Unified Frame Acquisition and Symbol Timing Estimation for CPM Return Link Transmission

Unified Frame Acquisition and Symbol Timing Estimation for CPM Return Link Transmission S. Cioni, G.E. Corazza, R. Pedone, C. Togni, and M. Villanti DEIS/ARCES, University of Bologna Via V. Toffano, / - 4015 Bologna ITALY Email: {scioni, gecorazza, rpedone, ctogni, mvillanti}@arces.unibo.it Abstract This paper tackles the problem of unified frame and symbol timing synchronization for the return link of a DVB satellite system with Continuous Phase Modulation. Robust schemes are introduced to cope with the carrier frequency uncertainty affecting the received signal. The novel approach employs the same detector to recover the frame alignment and the symbol synchronism, based on Post Detection Integration strategy. It is shown that this unified approach is able to provide quasi-optimal performance limiting complexity at the same time. Keywords CPM, Frame Acquisition, Timing Synchronization, PDI techniques I. INTRODUCTION The large diffusion of broadcast services via satellite has motivated the recent development of an upgraded version of the Digital Video Broadcasting via Satellite (DVB-S), identified as DVB-S, aiming at providing enhanced system capacity through robust channel coding and adaptivity to actual channel conditions. In this framework, the capability of direct interactivity through a Return Channel via Satellite (RCS) is of primary importance and its formalization is the objective of the DVB-RCS standard [1]. To facilitate the diffusion of DVB-RCS terminals in the mass market, the ESA funded BSDT project (Broadband Satellite Digital Transmission) [] is evaluating the possibility of adopting Continuous Phase Modulation (CPM) to reduce the impact of low-cost non linear high power amplifiers. In fact, CPM is characterized by constant signal envelope that provides inherent robustness against non linear effects. This translates directly into complexity reduction because the typical countermeasures of linear modulations, e.g., predistortion techniques [3] are not necessary anymore. On the other hand, the modification of the signal waveform with respect to the DVB- RCS recommendation requires to completely re-design the transmit-receive chain, starting from synchronization issues up to data demodulation and decoding. In particular, in this paper we propose a method to achieve robust frame acquisition with a first coarse epoch estimate, followed by a further refining to provide accurate symbol timing recovery. Conventionally, frame acquisition is performed adopting a pilot aided approach, by inserting a Unique Word (UW) at the beginning of the frame that has to be identified in the transmission flow. This is achieved by discretizing the uncertainty region (frame epoch domain) into a finite number of cells or hypotheses, thus transforming the estimation problem into a discrete delay detection problem. We identify as H 1 the cell(s) corresponding to the correct alignment with the received UW (synchronous case), while H 0 indicates all misaligned cells. The most common discriminant between H 0 and H 1 is that the H 1 hypotheses are about the UW correlation peak, while all H 0 occur in correspondence of out-of-phase autocorrelation values. In this discretization process, a single hypothesis per symbol can be adopted if symbol timing recovery precedes frame synchronization, because in this case most of the useful energy is collected and limited Inter-Symbol Interference (ISI) is present. Unfortunately, this approach is not a viable solution for the return link case, in which frame acquisition is the very first operation to be completed. Thus, the design must cope with a fractional symbol timing delay τ [ T, T ] that reduces the useful correlation peak value and introduces ISI. This requires to exploit a finer discretization step to boost the time uncertainty robustness, introducing a number of hypotheses per symbol N hps > 1 in the discretization process at the cost of increased complexity represented by the number of detection variables to be computed. In addition, a major issue when designing return link frame acquisition is represented by the carrier frequency uncertainty due to the receive-transmit oscillator mismatch, requiring the adoption of robust solutions. In particular, Post Detection Integration (PDI) techniques have been demonstrated to be a valuable approach to combat the effects of frequency mismatch when considering linear modulations [4], [5]. PDI limits coherent