Frequency Synchronization in Global Satellite Communications Systems

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Frequency Synchronization in Global Satellite Communications Systems

Qingchong Liu, Member, IEEE

Abstract—A frequency synchronization method is proposed and analyzed for global satellite communications systems employing low earth orbit satellites or medium earth orbit satellites. In these systems, the Doppler shift varies randomly and can be more than ten times larger than the symbol rate. The proposed method uses the satellite as the reference point and corrects frequency errors accordingly. It is shown the proposed method can achieve negli- gibly small frequency errors. By employing this method, the system bandwidth can be fully utilized and guard bands are no longer needed.

Index Terms—Doppler shift, frequency estimation, frequency synchronization, global satellite communications.

I. INTRODUCTION

I

N RECENT years medium earth orbit satellites and low earth orbit satellites have been employed to carry signals for large population of simultaneous users in global mobile satellite communication systems [1]. Satellite communications system standard using CDMA technology compatible to the third generation wireless systems is also developed [2]. As medium earth orbit satellites and low earth orbit satellites move at tens of kilometers per second relative to the earth, the high speeds can cause Doppler shift to be higher than 100 kHz [3]. The Doppler shift is random, varies with time and can be higher than the symbol rate. It can cause failure of packet detection, carrier frequency synchronization, serious degradation of demodulation performance and frequent failure of radio link [4]. For systems employing FDMA/TDMA, the traditional method of using guard bands to combat Doppler shift can result in a big waste of system bandwidth [5], [6]. For CDMA-based systems, the Doppler shift can increase system and hardware complexity and prolong acquisition process.

The code tracking performance in CDMA systems is severely degraded in the presence of Doppler shift. Therefore, compen- sating Doppler shift caused by the fast motion of satellites is important to achieve carrier frequency synchronization and to reduce frequency management complexity in global satellite communications systems.

This paper analyzes the effect of the Doppler shift to carrier frequency synchronization in communication systems employing non-geosynchronous satellites. An optimum method

Paper approved by R. Reggiannini, the Editor for Synchronization and Wire- less Applications of the IEEE Communications Society. Manuscript received June 1, 2001; revised May 28, 2002 and July 30, 2002. This work was supported in part by the National Science Foundation under Grant ANI-0112722 and Grant ANI-0113307. This paper was presented in part at the 1999 IEEE Wireless Com- munications and Networking Conference, New Orleans, LA, September 21–24, 1999.

The author is with the Department of Electrical and Systems Engineering, Oakland University, Rochester, MI 48309-4478 USA (email: qliu@oakland.

edu).

Digital Object Identifier 10.1109/TCOMM.2003.809751

to compensate the random Doppler shift of large range and to achieve carrier frequency synchronization at the input of the demodulator is proposed and analyzed.

II. FREQUENCYERRORANALYSIS

In this section, we consider the frequency errors in communications systems employing fast moving satellites. These errors include the Doppler shift and the satellite translation error. The Doppler shift dominates the total error in the received carrier frequency.

Let the transmitted signal be

(1) where is the baseband signal and is the carrier frequency. The received signal can be written as

(2) where is noise, and

(3) is the received carrier frequency, is the relative speed between the transmitter and the receiver, is the angle between the relative velocity and the signal propagation direction, and is the light speed. The second term in (3) is the Doppler shift.

Let , which is called the fractional

Doppler shift hereafter.

Consider the Doppler frequency in the forward link. Let be the transmitted carrier frequency from the satellite access node located on the ground for the th user terminal inside the th spot beam. It is also a variable of time because even during the same call this carrier frequency can change from time slot to time slot to have frequency diversity for service quality purposes. Let be the fractional Doppler of the link between the satellite access node and the satellite. This link is called the feeder link. The received carrier frequency at the satellite is

(4) Since the feeder link and the mobile link use different frequency bands, the carrier frequency has to be translated from the frequency band for the forward feeder link to the frequency band for the forward mobile link. The mobile link is between the satellite and the user terminal. Let be the fractional satellite translation error and be the satellite translation frequency. The transmitted carrier frequency by the satellite for the mobile link is

(5)

(2)

Let be the fractional Doppler of the mobile link for the th user in the th spot beam. The received carrier frequency by this user terminal can be written as

(6) where

(7) is the total frequency error caused by both Doppler shift and satellite translation error for the forward link at the user terminal

and is usually

negligible.

