the complex additive Gaussian noise whose two-side power spectral density is N 0 2 . To investigate the complex samples in the estimation interval − N ≤ i ≤ N , we first remove the modulation by a Mth-power nonlinear transformation, namely,
(
j 2πΔf ⋅iTs +ϕi ( 2π zi = e (
M ) +θ 0 )
+ ni
)
M
= ri
M
j M arg ( ri ) ) e( (4)
Such a transformation will change the carrier phase interval from [ −π , π ] into [ − π M , π M ] . When the SNR of ri is high, we can take a simple approximation as follow [7]
arg ( ri ) = ( 2πΔf ⋅ iTs + ϕi ( 2π M ) + θ 0 ) + ui
(5)
in which is the equivalent phase noise to ni , who is also Gaussian distributed with zero mean, and yields σ u 2 = σ n 2 2 . The result of this nonlinear transformation can be written as αi = arg (z i ) = M arg (ri )
= M (2πΔf ⋅ iTs + θ0 + ui ) + i ⋅ 2π
(6)
Without the influence of modulation, carrier frequency offset can be evaluated form sample series {α i } . Note that samples
{α i }
are linearly proportional to the
frequency offset Δf . In particular, the maximum
© 2012 ACADEMY PUBLISHER
JOURNAL OF NETWORKS, VOL. 7, NO. 8, AUGUST 2012
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likelihood (ML) estimation is equivalent to an unbiased least mean-square (LMS) estimation, with the following result: N ⎞ pf = ⎛⎜ Δ ⎜⎜ ∑ iαi ⎟⎟⎟ ⎝⎜i =−N ⎠⎟ ⎛ N ⎞ = ⎜⎜⎜3 ∑ iαi ⎟⎟⎟ ⎝⎜ i =−N ⎠⎟
N ⎛ ⎞ ⎜⎜8πT i 2 ⎟⎟⎟ s∑ ⎜⎝⎜ ⎠⎟
(7)
−N
(
))
(
2πTs L L2 − 1
M ⋅ 2πΔfTs + M (ui − ui −1 ) ∈ (−π, π)
in which L is the total number of samples in the confidence interval, and L=2N+1. The variance of this estimation reads:
(16πT L (L − 1))
σ 2 p = 3σα2
2
(8)
2
s
Δf
with
(
)
)
)
σα2 = σu 2 = σn 2 2 = 4 Eb N o
(9)
Substituting σα2 into (8) yields
(
(
σ 2 p = 3 4πTs 2L L2 − 1 Eb N o
(10)
As we can see, it is much easier to avoid 2π phase ambiguities if the phase differences {βi } are use, instead of the absolute phases {αi } :
(
)
= M ⋅ 2πΔfTs + M (ui − ui −1 )
(11)
Then (7) can be rewritten in terms of {βi } : pf = Δ
N
∑ w (i ) β
i =−N
Secondly, SNR of the received signal will also have significant impact on the performance of estimation. Note that in (11), the noise item raises when SNR decreases; meanwhile, (5) will no longer be workable when SNR is too low. The lower SNR becomes, the harder it will be to eliminate the 2π phase ambiguities, and thus algorithm’s performance will degrade severely. In order to verify the performance of the algorithm, we conducted a series of simulation. Mean value and variance of the estimated frequency offset are shown in Fig 7 and Fig 8. These curves are calculated over different values of the carrier phase θ 0 . Simulation results show that the presented frequency estimation algorithm is unbiased, and the estimation range is close to theoretical upper limit (1/2M) in case of high SNR. fd-est vs fd 1 Eb/No=5dB Eb/No=10dB Eb/No=15dB Eb/No=20dB Eb/No=25dB
0.9
βi = αi − αi −1 = arg z i z i*−1
i
=
N
∑ w (i ) arg (z z )
i =−N
* i i −1
(12)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
with
(
)
w (i ) = 3 (N + 1 + i )(N − i ) 4πTs 2L L2 − 1 (13)
For the specific implementation, we can construct the ML estimator as a FIR filter, as shown in Fig 6, and store
{w (i )} as filter coefficients in advance.
Since the frequency offset Δf has been corrected and the residual error is small enough, the deviation of carrier phase can be estimated, for instance, by using V&V’s algorithm as in Fig 6. IV. SIMULATION RESULTS AND PERFORMANCE ANALYSES
© 2012 ACADEMY PUBLISHER
(14)
thus M ⋅ 2πΔfTs < π , and so ΔfTs < 1 2M .
