THE DIGITAL video broadcasting return channel system

IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 4, DECEMBER 2005 543 Joint Frequency Offset and Carrier Phase Estimation for the Return Channel for Digital Video Broadcasting Dae-Ki Hong and Sung-Jin Kang Abstract This paper investigates the design of joint frequency offset and carrier phase estimation of a multi-frequency time division multiple access (MF-TDMA) demodulator that is applied to a digital video broadcasting return channel system via satellite (DVB-RCS). The proposed joint estimation algorithm is based on the interpolation technique for two correlation values in the frequency and phase domains. This simple interpolation technique can significantly improve frequency and phase resolution capabilities of the proposed technique without increasing the number of the correlation values. In addition, the overall block diagram of a digital communications receiver for DVB-RCS is presented, which was designed using the proposed estimation algorithms. Index Terms Carrier phase estimation, DVB-RCS, frequency offset estimation, interpolation, joint estimation, MF-TDMA. I. INTRODUCTION THE DIGITAL video broadcasting return channel system via satellite (DVB-RCS) was specified by the technical group of an ad-hoc European telecommunications standards institute [1] [3]. It specifies a satellite terminal [also known as a return channel satellite terminal (RCST)] that supports a twoway DVB satellite system. DVB-RCS provides the interaction channel for geostationary orbit satellite interactive networks with fixed RCSTs. Fig. 1 shows the reference model that will be used within DVB for interactive services. In the reference model, two channels are established between the service provider and the user. A unidirectional broadband broadcast channel that includes video, audio, and data is established from the service provider to the users. A bi-directional interaction channel is established between the service provider and the user for interaction purposes. It is formed through a Return interaction path (return channel): Used to make requests to the service provider, to answer questions, or to transfer data; and Forward interaction path: Used to provide information from the service provider to the user and any other required communication for the provision of the interactive service. The satellite interactive network comprises the following functional blocks, as shown in Fig. 1: Network control center (NCC): Provides monitoring and control functions; Traffic gateway (TG): Receives the RCST return signals; and Feeder: Transmits the forward link signal. Manuscript received November 11, 2003; revised April 6, 2005. The authors are with the Wireless Network Research Center, Korea Electronic Technology Institute (KETI), #68 YaTap-Dong, BunDang-Gu, SungNam-Si, KyoungGi-Do 463-816 Korea (e-mail: hongdk@keti.re.kr; sjkang@keti.re.kr). Digital Object Identifier 10.1109/TBC.2005.854171 Fig. 1. Fig. 2. Reference model for a satellite interactive network. Block diagram of the RCST return link base-band signal processing. The forward link carries signals from the NCC and user traffic to the RCSTs. The signaling from the NCC to the RCSTs that is necessary to operate the return link system is called forward link signaling (FLS). Fig. 2 represents the generic digital signal processing to be performed at the RCST transmitter and receiver. The signal processing to be performed by each subset is described in the following sections. The synchronization of the RCST is based on network clock reference (NCR) information contained within the FLS. The parameters that must be synchronized are the carrier, the burst, and the symbol clock. Carrier synchronization: The RCST reconstructs the reference clock from the received NCR information in the FLS. The RCST then performs a comparison to determine the offset between the local reference clock that controls the RCST upconverter local oscillator and the reference clock recovered from the received NCR. Then the RCST compensates the carrier frequency according 0018-9316/$20.00 2005 IEEE