The first term in the right-hand side of (7) is called the forward feeder link Doppler shift. Usually it is a continuous random variable in the range of several dozens of kilohertz. The second term in the right side of (7) is called the satellite translation error. The translation frequency is several gigahertz and the the fractional satellite translation error is a random variable. The satellite translation error is a random variable uniformly distributed in a range of several dozens of hertz. The third term is called the forward mobile link Doppler shift. It is a random variable distributed in the range of several dozens of kilohertz. Therefore, the total frequency error in (7) is a continuous random variable in a range of several dozens of kilohertz.

For example, in a satellite PCS system [1], the satellite orbits are circles at 10 355 km altitude, which gives a maximum fractional Doppler shift of . The forward feeder link uses 5 GHz as the center carrier frequency and the mobile link em- ploys 2 GHz as the center carrier frequency. The forward feeder link Doppler shift is a random variable in the range

kHz and the forward mobile link Doppler shift is a random variable in the range kHz. The satellite translation error is a random variable uniformly distributed in Hz. The total frequency error in the forward link is a random variable in the range kHz, which is larger than its 25.2-kHz carrier bandwidth for each user terminal. In the Globalstar system, the Doppler shift can be 104 kHz [3], which is 43 times higher than the bit rate of user terminals. If not corrected properly, the frequency error can easily cause failure of carrier frequency synchronization.

Consider the Doppler shift in the return link, which is from user terminal to satellite access node. Let be the transmitted carrier frequency by the th user terminal in the th spot beam. The received carrier frequency by the satellite is

(8) Let be the satellite translation frequency from the mobile link to the feeder link. The transmitted carrier frequency by the satellite is

(9) The received carrier frequency by the radio frequency terminal

is which can be written as

(10)

where

(11) is the total frequency error for the return link and is negligible. The first term in the right-hand side of (11) is the return mobile link Doppler shift, which is a random variable of approximately the same range as the forward mobile link Doppler shift. The second term in (11) is the satellite translation error. The third term in (11) is the feeder link Doppler shift.

For example, in a global satellite communications system [1], the center carrier frequency for the return feeder link is 7 GHz.

For the return link the feeder link Doppler shift is a continuous random variable in the range kHz and the satellite translation error is a random variable uniformly distributed in Hz. The total frequency error for the return link is a random variable in the range kHz.

III. FREQUENCYSYNCHRONIZATION FORCONTROLCHANNELS

Control channels are employed to carry system information for system control and synchronization purposes. The information includes the system time, the access frequency and the median Doppler shift for each spot beam, etc. Control channels are in the forward link and can have very large value of the random Doppler shift, which must be precorrected to make sure user terminals can achieve frequency synchronization with control channels. For each spot beam, the median Doppler shift line is defined as a curve on the Earth’s surface [5], where the Doppler shift has the median value within the spot beam. The Doppler shift and the satellite translation error for each control channel has to be precorrected such that the received carrier frequency on the median Doppler shift line is the preassigned nominal frequency.

Let be the control channel nominal frequency for the th spot beam and be the carrier frequency transmitted by the radio frequency terminal. Applying (6), we have

(12) where

(13) is the total frequency correction at the satellite access node and is the fractional Doppler shift on the median Doppler shift line for the th spot beam. The term is negligible. In other words, when the transmitted frequency at the satellite access node is (12), the received frequency on the median Doppler shift line is .

The first term in the right-hand side of (13) is the forward feeder link Doppler shift correction, which can be partitioned into

(14) where is the center carrier frequency for the forward feeder link. In (14) the first term in the right hand side is called the

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center Doppler shift correction and the second term is called the residual Doppler shift correction, both for the forward feeder link. The center Doppler shift correction can be performed by the radio frequency terminal once for all of the channels in the forward link. The residual Doppler shift correction, which is usually several dozens of hertz, varies from channel to channel and should be corrected by the satellite base station subsystem [5]. The second term in the right hand side of (13) is the Doppler shift correction for the forward mobile link, which varies from spot beam to spot beam and should be performed by the satellite base station subsystem. The third term in the right-hand side of (13) is the satellite translation error, which also should be corrected by the satellite base station subsystem. In other words, the total frequency correction (13) at the satellite access node can be written as

(15) where

(16) is the center Doppler shift correction for the forward feeder link performed by the radio frequency terminal [5] and

(17) is the correction performed by the satellite base station subsystem for each channel.