Mean of Estmated Frequency offset: ∆f*2MT
Δf
From the about derivation of estimation method we can see, the algorithm performance is closely related to two factors, namely, the magnitude of carrier offset and SNR. Firstly, the carrier frequency offset cannot exceed the algorithm’s capability, which is derived when calculating arguments {βi } in (11). To avoid phase aliasing, we make
0
0.2
0.4 0.6 Frequency offset: ∆f*2MT
0.8
Figure 7. Mean value vs normalizes frequency offset
1
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JOURNAL OF NETWORKS, VOL. 7, NO. 8, AUGUST 2012
var of fd-est vs fd
-2
10
Eb/No=5dB Eb/No=10dB Eb/No=15dB Eb/No=20dB Eb/No=25dB
-3
Var of Estmated Frequency offset
10
-4
10
-5
10
-6
10
-7
10
-8
10 -4 10
-3
10
-2
-1
10 Frequency offset: ∆f*2MT
0
10
10
Figure 8. Variance vs normalized frequency offset
The variance of estimated frequency at different Eb/No (dB) in Fig 9 indicates that, at high SNR, performance of the algorithm proposed is approaching MCBR [12], namely,
(16πT L (L − 1))
σ 2 p = 3σα2
2
2
s
Δf
Fig 10 images the change of constellations in different sectors in the monitoring receiver. Simulations are performed as Eb/No varies, and the results show shat, with the algorithm we proposed in this paper, the frequency offset and the phase deviation of carrier can be efficiently estimated and corrected . -3
Var of Estm ated Frequency offset
10
∆f*2MT= ∆f*2MT= ∆f*2MT= ∆f*2MT= ∆f*2MT= MCRB
-4
10
Figure 10. Changes in constellation
(15)
0.0 0.2 0.4 0.6 0.8
V. CONCLUSION In this paper, we present a carrier estimation method for the need of MF-TDMA signal monitoring: the algorithm demands no aid of priori data, and has a low computational complexity. The proposed method consists of the estimation of carrier phase and frequency offset. Simulation results have proved that, the presented frequency estimation algorithm is unbiased, and the estimation performance is close to theoretical upper limit. In conclusion, the receiver architecture we described with this algorithm has a wide capture range and is very suitable for the monitoring of burst communication signal. REFERENCES
-5
10
[1] -6
[2]
10
[3]
-7
10
5
10
15 Eb/No(dB)
20
[4]
Figure 9. Variance vs Eb/No [5]
[6]
© 2012 ACADEMY PUBLISHER
Jun He and Hua Deng, ”MF-TDMA Signal Detection and Parameter Estimation System,” Communications Technology, vol. 9, pp. 32-33, 2008. X. T. Vuong, F. S. Zimmermann and T. M. Shimabukuro, “Performance analysis of Ku-band VSAT networks,” IEEE Communications Magazine, vol. 26, pp. 25-33, 1988. Xuping Jiang, “A Non-Data-aided Frequency Offset Estimation Algorithm for Burst Transmission,” Electronic Science and Technology, vol. 23, pp. 100-102, 2010. Zhenyan Qin and Jiyu Zheng,"A None-Data-Aided Carrier Frequency Offset Estimation Algorithm Based on Maximum Likelihood", Journal of Gui lin University of El ectronic Technology, Vol. 29, No. 3, pp. 2206-228, 2009. Luise, M. and R. Reggiannini, Carrier frequency recovery in alldigital modems for burst-mode transmissions. Communications, IEEE Transactions on, vol. 43(234): pp. 1169-1178, 1995. B. E. Paden, “Matched nonlinearity for phase estimation of a pskmodulated carrier,” IEEE Transactions on Information Theory, vol. IT-32, pp. 419-422, 1986.