integration over a UW subsequence to contain the energy degradation induced by the frequency error below an affordable level, and finally introduces accumulation after non linear processing to fully exploit the known UW field. The application of PDI to CPM signals is a novel result presented in this paper. Notably, frame synchronization for the return link reduces to a packet acquisition problem. Under the assumption of packet presence, the uncertainty domain is typically reduced and quantified by the guard period foreseen in the transmission flow. Given this contained extension, the decision is in favor of the largest accumulated variable in the uncertainty region, corresponding to the adoption of the MAX criterion [6]. 1519

To achieve final accurate timing estimation, the classical approach foresees to perform symbol timing estimation after frame acquisition introducing ad-hoc schemes. However, the solutions known in the literature manage to provide satisfactory performance without carrier frequency uncertainty [7], or ad-hoc algorithms for the minimum shift keying (MSK) modulation scheme are presented [8]. When a considerable frequency offset is present, a re-design is necessary to meet the robustness requirements. A further novel idea of the paper is to exploit the inherent robustness of the PDI-based frame detector circuit also for symbol timing estimation, refining the output of frame acquisition fully reusing the PDI detector with the MAX strategy jointly with interpolation techniques in favor of reduced complexity. II. SYSTEM MODEL The CPM modulated signal can be expressed as Es s(t) = T ejψ(t,α) (1) where E s represents the energy per symbol interval T, α = {α i } i= is a sequence of data symbols pertaining to the M- ary alphabet {±1, ±3,..., ±(M 1)}, and ψ(t, α) is given by ψ(t, α) =πh + i= α i q(t it ) () where h is the CPM modulation index and q(t) is the phase pulse function, which is related to the frequency pulse function g(t) by q(t) = t g(τ)dτ (3) The phase pulse is a monotic function in the interval [0, LT ], where L is the CPM correlation length, and it is normalized such that q(t) = 1 for t LT. In this work, we refer to the L-RC modulation scheme, thus the considered frequency pulse function is the raised-cosine (RC). The received CPM signal passes through an anti-aliasing filter (AAF) with bandwidth B AAF to limit the noise components. For simplicity, a rectangular shape is considered. Considering an oversampling factor N, the sampled signal at the rate 1 T s = N T, can be expressed by Es r m = T ej[ψ(mts τ,α)] e j[πm fts+θ] + n m (4) where f, θ and τ are the carrier frequency error, the unknown phase, and the residual timing offset, respectively. Finally, n m are the AWGN random variables that are Gaussian zero-mean distributed with variance σn. The considered frame structure for generic satellite return link burst transmission is depicted in Fig. 1. The known preamble has a length of L UW symbols followed by the payload information, which is modeled as random data. Although network synchronization is performed by the user terminal, a guard time should be considered at the receiver side. This guard time is called searching window and defines the extension in symbols, N S, of the uncertainty region for the frame acquisition problem. Regarding CPM parameters, the capacity analysis in [] has shown that the modulation scheme with h = 7, L =3, M =4is a good candidate for satellite return link transmission. III. FRAME SYNCHRONIZATION TECHNIQUES In the conventional frame synchronization approach with linear modulations, the received signal undergoes symbol matched filtering (MF) and sampling, providing the input to be processed by the detection circuit after a decimator that reduces the number of samples according to N hps adopted for the uncertainty region discretization. Unfortunately, with CPM signals the concept of matched filtering is not straightforwardly applicable, and a different approach has to be pursued. An optimal solution is proposed in [9], where the received signal is projected onto an ad-hoc signal space composed by a large number of dimensions to reduce the signal distortion, at the cost of large complexity. To counteract this problem, in this paper the sampled signal, which is in general characterized by an oversampling factor N, is directly processed by the detector that employs a locally generated UW replica characterized by the same oversampling factor. In this way, it is possible to identify the best performance/complexity trade-off