The fractional Doppler shift of the feeder link and the fractional satellite translation error, which are both time varying, can be measured by two pilot loops in the feeder link operated by the radio frequency terminal [5]. Let be the transmitted frequency of the radio frequency terminal and be the corresponding satellite translation frequency, . Then, the received frequency by the radio frequency terminal from the loop back is

(18) The received carrier frequency can be estimated using maximum likelihood estimator [7]. Let , , be the estimated frequency, and . The instantaneous fractional Doppler shift can be estimated as

(19)

and the fractional satellite translation error can be estimated as (20) It can be shown the estimation errors and

have zero mean, i.e.,

(21) and

(22)

The variance of the estimation error is

(23) where is the variance of , . The variance of the estimation error is

(24) Minimizing and is sufficient to minimize and . This can be achieved by converting received signals to baseband and then measuring the carrier frequency. Applying the maximum-likelihood estimator in [7], we have

(25)

where , is the

signal-to-noise power ratio and is the number of samples used. Therefore, the variance of the estimated instantaneous fractional Doppler shift is

(26) The variance of the estimated fractional satellite translation

error is

(27) The variance is minimized if is minimized. System de- signer can focus on minimizing .It is critical to make and small enough so that their effect to all channels is negligible.

IV. MEASURINGUSER TERMINALFRACTIONAL

DOPPLERSHIFT

Assume that the th user terminal in the th spot beam wants to establish a communication link. This user terminal starts to search in a set of prestored frequencies for control channels. These frequencies are remembered in the memory of each user terminal. For each spot beam there is at least one control channel carrying system time and access frequency for the access channel. As discussed in the previous section, the received carrier frequency on the median Doppler line of each spot beam is the nominal frequency. User terminals located off the median Doppler line still experience Doppler shift when trying to synchronize to the control channel. Usually the maximum Doppler shift difference from the edge to the median Doppler line in the same spot beam is a few kilohertz. Then, it is not difficult for a user terminal to be synchronized to the control channel.

After demodulating the control channel signal, the user terminal knows the access frequency assigned as the access channel to the spot beam. The user terminal sends an access request to the satellite access node via the access channel. The satellite access node has to detect the access request burst in the presence of Doppler shift. The satellite access node has to measure the Doppler shift in the access request signal in real time. The measured Doppler shift is used to demodulate the access request and derive the user terminal fractional Doppler shift

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. The fractional Doppler shift is used for user terminal position determination [3] and traffic channel frequency synchronization [5], [6].

We propose that the Doppler shift of the access channel on the median Doppler line for each spot beam is calculated in real time by satellite access node and transmitted to user terminals along with the access frequency . In other words, the pair is sent to user terminals through the control channel, where is the corresponding Doppler shift in the access channel, which is

(28) where is the fractional Doppler shift for the median Doppler shift line in the th spot beam and can be calculated using the knowledge of the satellite orbit [3]. The user terminal sends access request at the carrier frequency . The received carrier frequency by the satellite access node for the access channel is

(29) For the return feeder link, the radio frequency terminal performs center Doppler correction by adding the following amount to the received carrier frequency [5]

(30) where is the center frequency for the return feeder link. Also the radio frequency terminal performs down-conversion. Let the down-conversion frequency at the radio frequency terminal be . Then the input carrier frequency to the satellite base station subsystem is

(31) Before demodulation, the satellite base station subsystem performs the return feeder link Doppler correction, satellite translation error correction and downconversion by deducting from the carrier frequency the following amount

(32) which is the received carrier frequency for the access channel if the user terminal is on the median Doppler line. At the input of the modem inside the satellite base station subsystem, the frequency offset of the access channel will be

, i.e.

(33) Usually is around 1 kHz. The modem detects the access request signal [4], estimates the frequency offset [7]

and compensates it before demodulation [5].

Let be the estimate of the frequency offset for the access channel. It is used to derive the fractional Doppler of the user terminal by applying

(34)

where is the fractional Doppler shift for the median Doppler shift line of the th spot beam and is the measured fractional Doppler shift for the feeder link. The value can be calculated according to the satellite orbit [3] and is obtained in the previous section. The value

is employed for traffic channel frequency synchronization [5], [6] and position determination [3].

Let . Usually

is about 1 kHz. Using the proposed method, the range of the random Doppler shift for access channels at both the satellite and the satellite access node is , which is much smaller than that in the traditional systems. In [7], it was shown that the Cramer–Rao bound of the unbiased frequency estimator for a complex tone is

(35) where is the sampling frequency, is the signal-to-noise power ratio and is the number of samples. In traditional systems where user terminals sends access request at the nominal carrier frequency , the sampling frequency has to satisfy [7]. For a system where user terminals transmit access request at the frequency , the sampling frequency has to be not less than . It can be shown that the variance of the frequency estimator is

(36) It satisfies

(37)

where is the maximum Doppler shift

in the access channel in traditional systems and is the variance of the corresponding frequency estimator. Since , the variance of the frequency estimator in the system employing the proposed method is much smaller than that in the traditional

system. For example, for a global

satellite communications system [1], where kHz and kHz. Therefore, the proposed method significantly improves the performance of the Doppler shift measurement for access channels. It helps dramatically to improve the overall system performance, including demodulation performance and user terminal position determination. It also helps to improve frequency synchronization for traffic channels. Because the maximum Doppler shift observed at the satellite access node is very small compared with the bandwidth of each channel, the adjacent channel interference caused by Doppler shift is very small and does not cause loss of access request.