544 IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 4, DECEMBER 2005 to this offset. The normalized root mean square carrier frequency accuracy must be better than. Burst synchronization: For the purpose of synchronizing to the network, the RCST reconstructs, in addition to the reference clock, the absolute value of the NCC reference clock. The RCST compares the reconstructed value with the NCR value given by the burst time plan. The time reference for counting timeslots occurs when the values are equal. The burst synchronization accuracy must be within 50% of a symbol period. Clock synchronization: The symbol clock for the transmitter must be locked to the NCR-based clock to avoid time drift with respect to the NCC reference clock. The RCST need not compensate for the symbol clock Doppler. The symbol clock accuracy must be within 20 ppm from the nominal symbol rate value in the time-slot composition table. The symbol clock rate must have a short-term stability that limits the time error of any symbol within a burst to 1/20 symbol duration. There are four kinds of return channel bursts in DVB-RCS: common signaling (CSC) burst, acquisition (ACQ) burst, synchronization (SYNC) burst, and traffic (TRF) burst. Their typical functions are initial access, coarse synchronization, fine synchronization, and user data transfer, respectively. TRF bursts are used to carry useful data from the RCST to the Gateway. A TRF is usually followed by a guard time to decrease transmitted power and compensate for time offset. SYNC and ACQ bursts are required to accurately position RCST burst transmissions during and after log-on. Two separate burst types are defined for this purpose (ACQ and SYNC). CSC bursts are only used by an RCST to identify itself during log-on. This paper is organized as follows. Section I describes the reference model for satellite interactive networks and the base-band physical layer specification for synchronization of the DVB-RCS system. Section II presents the received signal model and the conventional algorithm for the estimation of the frequency offset and the carrier phase. In Section III, the principle of the proposed joint frequency offset and carrier phase estimation is proposed, and the digital receiver structure for the return channel system is explained. Section IV discusses the simulation results. The conclusions and further research follow in Section V. II. RECEIVER SYNCHRONIZATION Receiver synchronization is the main issue in the modem design of the return channel of DVB systems. The most important issues in receiver synchronization include symbol timing recovery, carrier frequency synchronization (carrier frequency offset and carrier phase recovery), and burst synchronization. Symbol timing recovery and burst synchronization can be accomplished using the digital algorithm proposed in [14]. The remaining issue is carrier synchronization. Many of the works cited in the literature [4] [13] are devoted to the investigation of frequency offset and carrier phase estimation algorithms using time and frequency domain approaches. Time domain approaches use averaging or correlations among received samples when estimating the frequency offset and the carrier phase [4] [9]. Viterbi and Viterbi ([4], V&V algorithm) present a very efficient blind algorithm for carrier phase estimation in -ary phase shift keying transmission. Their algorithm uses an averaging method and yields accurate phase recovery for burst transmission. A practical modification of the V&V algorithm has been proposed for on-board implementation [5]. However, the accuracy of the V&V algorithm is severely degraded when frequency offset occurs. The joint estimation algorithm can overcome this problem. Various other types of frequency offset estimation using correlation methods are covered in [6] [9]. The main thresholds used to evaluate the performance of the frequency estimator are its estimation accuracy at low average-bit-energy-to-noise-spectral-density ratios, and its estimation range [9]. With respect to frequency domain approaches, the approach used for frequency offset and carrier phase estimation is the discrete Fourier transform (DFT) and subspace-based algorithm [10] [12]. However, the DFT-based estimation [10] is not precise enough to be applied in real applications, because the number of discrete samples limits the resolution of the DFT algorithm. To improve the resolution of the DFT, subspace-based estimation may be used [11]. An overview of subspace methods is given in [12]. However, subspace methods are also too complex to realize in real applications. As such, a simple method of improving the frequency and phase resolutions is needed. In this paper, a simple joint estimation algorithm for the frequency offset and the carrier phase is proposed. The proposed joint estimation algorithm is based on the interpolation technique for two correlation values in the frequency and phase domains. The proposed algorithm is a combination of the time domain and the frequency domain