JOURNAL OF NETWORKS, VOL. 7, NO. 8, AUGUST 2012
[7]
F. Gardner, “A BPSK/QPSK Timing-Error Detector for Sampled Receivers,” IEEE Transactions on Communications, vol. 34, pp. 423- 429, 1986. [8] A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSKmodulated carrier phase with application to burst digital transmission,” IEEE Transactions on Information Theory, vol. 29, pp. 543-551, 1983. [9] Kay, S., A fast and accurate single frequency estimator. Acoustics, IEEE Transactions on Speech and Signal Processing, vol. 37(12): pp. 1987-1990, 1989. [10] Xiao, Y.C., et al., Fast and accurate single frequency estimator. Electronics Letters,. Vol. 40(14): pp. 910- 911, 2004. [11] S. Bellini, C. Molinari and G. Tartara, “Digital frequency estimation in burst mode QPSK transmission,” IEEE Transactions on Communications, vol. 38, pp. 959-961, 1990. [12] A.N. D'Andrea, U. Mengali, R. Reggiannini, “The modified cramer- rao bound and its application to synchronization problems,” IEEE Trans. Commun, vol. 42, pp. 1391-1399, 1994. Xi Liu, was born in Liaoning province of China, in 1983. He received his B.S. degree in electronics and information engineering and in applied mathematics in 2001. He is currently a PhD student in School of Electric and Information Engineering in Beihang University (BHU). His research interest is in satellites telemetry tracking and command (TT&C), and inter-satellites communication technology.
Wenquan Feng, was born in Sichuan province of China, in 1970. He received his PhD degree in Beihang University (BHU) and is currently a professor of School of Electric and Information Engineering in BHU. In recent years, he has presided over more than 10 scientific programs , published over 20 papers, including over 10 EI-indexed papers, edited and published two monographs. His research interest is in modern digital communication system, telemetry and telecontrol technology, aerospacecraft test and simulation, etc. Chunsheng Li, professor of School of Electric and Information Engineering in Beihang University (BHU). He received his PhD degress in communication and electronic systems , in BHU, 1998. In recent years, he has presided over more than 20 scientific programs , guided 20 graduated students, edited and published 4 monographs, and published over 80 scientific papers. His research insterests include spaceborne SAR system and simulation technology, information fusion on mutisource remote sensing images, signal gathering and processing ,etc. Chao Ma, was born in Neimenggu province of China, in 1987. He received his B.S. degree in Beihang University (BHU) in 2010, and is currently a graduated student in School of Electric and Information Engineering in BHU. His research interest is in satellites telemetry tracking and command techmology.
© 2012 ACADEMY PUBLISHER
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JOURNAL OF NETWORKS, VOL. 7, NO. 8, AUGUST 2012
A Carrier Estimation Method for MF-TDMA Signal Monitoring Xi Liu School of Electronics and Information Engineering, Beihang University, Beijing, China Email: [email protected]
Wenquan Feng, Chunsheng Li, Chao Ma School of Electronics and Information Engineering, Beihang University, Beijing, China Email: [email protected], [email protected], [email protected]
Abstract—Based on the need of MF-TDMA signal monitoring, this paper investigates the estimation method for frequency offset and carrier phase. The procedure for timing recovery is introduced, and then an effective algorithm is deduced for estimating carrier frequency and phase. The proposed open-loop algorithm demands no preambles and has a wide capture range. In addition, the overall block diagram of a monitoring receiver, which we designed with the proposed estimation algorithm, is presented.
to establish a monitoring system at NCC, so as to find out anomalies and make adjustment in time.
Index Terms—Carrier phase estimation; Frequency offset estimation; MF-TDMA; VSAT;
I. INTRODUCTION MF-TDMA is a two-dimensional multiple access type which combines frequency division with time division. By frequency hopping, variable rate and virtual circuit technology, flexible MF-TDMA network can be achieved between different terminal stations [1]. Because of its flexibility and extensibility, MF-TDMA satellite communication system has been applied more and more. Key points in MF-TDMA satellite communication system involve timing recovery, capture and synchronization, control of power and frequency, etc. Based on this, this paper discusses on the carrier estimation methods for MF-TDMA signal in VSAT satellite network monitoring. As shown in Fig 1, VSAT satellite communication system is comprised of the network control center (NCC), the satellite transponder and VSAT stations [2]. There are three typical transmission patterns in VSAT satellite network: CDMA, SCPC and TDMA. If multiple carriers coexist in a common transponder band, TDMA transmission turns to be MF-TDMA, which can provide more changeful service and is more flexible. MF-TDMA network is more efficient while the implementation techniques are complex: solar outage, rainfall, or improper operations on VSAT stations will impact the quality of communication. Consequently, it is necessary
© 2012 ACADEMY PUBLISHER doi:10.4304/jnw.7.8.1170-1175
Figure 1. VSAT system configuration
In general, VSAT network is power limited, rather than frequency limited system, in which modulation scheme that has the highest power efficiency should be adopted. Therefore, coherent QPSK or BPSK is selected in most cases. For the digital communication systems with PSK modulation, there are two types of carrier synchronization methods [3]: one is using a feedback closed-loop to track the carrier frequency and phase of the received signal, such as quadratic loop and Costas loop; and the other one is the direct estimation of received carrier using open loop structure. In MF-TDMA systems, carrier parameters may vary as the burst slots come from different VSAT stations, which have caused considerable difficulty for closed-loop carrier recovery. For this reason, the open loop maximum likelihood estimation of carrier parameters is mostly studied at present. The open loop estimation methods can be divided into two groups according to weather the training sequences preamble or not: the DA (data-aided) algorithms and the NDA (non-data-aided) algorithms [4]. For the application fields of MF-TDMA signal monitoring, as it is difficult to be informed of preamble sequences, therefore the NDA algorithms are usually adopted. Based on the premised demand, this paper
JOURNAL OF NETWORKS, VOL. 7, NO. 8, AUGUST 2012
1171
proposes an open loop carrier estimation method and the corresponding architecture of monitoring receivers [5-6].