Fig. 1 plots the standard deviation obtained in (36). It can be seen that the standard deviation of the estimate of the access

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Fig. 1. Standard deviation of Doppler shift estimation versus SNR. The maximum Doppler shift is r = 10:05 kHz in the mobile link before correction. After the proposed Doppler shift correction, the maximum Doppler shift isr = 1 kHz in the mobile link. The signal length N is 100 symbols for the diamond line. The signal length is increased by 10 symbols in each line from the top to the bottom, ie.,N = 140 in the dashed line.

channel Doppler shift is less than 1.4 Hz when the access request signal length symbols and the signal-to-noise power ratio is not less than 5 dB.

V. FREQUENCYSYNCHRONIZATION FORTRAFFICCHANNELS

After the satellite access node successfully receives the access request from the user terminal, the satellite access node allocates carrier frequencies to the user terminal to transmit and receive, which are called the traffic channels. These frequencies are car- ried to the user terminal through the control channel. Once the user terminal receives these frequencies, it starts to transmit and receive. However, frequency errors including Doppler shift and satellite translation error have to be carefully taken care for traffic channels to maintain acceptable demodulation performance. As shown in Section II, Doppler shift dominates the total frequency error. The best reference point of Doppler shift correction is the satellite for traffic channels and access channels. Doppler shift can be corrected in such a way that the received carrier frequency at the satellite is always the nominal frequency. By doing this, there is no need to employ guard bands and the demodulation performances will not be degraded both on board the satellite and at the user terminal and the satellite access node. This is desirable by the new generation of satellite communications systems, which aims at better utilization of system bandwidth and to have demodulation on board satellites.

Using the satellite as the reference point, the feeder link residual Doppler shift and the satellite translation error can be corrected by the satellite base station subsystem; the feeder link center Doppler shift can be corrected by the radio frequency terminal; and the mobile link Doppler shift can be compensated by the user terminal guided by the satellite access node. For traffic channels, the satellite access node needs to send two pairs of frequencies. The first pair is ,

where is the nominal carrier frequency for the user terminal to transmit and

(38) is the corresponding correction for Doppler shift, and is the fractional Doppler shift of the user terminal measured from its access request signal. The second pair is for the user terminal to receive, where (39) is the Doppler shift correction.

A. Return Link

For the traffic channel in the return link, the user terminal transmits at the frequency

, i.e.,

(40) The received carrier frequency at the satellite is the nominal frequency when there is no estimation error for . The received carrier frequency at the radio frequency terminal is

(41) where is the satellite translation frequency. The frequency

can be written as

(42) where the third term on the right side is the residual Doppler shift of the mobile link, the fourth term is the satellite translation error, the fifth term is the feeder link Doppler

shift and . In the received

carrier frequency at the radio frequency terminal, the

Doppler shift of a large range in the

mobile link is reduced to the residual Doppler shift of a much smaller range, i.e.,

. The distance between the received carrier frequencies for any two adjacent channels satisfies

(43) where is the carrier bandwidth and is usually less than 0.2 Hz. The order of magnitude of the second term on the right-hand side of (43) is less than that of the standard deviation of the mobile link Doppler shift estimated from the access channel. The latter is at most few Hertz. Therefore, the overlap between any two adjacent channels is less than a few Hertz in the worst case and no guard band is needed.

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For each channel, the radio frequency terminal performs center Doppler shift correction and the satellite base station subsystem performs the correction for both the residual Doppler shift in the feeder link and the satellite translation error. All the information contained in (42) is known to the satellite base station subsystem prior to processing the traffic channel signal.

The satellite base station subsystem can perform corrections for the residual Doppler shift in the feeder link and the satellite translation error. The input signal to the demodulator located in the satellite base station subsystem can be written as

(44) where is the baseband signal, is noise and

(45) is the residual frequency error. The residual frequency error has zero mean. Its variance satisfies

(46) where is the variance of the estimated fractional satellite translation error, is the variance of the estimated fractional Doppler shift in feeder link, and is the variance of the estimated mobile link Doppler shift, and

. Variances on the right-hand side of (46) are given in (27), (26) and (36).