approaches. This simple interpolation technique can significantly improve the frequency and phase resolution capabilities of the proposed technique without increasing the number of the correlation values. The frequency offset estimation accuracy of the algorithm is close to the Cramer-Rao bound (CRB) for by as low as 0 db. In addition, even in the case of a large frequency offset, the accuracy of the carrier phase estimation using the joint algorithm is better than that using the V&V algorithm. Suitable areas of application for this algorithm include joint estimation of the carrier phase as well as of fine frequencies. A. The Received Signal Model Burst quadrature phase shift keying (QPSK) transmission of digital data is employed in DVB-RCS systems (satellite TDMA systems). Assuming perfect symbol synchronization, the received sequence in a QPSK burst can be written as in which is the transmitted symbol phase taking on values in. is the frequency offset, is the symbol period, is the carrier phase, is the additive white Gaussian noise (AWGN) sample, and is the burst length. The modulation components in the received samples can be removed by multiplying the complex conjugate of the known (1)

IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 4, DECEMBER 2005 545 data. Therefore, the received sequence for data-aided (DA) estimation 1 can be obtained from in which is due to the AWGN. B. Conventional Frequency Offset Estimation Algorithms The time domain frequency estimators proposed in [6] [9] exploit the sample correlations in which is a design parameter not greater than.to explain the method, (3) is rewritten as, with. Note that has the same statistics as. Substituting into (3) yields with In particular, the maximum likelihood (ML) estimator algorithm of can be derived using the methods indicated in [9], with the following result: in which is a smoothing function given by is the value of reduced to the interval, and is the principal value of the argument of. The estimation range is 20% of. Note that the sample correlation is required for the ML estimation algorithm, and that the computational complexity of the sample correlation is very high. The smoothing function is also required. To reduce the complexity, the approximated correlation [Mengali and Morelli (M&M) algorithm] is used instead of the sample correlation under the assumption of the unity samples. Nevertheless, this requires redundant hardware memory [9]. Another estimation algorithm is the Fits algorithm [6], which reads With this algorithm, the estimation range,, is less than. Finally, the Luise and Reggiannini (L&R) estimator [7] reads 1 For non-data-aided (NDA) estimation, the term r can be obtained by multiplying ^r by 4. (2) (3) (4) (5) (6) (7) (8) (9) and its estimation range,, is less than. Note that all estimation algorithms use the sample correlation, and the computation of the sample correlation requires complex multiplications. C. The Carrier Phase Estimation Algorithm Carrier phase estimation is necessary for coherent demodulation of QPSK modulated signals employed in the return channel of DVB systems. For burst transmission (typically for TDMA), the acquisition time has to be as short as possible. This constraint necessitated the discarding of feedback structures and focusing on feedforward synchronizers such as a V&V algorithm. This well-known NDA V&V algorithm is presented in [4]. The V&V algorithm cannot estimate the carrier phase when the frequency offset occurs. As such, it is assumed that the frequency offset estimation is perfect (i.e., ). The modulation is removed by applying a nonlinear operation on the received sequence,, yielding (10) in which is the magnitude of the complex valued samples,, and is a nonlinear transformation of. In a practical implementation, with. The estimation of the carrier phase is given by (11) for an average window length of, in which is a modulation level (i.e., for QPSK). III. THE PROPOSED JOINT FREQUENCY OFFSET AND CARRIER PHASE ESTIMATION ALGORITHM The DFT of the received sequence in (2) can be expressed as 2 (12) If is assumed, then (12) can be reconstructed as a sinc function, expressed as (13) in which is defined as, and the subscript (burst length) represents the circular shift duration of the spectrum. The subscript is ignored for simplicity. Therefore, a frequency offset can be estimated from the value of that corresponds to the absolute maximum of. Moreover, a phase offset estimate,, can be easily obtained from. 2 To simplify the explanation, it is assumed that there is no noise.