by simply varying N. In fact, by increasing N the signal distortion is reduced, but the computational complexity rapidly increases, because the synchronization subsystem has to process a signal segment of length N L UW. Notably, this approach provides a considerable improvement if the frontend filter has a band B AAF N T. As a side effect, for large values of B AAF the presence of adjacent channel becomes a source of additional interference, which has to be taken into account. The adoption of an oversampled UW to reduce the CPM signal distortion allows to apply all techniques adopted for frame synchronization with linear modulation, obtaining similar conclusions. However, it is worthwhile noting that the intrinsic memory introduced by CPM modulation has a direct impact on the signal autocorrelation function, as shown in Fig., where h = 7, L = 3, M = 4, N = 16 have been considered, with a UW of length L UW = 48 and pattern according to [1]. In the figure, the comparison with the linear QPSK case with squared root raised-cosine (SRRC) impulse waveform is also reported, showing that the main lobe of the CPM signal is significantly wider with a twofold effect: on the one hand, the CPM frame synchronization performance is expected to be more robust against timing errors, on the other hand, it could be difficult to achieve very accurate timing estimation. Nevertheless, in the following we verify that an integrated solution frame/timing synchronization achieves satisfactory performance. In order to achieve good performance in the presence of frequency errors, Post Detection Integration (PDI) can be 150

fruitfully employed, as shown in [6]. PDI detectors perform coherent integration over a segment of the received signal, followed by a second integration phase after a non-linear operation. In particular, we consider three different UW detector schemes, as reported in Fig. 3: NCPDI (Non Coherent PDI), DPDI (Differential PDI)[4], and GPDI (Generalized PDI) [5]. Introducing a non ambiguous notation, L coh indicates the coherent integration length, while L pdi identifies the PDI length. To exploit the entire UW length, the pair (L coh,l pdi ) must satisfy the design constraint L coh L pdi = L UW.Tominimize the acquisition delay, a passive implementation of the coherent correlation stage is considered. The decision variable for NCPDI, DPDI, and GPDI can be written respectively as Λ GPDI = Λ NCPDI = k=0 Λ DPDI = k=0 x k + k=1 n=1 x k (5) x k x k 1 x k x k n k=n where x k is the received value after ADC, sampling, and coherent correlation over L coh symbols, defined as x k = (k+1)l cohn 1 m=kl cohn (6) (7) r m c m (8) being r m the m-th received sample, and c m the known m-th CPM symbol of the UW pattern. Notably, r m is affected by non-ideal symbol timing recovery quantified through the fractional displacement τ [ T, T ]. Note that, when B AAF = 1 T, N =1must be considered in Eq. (8), because the samples r m within a symbol are strongly correlated, so no useful contribution is provided by summing them together. In general, DPDI is more robust than NCPDI against large frequency errors, due to the reduced noise enhancement. GPDI combines NCPDI and DPDI, and further adds other terms to fully exploit phase continuity to the aim of easing detection robustness against large frequency offsets. Finally, the frame acquisition decision is taken according to the MAX strategy, as discussed in Sec. I, by selecting the largest accumulated variable between the (N S +1)N hps computed variables. Obviously, larger N hps provide better performance at the price of increased complexity. IV. SYMBOL TIMING ESTIMATION A feedforward (FF) non data-aided (NDA) algorithm derived from the maximum likelihood (ML) theory has been presented in [10]. Unfortunately, without exploiting the data information, this approach fails to achieve satisfactory performance still in the presence of only timing offset for CPM modulation schemes with memory length L larger than 1. A data-aided (DA) version of [10] can be easily derived as discussed in [7]. Nevertheless, the algorithm in [7] does not consider the presence of carrier frequency error at the receiver side. In the following, we derive a new FF symbol timing estimation algorithm, which is integrated with the frame detector and robust with respect to strong carrier frequency error. From [7], in the absence of frequency offsets, the DA timing estimate is related to the maximum value of the autocorrelation function as follows ˆτ = argmax{λ(r τ)} (9) τ NL Λ(r τ) X( τ) 0 