B. Forward Link

For the traffic channel in the forward link, the satellite access node transmits at the carrier frequency

(47) The distance between the carrier frequencies for any two adjacent channels is , where is the carrier bandwidth for each channel and is usually less than 0.2 Hz. Therefore, the Doppler shift no longer causes interference between adjacent channels, and guard bands are not needed.

After the translation from the feeder link to the mobile link, the carrier frequency transmitted by the satellite to the user terminal is

(48) The received carrier frequency at the user terminal is

(49) which can be written as

(50)

where on the right-hand side, the first term is the nominal forward mobile link carrier frequency, the second term is the mobile link Doppler shift, the third term is the residual Doppler shift in the feeder link, the fourth term is the residual translation

error, and . The received signal at

the user terminal can be written as

(51) where is the baseband signal and is noise.

As the user terminal has received the Doppler shift correction through the control channel,

, the user terminal can perform Doppler shift correction by adding to the received carrier frequency in the downconversion process. After down-conversion, the input signal to the demodulator can be written as

(52) where

(53) is the frequency error. It has zero mean. Its variance satisfies

(54) where is given in (27), is given in (26), is given in

(36), and .

VI. APPLICATION

Results obtained in this letter have been applied to a real global satellite communications system using intermediate orbit satellites and FDMA/TDMA [1]. This system was designed for voice and PCS applications. The parameters used in the following is given in [1].

The system has an 6-h intermediate circular orbit at 10 355-km altitude. Its mobile link uses the frequency band [1.98,2.01] GHz for uplink and the frequency band [2.17,2.20]

GHz for downlink. Its feeder link uses 5.2 GHz for uplink and 6.9 GHz for downlink. The carrier bandwidth is 25.2 kHz.

The translation frequency is GHz from mobile link to feeder link and GHz from feeder link to mobile link. The fractional Doppler shift in this system is in the range . The Doppler shift in the mobile link is in the range [ 10.05,10.05] kHz for the uplink and in the range [ 11,11] kHz for the downlink. The Doppler shift in the feeder link is in the range kHz for the uplink and in the range kHz for the downlink.

In (46) and (54), it is shown to minimize the variance of the frequency error at receivers for traffic channels, the variance must be minimized for the estimated Doppler shift in access channel, the estimated fractional satellite translation error and the fractional feeder link Doppler. Let the two pilot tones used in Section III to estimate the fractional Doppler shift of the feeder link and the fractional satellite translation error be sepa- rated by 30 MHz, i.e., MHz, which is the system

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Fig. 2. Standard deviation of the estimated fractional satellite translation error versus the signal length.

bandwidth [1]. The sampling frequency in (26) and (27) is kHz.

Fig. 2 plots the standard deviation of the estimated fractional translation error in (26) versus the signal length in symbols used for estimation. Fig. 3 plots the standard deviation of the estimate fractional Doppler shift in (27) versus the signal length

used. When symbols are used and ,

and . One has Hz,

Hz, Hz and Hz.

In Fig. 1, it is shown that Hz, assuming the access channel has SNR not less than 5 dB and 100 symbols are used to estimate the user terminal Doppler shift. The standard deviation of the return link traffic channel frequency error satisfies Hz, when received at the radio frequency terminal.

The standard deviation of the forward link traffic channel frequency error satisfies Hz after Doppler shift correction at the user terminal. Both and is less than 0.1%

of the 25.2 KHz carrier bandwidth. Therefore, the standard deviation of traffic channel frequency error is negligibly small.

One can conclude that it is critical to have a reasonably high SNR and enough many symbols to estimate the fractional Doppler shift in the feeder link and the fractional satellite translation error, as discussed in Section III. As two pilot tones are dedicated to these estimations, using a few thousand symbols for estimation is implemented in the example system.

In traditional systems, traffic channel frequency errors are high and frequency estimator has to be implemented in each user terminal. When the proposed method is employed, and become negligibly small and frequency estimator is no longer

Fig. 3. Standard deviation of the estimated fractional Doppler shift in the feeder link versus the signal length.

needed in user terminal. This can bring obvious cost reduction to user terminal.

VII. CONCLUSIONS

A low complexity frequency synchronization method is proposed and analyzed for global satellite communications systems employing nongeostationary satellites. This method significantly reduces the variance of the Doppler shift estimate for access channels. It helps to greatly improve performance of access request signal detection, position determination and demodulation. For traffic channels, it can achieve negligibly small frequency errors. When the proposed method is employed, no guardband is needed and the system bandwidth can be fully used to 100% for FDMA/TDMA based systems.

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