We consider performing the monitor at intermediate frequency, thus the architecture of the sampling receiver can be shown as in Fig 5.
II. ARCHITECTURE OF THE MONITORING RECEIVER In this paper, we take QPSK for example and express the received MF-TDMA signal as:
((
r (t ) = ∑ Ak (t ) exp j 2π fk t + ϕk (t ) + θk
)) + n (t )
(1)
in which Ak ( t ) is the amplitude of received signal, f k is the carrier frequency, θ k is the carrier phase deviation,
ϕk ( t ) is the modulated symbol phase taking values in
{ 1 4π ,3 4π ,5 4π , 7 4π }, n ( t ) is the additive white Gaussian noise, and the subscript k represents the ordinal number of the multiple carriers. Fig 2 represents the time-frequency two-dimensional expansion of this MF-TDMA signal as in (1). Spectrogram of this signal and the time-domain envelope of a single channel are shown in Fig 3 and Fig 4.
Figure 5. System diagram of monitoring receiver
First, the receiver quantizes the IF multi-carrier signal by using band-pass sampling, and the local NCO is set to the center frequency of one of the MF-TDMA carriers. After the quadrature down-conversion, the sampling rate is reduced to integer multiples of the symbol rate to facilitate further processing. Then, after the matched filter, we get the complex samples of the baseband TDMA signal. For MF-TDMA signal monitoring system, the top priority is to obtain measurement indices (such as slot power, frequency offset, EVM, etc.) of each channel. If there is any anomalous value, the monitoring system should give an alarm timely. In this paper, we focus on the carrier estimation method of the baseband samples. III. ALGORITHM DESCRIPTION In traditional receivers, feedback loops are commonly used for carrier synchronization, in which the hang-up effect may limit the capture range and slowdown the process of carrier acquisition. Accordingly this article proposes using open-loop estimation method in monitoring receiver, and puts forwards corresponding algorithm suitable for MF-TDMA burst communication.
Figure 2. Sketch map of time-frequency expansion -14
x 10
3.5 3
PSD(W /Hz)
2.5 2 1.5 1 0.5 0 55
60
65
70 Frequency(MHz)
75
80
Power Envelope
Figure 3. Spectrogram of MF-TDMA signal
85
A. Timing recovery Monitoring system receives burst signals from different VSAT stations, so separate estimation for each burst slot is needed. The purpose of timing recovery is to figure out the optimal sampling time, so as to gain the maximum receiving signal-to-noise ratio (SNR) during demodulation. In this paper, Gardner’s timing-error detection algorithm is applied for optimal sampling-points verdict. Pivotal ideas of Gardner’s algorithm are listed as follows: take sample points, of which any adjacent two are half a symbol cycle apart, into account, and use their amplitudes and polarity changes to calculate the timing error [11]. The specific algorithm is u(r ) = I (r − 1 / 2)[I (r ) − I (r − 1)] +Q(r − 1 / 2)[Q(r ) − y(r − 1)]
(2)
Symbols
Figure 4. Time-domain envelope of a single channel
© 2012 ACADEMY PUBLISHER
where I and Q represent the inphase and quadrature samples, and the index r is used to designate the number of symbols: r represents the current sample point, r-1 represents the sample point of the last symbol, and use r-
1172
1/2 to denote the sample lying midway between the rth and the (r-1)th sample. Therefore, the error calculation only requires to sample the baseband signal at the 2 times of the symbol rate. Gardner’s algorithm is independent from carrier estimation, as a result, the timing recovery can be performed before or after the carrier synchronization. In the monitoring receiver as we described in Fig 5, modified open-loop timing recovery method is adopted for the convenience of processing. We first reduce the sampling frequency, after the quadrature down-converter, to Q times of the symbol rate (Q is an even integer greater than 2). After the matched filter, use (2) to calculate timing error of the Q columns sampled data. And finally, we pick the