546 IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 4, DECEMBER 2005 TABLE I COMPLEXITY AND ESTIMATION RANGE OF FREQUENCY OFFSET ESTIMATION ALGORITHMS However, in the DFT-based algorithm, the spectrum resolution of the DFT is severely limited by the number of discrete samples. For example, if the frequency offsets are not integer multiples of, then the frequency offset estimate produces significant frequency offset estimation errors because the number of discrete samples limits the resolution of the DFT algorithm. To improve the resolution of the DFT algorithm, additional known data sequences must be inserted. However, this technique increases the amount of redundant information, making it necessary to design a new technique that will improve the DFT resolution without increasing the known data sequence. One of the most efficient ways to improve the DFT resolution is the interpolation technique in the frequency domain. In this section, the joint estimation algorithm of the frequency offset and the carrier phase is proposed using linear interpolation of the frequency samples. The complexity and estimation ranges of the proposed algorithm are analyzed and compared with those of other algorithms. The asymptotically unbiased property is proven. In addition, the block diagram of the digital receiver for a return channel system is presented using the proposed joint estimation algorithm and the symbol timing estimation algorithm in [14]. A. The Proposed Frequency Offset Estimation Algorithm The estimation ranges of conventional algorithms are moderate or wide (see Table I). In real situations, however, wide estimation ranges are redundant. Moreover, conventional algorithms are extremely complex. Hence, the design of a simple frequency offset estimation algorithm with high estimation accuracy and a moderate estimation range is critical. The proposed frequency offset estimator is based on the equation,, and it is expressed as 3 Fig. 3. Amplitude spectrum of the received sequence with frequency shift at the main lobe. The principle of the proposed algorithm is based on the frequency domain analysis depicted in Fig. 3. The first term,, in the denominator of (14) is the amplitude of the zero frequency component of the frequency-shifted sample,. 4 The second term,,in the denominator of (14) is the amplitude of the first integer frequency component of the frequency-shifted sample,. Hence, the proposed estimation is based on the interpolation of the two correlation values of the frequency-shifted version of the received sequence. The subtraction of is the correction of the frequency shift operation. The proposed algorithm is a combination of the time domain and the frequency domain methods. A comparison of the computational complexities of several estimation algorithms is shown in Table I. The proposed algorithm requires only complex multiplications. Its estimation range,, is less than. With the other algorithms, multiplications are required to compute the sample correlation. is the design parameter. The proposed algorithm is therefore very simple for the typical values of and. The equality between and can be proven as follows. Using (13), the proposed estimation algorithm can be expressed as (15) (14) in which is, as mentioned previously. 3 If the frequency shift is not included, then ^f (1=T N )fj (1)j=(j (0)j + j (1)j)g. The performance of this estimator will be included in simulation section. After some manipulations, the following simplified expression can be obtained (16) 4 (N 0 0:5) or (0:5) is not a DFT sample because a DFT index is generally an integer. This non-integer index is introduced just for notational convenience. For example, (0:5) is the amplitude of the frequency component of the midpoint frequency between (0) and (1).

IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 4, DECEMBER 2005 547 especially well-suited for easy hardware implementation. It can be used for satellite or terrestrial modems that require fast carrier phase estimation before the oscillator in the receiver enters a steady state. The equality of and can be proven as follows. From (13), the is computed as. Therefore, the desired result for the expression in (18) can be obtained as follows: Fig. 4. Phase spectrum of the received sequence with frequency shift at the main lobe. Using the definition of the sinc function, the equation can be further simplified as Hence, the proposed algorithm is asymptotically unbiased. (17) B. The Proposed Carrier Phase Estimation Algorithm The carrier phase can be estimated with the help of the estimated frequency offset and. Using the linear phase property of the sinc function, a simple estimation algorithm for the carrier phase is given by (18) The principle of the proposed algorithm is based on the phase domain analysis depicted in Fig. 4. The first term of (18),, is the gap between the estimated frequency offset and the zero frequency. The second term is the phase of the zero frequency component of the frequency-shifted sample,. The third term of (18),, is the gap between the estimated frequency offset and the first integer frequency. The last term of (18) is the phase of the first integer frequency component of the frequency-shifted sample,. Hence, the proposed estimation is based on the interpolation of the two-phase values of the frequency-shifted version of the received sequence. Correction of the frequency is not required in carrier phase estimation because the phase is independent of the frequency. The computational complexity increment for the carrier phase estimation is negligible. This is very simple