1 = r m c m (10) m=0 where L 0 is the observation window. It shall be noted that the expression in Eq. (10) is identical to the decision variable for the NCPDI detector in Eqs. (5)-(8) with L coh = L 0 and L pdi =1. Introducing the carrier frequency uncertainty, the expression of the likelihood function can be manipulated leading to GPDI as shown in [5]. This suggests to perform symbol timing estimation by exploiting the same detection variable already computed for frame synchronization purposes. The benefits of this integration becomes particularly useful in the presence of strong carrier frequency errors. In fact, GPDI along with the MAX approach provides a very robust strategy to combat the degradation induced by carrier frequency uncertainty. To allow accurate symbol timing estimation, several hypotheses per symbol are considered, selecting in particular N hps = N, and a first coarse symbol timing estimate can be obtained by directly reusing the Λ GPDI functional from Eq. (7): { ˆτ =argmax Λ GPDI (r τ) } (11) τ where τ [0,..., N(N S +1)T s ]. Then, this first discretized timing estimate can be further refined by interpolating the GPDI outputs according to a specific interpolation technique. In particular, a parabolic interpolation has been applied in the following to provide numerical results, considering the maximum GPDI output and the two adjacent accumulated variables. V. NUMERICAL RESULTS AND DISCUSSION In the following, the simulation results of the proposed frame detectors and symbol timing recovery for satellite CPM based return link are presented. Under the assumption of packet presence, the MAX procedure adopted for frame synchronization can terminate only with an overall false alarm event or with a correct packet acquisition, after the whole scan of the uncertainty region. Thus, acquisition performance is provided in terms of overall false alarm probability, P FA, while the correct detection probability can be straightforwardly derived by the relation P D =1 P FA. In particular, a false alarm event is declared 151

if the difference between the estimated and the actual frame epoch is larger than T. It is worthwhile noting that the desired P FA performance target has to be at least one order of magnitude below the required packet error rate to avoid a systematic floor in the final data decoding performance. Thus, a practical performance requirement for frame synchronization is given by P FA < 10 5. Frame and symbol timing acquisition performance is evaluated considering the deterministic UW of length L UW = 48 and pattern of the DVB-RCS standard [1], symbol rate equal to 1/T = 16 kbaud, carrier frequency offset equal to f =khz (corresponding to a large normalized error ν = ft =0.15), and a practical value for the uncertainty region equal to 10 µs, i.e., N S =. CPM modulation with h = 7, L = 3, and M = 4 is assumed. The ADC is supposed to operate with oversampling factor N =4to have moderate signal distortion. The unknown symbol timing error is modeled as the contribution of an integer offset in the range [0,N S ] (recovered by the frame acquisition subsystem) and a fractional component uniformly distributed in the interval τ [ T, T ], which is estimated by the symbol timing recovery algorithm. Figure 4 shows the frame acquisition performance comparison between the different PDI detectors, considering an ideal AAF with bandwidth B AAF = 4 T, so neglecting the presence of possible adjacent channel interference, which is left for future investigations. Note that the relative behavior of the detector is a general result that can be generally applicable also to the practical case with B AAF = 1 T.Theverylarge frequency error forces to limit at most the coherent correlation length; thus, L coh =1has been selected for GPDI, while L coh =is selected for NCPDI and DPDI. It can be seen that GPDI shows the best performance and it is able to meet the performance requirement at E s /N 0 =db. The impact of the AAF filter bandwidth is shown in Fig. 5, where P FA vs. E s /N 0 is reported for the two cases B AAF = 4 T and B AAF = 1 T, with ν = 0.15. In the figure, the cases N hps equal to and 4 are reported, showing that the acquisition performance improves by increasing N hps thanks to the more accurate discretization about the peak of the autocorrelation function. Then, by limiting the filter bandwidth, the performance degrades due to the distortion induced on the received useful signal, along with the further degradation due to the presence of the frequency error, because