column which has the minimum variance as the optimal samples. A necessary consideration is that, during one frame period, there are time slots when no data burst but only exists noise, and it is meaningless to calculate timing error at such idle slots. Also, timing error of burst data slots may differ, as they came from different VSAT stations. In order to improve the accuracy of the timing recovery, we use a module called “Slot Extraction” to extract data slots from the energy envelop of modulated carriers. Then, timing error is calculated for each data slot separately. B. Carrier esitimation For non data-aided (NDA) carrier estimation, the Viterbi & Viterbi algorithm, as in [8], is a classic openloop nonlinear phase estimation algorithm, and has been widely used. Generally, the process of V&V estimation can be divided into three steps: first, the modulation is removed by a nonlinear transformation; then, average the phase in the estimation interval; at the final, equivocation of estimated carrier phase should be eliminated. Consider that the MF-TDMA signal being monitored in VSAT network is relayed transparently by the geosynchronous satellite, the dynamic range of carrier frequency is small enough that the Doppler shift can be neglected. Therefore, dominated carrier frequency offset comes from the deviation of frequency standard on different VSAT equipments. Due to the need of average process on estimated phase, the V&V algorithm requires the normalized frequency offset to meet: ΔfTs ≤ 0.05 , in which Δf is the carrier frequency offset, and Ts is the period of one symbol. When the frequency offset Δf exceeds a certain limit, the performance of V&V’s estimation algorithm will descend obviously. For this reason, we consider to evaluate the frequency offset and try to make corresponding compensation before the phase estimation [9-10]. The structural model of the carrier estimation method proposed in this paper is shown as in Fig 6.
JOURNAL OF NETWORKS, VOL. 7, NO. 8, AUGUST 2012
Δof
Figure 6. Structural model of the carrier estimation
For the facility of analyzing, we assume that the timing of samples has been accurately recovered after the matched filter, and the complex baseband samples can be expressed as in (3). ri = x i + j ⋅ yi
((
(
))
)
= exp j 2πΔf ⋅ iTs + ϕi 2π M + θ0 + ni
in
which ϕi ( 2π M )
represents
the
M-ary
(3)
PSK
modulated ui data, θ 0 is the initial phase, and ni represents the complex additive Gaussian noise whose two-side power spectral density is N 0 2 . To investigate the complex samples in the estimation interval − N ≤ i ≤ N , we first remove the modulation by a Mth-power nonlinear transformation, namely,
(
j 2πΔf ⋅iTs +ϕi ( 2π zi = e (
M ) +θ 0 )
+ ni
)
M
= ri
M
j M arg ( ri ) ) e( (4)
Such a transformation will change the carrier phase interval from [ −π , π ] into [ − π M , π M ] . When the SNR of ri is high, we can take a simple approximation as follow [7]
arg ( ri ) = ( 2πΔf ⋅ iTs + ϕi ( 2π M ) + θ 0 ) + ui
(5)
in which is the equivalent phase noise to ni , who is also Gaussian distributed with zero mean, and yields σ u 2 = σ n 2 2 . The result of this nonlinear transformation can be written as αi = arg (z i ) = M arg (ri )
= M (2πΔf ⋅ iTs + θ0 + ui ) + i ⋅ 2π
(6)
Without the influence of modulation, carrier frequency offset can be evaluated form sample series {α i } . Note that samples
{α i }
are linearly proportional to the
frequency offset Δf . In particular, the maximum
© 2012 ACADEMY PUBLISHER
JOURNAL OF NETWORKS, VOL. 7, NO. 8, AUGUST 2012
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likelihood (ML) estimation is equivalent to an unbiased least mean-square (LMS) estimation, with the following result: N ⎞ pf = ⎛⎜ Δ ⎜⎜ ∑ iαi ⎟⎟⎟ ⎝⎜i =−N ⎠⎟ ⎛ N ⎞ = ⎜⎜⎜3 ∑ iαi ⎟⎟⎟ ⎝⎜ i =−N ⎠⎟
N ⎛ ⎞ ⎜⎜8πT i 2 ⎟⎟⎟ s∑ ⎜⎝⎜ ⎠⎟
(7)
−N
(
))
(
2πTs L L2 − 1
M ⋅ 2πΔfTs + M (ui − ui −1 ) ∈ (−π, π)
in which L is the total number of samples in the confidence interval, and L=2N+1. The variance of this estimation reads:
(16πT L (L − 1))
σ 2 p = 3σα2
2
(8)
2
s
Δf
with
(
)
)
)
σα2 = σu 2 = σn 2 2 = 4 Eb N o
(9)
Substituting σα2 into (8) yields
(
(
σ 2 p = 3 4πTs 2L L2 − 1 Eb N o
(10)
As we can see, it is much easier to avoid 2π phase ambiguities if the phase differences {βi } are use, instead of the absolute phases {αi } :
(
)
= M ⋅ 2πΔfTs + M (ui − ui −1 )
(11)
Then (7) can be rewritten in terms of {βi } : pf = Δ
N
∑ w (i ) β
i =−N
Secondly, SNR of the received signal will also have significant impact on the performance of estimation. Note that in (11), the noise item raises when SNR decreases; meanwhile, (5) will no longer be workable when SNR is too low. The lower SNR becomes, the harder it will be to eliminate the 2π phase ambiguities, and thus algorithm’s performance will degrade severely. In order to verify the performance of the algorithm, we conducted a series of simulation. Mean value and variance of the estimated frequency offset are shown in Fig 7 and Fig 8. These curves are calculated over different values of the carrier phase θ 0 . Simulation results show that the presented frequency estimation algorithm is unbiased, and the estimation range is close to theoretical upper limit (1/2M) in case of high SNR. fd-est vs fd 1 Eb/No=5dB Eb/No=10dB Eb/No=15dB Eb/No=20dB Eb/No=25dB
0.9
βi = αi − αi −1 = arg z i z i*−1
i
=
N
∑ w (i ) arg (z z )
i =−N
* i i −1
(12)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
with
(
)
w (i ) = 3 (N + 1 + i )(N − i ) 4πTs 2L L2 − 1 (13)
For the specific implementation, we can construct the ML estimator as a FIR filter, as shown in Fig 6, and store
{w (i )} as filter coefficients in advance.
Since the frequency offset Δf has been corrected and the residual error is small enough, the deviation of carrier phase can be estimated, for instance, by using V&V’s algorithm as in Fig 6. IV. SIMULATION RESULTS AND PERFORMANCE ANALYSES
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(14)
thus M ⋅ 2πΔfTs < π , and so ΔfTs < 1 2M .
Mean of Estmated Frequency offset: ∆f*2MT
Δf
From the about derivation of estimation method we can see, the algorithm performance is closely related to two factors, namely, the magnitude of carrier offset and SNR. Firstly, the carrier frequency offset cannot exceed the algorithm’s capability, which is derived when calculating arguments {βi } in (11). To avoid phase aliasing, we make
0
0.2
0.4 0.6 Frequency offset: ∆f*2MT
0.8
Figure 7. Mean value vs normalizes frequency offset
1
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var of fd-est vs fd
-2
10
Eb/No=5dB Eb/No=10dB Eb/No=15dB Eb/No=20dB Eb/No=25dB
-3
Var of Estmated Frequency offset
10
-4
10
-5
10
-6
10
-7
10
-8
10 -4 10
-3
10
-2
-1
10 Frequency offset: ∆f*2MT
0
10
10
Figure 8. Variance vs normalized frequency offset
The variance of estimated frequency at different Eb/No (dB) in Fig 9 indicates that, at high SNR, performance of the algorithm proposed is approaching MCBR [12], namely,
(16πT L (L − 1))
σ 2 p = 3σα2
2
2
s
Δf
Fig 10 images the change of constellations in different sectors in the monitoring receiver. Simulations are performed as Eb/No varies, and the results show shat, with the algorithm we proposed in this paper, the frequency offset and the phase deviation of carrier can be efficiently estimated and corrected . -3
Var of Estm ated Frequency offset
10
∆f*2MT= ∆f*2MT= ∆f*2MT= ∆f*2MT= ∆f*2MT= MCRB
-4
10
Figure 10. Changes in constellation
(15)
0.0 0.2 0.4 0.6 0.8
V. CONCLUSION In this paper, we present a carrier estimation method for the need of MF-TDMA signal monitoring: the algorithm demands no aid of priori data, and has a low computational complexity. The proposed method consists of the estimation of carrier phase and frequency offset. Simulation results have proved that, the presented frequency estimation algorithm is unbiased, and the estimation performance is close to theoretical upper limit. In conclusion, the receiver architecture we described with this algorithm has a wide capture range and is very suitable for the monitoring of burst communication signal. REFERENCES