compared with the complexity of the V&V algorithm. It can thus be concluded that the proposed algorithm is very simple and (19) Hence, the proposed algorithm is also asymptotically unbiased. C. Summary of the Proposed Algorithm and the Block Diagram of the Digital Receiver for the Return Channel System The new algorithm does not require any additional known data sequences. Furthermore, it does not require an increase in the number of the correlation values, meaning that hardware complexity is greatly reduced. It can also be used for DA and NDA estimation. The proposed algorithm can be summarized as follows: The received signal is uniformly sampled to obtain the received sequence; The two correlation values, ( and ), are computed; The frequency offset is estimated using (14); and According to the estimated frequency offset, the carrier phase is estimated using (18). A significantly improved carrier phase estimation can be expected using the proposed interpolation technique. A digital receiver for the return channel system is shown in Fig. 5. The signal is analog-to-digital converted to baseband immediately after downconversion. In the first stage, the signal is downconverted to (approximately) baseband by multiplying it with the complex output of an oscillator. Due to the residual frequency error, this complex baseband signal slowly rotates at an angular frequency equal to the frequency difference between the transmitter and receiver oscillators. The frequency of the oscillator is possibly controlled by a frequency control loop. The signal then enters an analog prefilter before it is sampled and quantized. All subsequent signal processing operations are performed digitally at a fixed processing rate. The symbol timing estimation and recovery is the first signal processing operation in the digital modem. A detailed description of the symbol timing estimation and recovery can be seen in [14]. After this, the frequency offset and the carrier phase are estimated jointly. The estimated frequency offset and the phase interpolation give the carrier phase estimate. The frequency offset is estimated using the proposed estimation algorithm, which was explained in the previous subsection, and is feedbacked to the

548 IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 4, DECEMBER 2005 Fig. 5. Block diagram of the digital receiver for the return channel system. Fig. 6. Normalized estimation error variance of the proposed DA frequency offset estimation algorithm. oscillator. The frequency of the oscillator can be controlled by the estimated frequency offset. The carrier-recovered signal is then further processed in an analog filter and subsequently sampled at every by a free-running oscillator. The carrier recovery block is implemented in feedforward fashion. Burst synchronization is the final operation. IV. SIMULATION RESULTS AND DISCUSSION Important issues concerning the proposed joint estimation algorithm include: i) whether it is biased or not; ii) how the frequency offset and carrier phase estimation error variances of the estimation algorithm compare with those of the other algorithms and the CRB; iii) how the computational complexity of the joint estimation algorithm compares with that of the conventional algorithm. In this section, the results of several Monte- Carlo simulations are presented to illustrate the performance and complexity of the proposed joint estimation. The modulation is QPSK, which is used for the return channel of DVB systems, and the length of sequence is 32 and 128. The DA and NDA estimations are also simulated. A. The Frequency Offset Estimation Error Variance of the Proposed Joint Estimation Figs. 6 and 7 show the normalized frequency offset estimation error variances for DA and NDA estimation with the proposed frequency offset estimation algorithm, Fig. 7. Normalized estimation error variance of the proposed NDA frequency offset estimation algorithm. respectively. The burst length is 128 symbols. The CRB is expressed as in [15] in which is the SNR. These figures show that the proposed frequency offset estimation algorithm can be applied to both DA and NDA estimation. When the frequency offset is zero, the frequency offset estimation accuracy of the clock-aided algorithm is close to the CRB for an as low as 0 db. However, the frequency offset estimation performance varies according to the channel frequency offset. This is due to the approximation of (13). Examining the frequency offset estimation error variance versus the normalized frequency offset is very important in deciding on the estimation accuracy, the estimation range, and the bias property of a frequency offset estimation algorithm. The normalized frequency offset estimation error variance of the proposed DA joint estimation algorithm is depicted in Fig. 8 versus the channel frequency offset. The is 10 or 20 db. The normalized frequency offset estimation accuracy of the algorithm is close to the CRB when the channel frequency offset is in the neighborhood of zero frequency offset. However, the proposed frequency estimation algorithm represents a slight bias at the 0.5 normalized frequency offset. In fact, an unbiased estimation at the steady-state point is preferred for oscillator

IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 4, DECEMBER 2005 549 Fig. 8. Normalized estimation error variance of the proposed DA frequency offset estimation algorithm versus the normalized frequency offset. Fig. 10. Estimation error variance of the proposed DA carrier phase estimation algorithm. Fig. 11. Estimation error variance of the proposed NDA carrier phase estimation algorithm. Fig. 9. Performance comparison of several frequency offset estimation algorithms. control (i.e., frequency tracking 5 ). The proposed joint estimation represents no bias at the steady-state point (zero frequency offset). However, if the frequency shift is not included in the proposed estimator, the estimation performance at steady state point is severely degraded. Hence, the frequency shift operation is required for oscillator control. Fig. 9 shows the normalized frequency offset estimation error variance for DA estimation with the proposed interpolation technique versus. It compares the variance of the algorithms proposed by Luise and Reggiannini [7], Lovell and Williamson (L&W) [8], and Mengali and Morelli [9]. The ideal CRB for frequency offset estimation is indicated as a reference. The design parameter for the L&R and M&M algorithms is set at 64. It is not greater than [9]. Apart from the L&W algorithm, which has a rather high threshold, all other algorithms virtually approach to the CRB up to. When the frequency offset is 0.0, the frequency offset estimation performance of the proposed algorithm is comparable to that of the M&M algorithm. This is a result of the unbiased property of the interpolation at the midpoint frequency. The performance of the proposed estimation algorithm is robust to the estimation error at all s. 5 The next operation in frequency offset estimation is oscillator control. B. The Carrier Phase Estimation Error Variance of the Proposed Joint Estimation The carrier phase estimation error variances of the DA and NDA estimation algorithms are shown in Figs. 10 and 11. The ideal CRB for carrier phase estimation is indicated as a reference. The CRB is expressed as in [15] The carrier phase estimation performance varies according to the channel frequency offset. The carrier phase performance is not comparable to the CRB due to the frequency offset estimation error. This is verified in Fig. 12. Examining the carrier phase estimation error variance versus the normalized frequency offset is also important in deciding on the estimation accuracy, the estimation range, and the bias property of a carrier phase estimation algorithm. The carrier phase estimation error variance of the proposed DA joint estimation algorithm versus the channel frequency offset is depicted in Fig. 12. The is 10 or 20 db. The perfect estimation means that there is no frequency offset estimation error. Hence, the vertical axis represents the pure carrier phase estimation error variance [i.e., ]. The carrier phase estimation accuracy of the algorithm is close to the CRB when the channel frequency offset is in the neighborhood of zero and 0.5 frequency offsets.

550 IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 4, DECEMBER 2005 However, the proposed frequency estimation algorithm represents a slight bias at a 0.4 normalized frequency offset. This is due to the approximation of (13). However, when there is a frequency offset estimation error (i.e., an imperfect estimation), the vertical axis represents the carrier phase estimation error variance with a frequency error [i.e., ]. In this case, the carrier phase estimation performance is degraded. This is due to the frequency offset estimation error. The carrier phase estimation error variances are shown in Fig. 13. The length of sequence is 32 symbols. The V&V algorithm [with ] performance for carrier phase estimation is also indicated [9]. NDA estimation is used to compare the estimation performance with the blind V&V algorithm. The carrier phase is 0. The lowest curve represents the ideal CRB for carrier phase estimation. The overlapping curve was obtained under the assumption of a perfect frequency offset estimation. The performance curve of the carrier phase estimation with a zero frequency offset is exactly the same as that of the V&V algorithm. This is because a perfect frequency offset estimation was achieved. In addition, it is close to the CRB at a high. The upper two curves were obtained with a frequency error. The performance of the V&V algorithm with a 0.5 normalized frequency offset was saturated as the increased, whereas the proposed carrier phase estimation was robust to the saturation effect due to the frequency offset. The performance of the carrier phase estimation is not comparable to that of the V&V algorithm with a zero frequency offset. This is because of the frequency offset estimation error of the joint estimation. In addition, the curves of the carrier phase estimation with 0.5 and 0 normalized frequency offsets do not represent the same performance. This is due to the variations in the bias. Therefore, in the proposed joint estimation algorithm, the amount and accuracy of the frequency offset are critical for a robust carrier phase estimation. Fig. 12. Carrier phase estimation error variance of the proposed algorithm versus the normalized frequency offset. V. CONCLUSIONS AND AREAS FOR FURTHER RESEARCH In this paper, the design of joint frequency offset and carrier phase estimation of an MF-TDMA demodulator that was applied to DVB-RCS was proposed. In addition, the overall block diagram of a digital communications receiver for DVB-RCS was presented, which was designed using the proposed estimation algorithms. The estimation accuracy and range of the joint algorithm were comparable to those of conventional algorithms. In addition, even when a large frequency offset occurred, the carrier phase estimation accuracy of the joint algorithm was better than that of the V&V algorithm. Fig. 13. 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