-5
10
[1] -6
[2]
10
[3]
-7
10
5
10
15 Eb/No(dB)
20
[4]
Figure 9. Variance vs Eb/No [5]
[6]
© 2012 ACADEMY PUBLISHER
Jun He and Hua Deng, ”MF-TDMA Signal Detection and Parameter Estimation System,” Communications Technology, vol. 9, pp. 32-33, 2008. X. T. Vuong, F. S. Zimmermann and T. M. Shimabukuro, “Performance analysis of Ku-band VSAT networks,” IEEE Communications Magazine, vol. 26, pp. 25-33, 1988. Xuping Jiang, “A Non-Data-aided Frequency Offset Estimation Algorithm for Burst Transmission,” Electronic Science and Technology, vol. 23, pp. 100-102, 2010. Zhenyan Qin and Jiyu Zheng,"A None-Data-Aided Carrier Frequency Offset Estimation Algorithm Based on Maximum Likelihood", Journal of Gui lin University of El ectronic Technology, Vol. 29, No. 3, pp. 2206-228, 2009. Luise, M. and R. Reggiannini, Carrier frequency recovery in alldigital modems for burst-mode transmissions. Communications, IEEE Transactions on, vol. 43(234): pp. 1169-1178, 1995. B. E. Paden, “Matched nonlinearity for phase estimation of a pskmodulated carrier,” IEEE Transactions on Information Theory, vol. IT-32, pp. 419-422, 1986.
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[7]
F. Gardner, “A BPSK/QPSK Timing-Error Detector for Sampled Receivers,” IEEE Transactions on Communications, vol. 34, pp. 423- 429, 1986. [8] A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSKmodulated carrier phase with application to burst digital transmission,” IEEE Transactions on Information Theory, vol. 29, pp. 543-551, 1983. [9] Kay, S., A fast and accurate single frequency estimator. Acoustics, IEEE Transactions on Speech and Signal Processing, vol. 37(12): pp. 1987-1990, 1989. [10] Xiao, Y.C., et al., Fast and accurate single frequency estimator. Electronics Letters,. Vol. 40(14): pp. 910- 911, 2004. [11] S. Bellini, C. Molinari and G. Tartara, “Digital frequency estimation in burst mode QPSK transmission,” IEEE Transactions on Communications, vol. 38, pp. 959-961, 1990. [12] A.N. D'Andrea, U. Mengali, R. Reggiannini, “The modified cramer- rao bound and its application to synchronization problems,” IEEE Trans. Commun, vol. 42, pp. 1391-1399, 1994. Xi Liu, was born in Liaoning province of China, in 1983. He received his B.S. degree in electronics and information engineering and in applied mathematics in 2001. He is currently a PhD student in School of Electric and Information Engineering in Beihang University (BHU). His research interest is in satellites telemetry tracking and command (TT&C), and inter-satellites communication technology.
Wenquan Feng, was born in Sichuan province of China, in 1970. He received his PhD degree in Beihang University (BHU) and is currently a professor of School of Electric and Information Engineering in BHU. In recent years, he has presided over more than 10 scientific programs , published over 20 papers, including over 10 EI-indexed papers, edited and published two monographs. His research interest is in modern digital communication system, telemetry and telecontrol technology, aerospacecraft test and simulation, etc. Chunsheng Li, professor of School of Electric and Information Engineering in Beihang University (BHU). He received his PhD degress in communication and electronic systems , in BHU, 1998. In recent years, he has presided over more than 20 scientific programs , guided 20 graduated students, edited and published 4 monographs, and published over 80 scientific papers. His research insterests include spaceborne SAR system and simulation technology, information fusion on mutisource remote sensing images, signal gathering and processing ,etc. Chao Ma, was born in Neimenggu province of China, in 1987. He received his B.S. degree in Beihang University (BHU) in 2010, and is currently a graduated student in School of Electric and Information Engineering in BHU. His research interest is in satellites telemetry tracking and command techmology.
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