a part of the useful spectrum is cut by the filter. The overall degradation is in the order of 1 db and 1.5 db at P FA =10 5 for N hps =4 and N hps =, respectively. The performance of the novel symbol timing estimation algorithm integrated with the frame detector architecture is depicted in Fig. 6, with and without carrier frequency error. As a benchmark, the modified Cramer-Rao bound (MCRB) for timing estimation with CPM is reported [8] ( ) 1 L Es MCRB = L 0 π h (M (1) 1) N 0 Interestingly, in the absence of carrier frequency error and with N hps = 4, the proposed technique is very close to the MCRB curve. It is important to underline that the curve N hps =4is able to achieve exactly the MCRB if the receive filter has a large bandwidth, i.e., B AAF = 4 T. Introducing a large frequency offset, ν =0.15, the integrated algorithm is still able to achieve satisfactory performance in terms of the standard deviation of estimation error. Finally, the approach with N hps =has rather similar performance for E s /N 0 < db, then a floor is present due to the large discretization of the possible timing hypotheses. VI. SUMMARY AND CONCLUSIONS The problem of frame acquisition and timing estimation for the return link DVB-RCS with CPM signals has been investigated, proposing a novel and unified approach that exploits the same detector for both procedures in favor of reduced complexity with no performance compromise. The robustness against large frequency errors is achieved through the exploitation of the generalized post detection integration (GPDI) detector with the MAX strategy. The result is that the proposed technique is able to provide very good frame acquisition performance along with symbol timing estimation performance close to the modified CRB. ACKNOWLEDGEMENT This work is supported in part by ESA/ESTEC Co. 19370, Broadband Satellite Digital Transmissions. REFERENCES [1] ETSI TR 101 790, Digital Video Broadcasting (DVB); Interaction channel for Satellite Distribution Systems; Guidelines for the use of EN 301 790, V1..1, Jan. 003. [] ESA/ESTEC Research Project, Broadband Satellite Digital Transmissions, Tech. Report, Co. 19370, Jan. 006. [3] G. Albertazzi, S. Cioni, G.E. Corazza, M. Neri, R. Pedone, P. Salmi, A. Vanelli-Coralli, and M. Villanti, On the Adaptive DVB-S Physical Layer: Design and Performance, IEEE Wireless Communication Magazine, vol. 1, pp. 6-68, Dec. 005. [4] G.E. Corazza, P. Salmi, A. Vanelli-Coralli, M. Villanti, Differential and Non-Coherent Post Detection Integration Techniques in the Return Link of Satellite CDMA Systems, Proceeding of IEEE Personal Indoor and Mobile Radio Comm. (PIMRC-00), Vol. 1, pp.300-304, Lisboa, Portugal, 15-18 Sept. 00. [5] G.E. Corazza, and R. Pedone, Generalized and Average Post Detection Integration Methods for Code Acquisition, Proceeding of the IEEE Int. Symp. on Spread Spectrum Techniques and Applications (ISSSTA- 004), Sydney, Australia, 30 Aug.- Sept. 004. [6] G.E. Corazza, R. Pedone, M. Villanti, MAX Strategy for Burst Frame Acquisition in Ka-band Satellite Systems, Proceeding of the 10th Ka and Broadband Comm. Conf., Vicenza, Italy, 30 Sept.- Oct. 004. [7] T.T.H. Simarmata, and J.V. Krogmeier, Experimentation with dataaided symbol timing estimation for CPM, Proceedings of the 43rd IEEE Midwest Symposium, vol. 1, pp. -5, Aug. 000. [8] U. Mengali and A. D Andrea, Synchronization Techniques for Digital Receivers, Ed. Plenum, 1997. [9] P.A. Laurent, Exact and Approximate Construction of Digital Phase Modulations by Superposition of Amplitude Modulated Pulses (AMP), IEEE Trans. on Comm., vol. 34, pp. 150-160, Feb. 1986. [10] A.N. D Andrea, U. Mengali, and M. Morelli, Symbol Timing Estimation with CPM Modulation, IEEE Trans. on Comm., vol. 44, pp. 136-137, Oct. 1996. 15

Frame Preamble N S L UW Search window Unique Word (UW) Random Data Fig. 1. Generic frame structure for satellite return link burst transmission 1.E-0 Pfa 1.E-03 1.E-04 NCPDI - Lcoh=, Nhps= Accumulated energy 50 45 40 35 30 5 0 15 10 5 CPM QPSK 1.E-05 1.E-06 DPDI - Lcoh=, Nhps= GPDI - Lcoh=1, Nhps= -8-7 -6-5 -4-3 - -1 0 1 3 4 5 6 7 8 Fig. 4. NCPDI, DPDI and GPDI comparison - P FA vs. E s/n 0, N hps =, L UW =48, ν =0.15, B AAF =4/T 0-6 -5-4 -3 - -1 0 1 3 4 5 6 Symbol time, t/t Fig.. Correlation function vs. delay normalized to T 1.E-0 Pfa 1.E-03 (a) 1.E-04 GPDI - Nhps=, B=4/T GPDI - Nhps=, B=1/T Σ Lcoh. Σ Lpdi 1.E-05 GPDI - Nhps=4, B=4/T GPDI - Nhps=4, B=1/T (b) 1.E-06-11 -10-9 -8-7 -6-5 -4-3 - -1 0 1 3 4 Σ Lcoh T s (. )* Σ Lpdi-1. Fig. 5. B AAF impact on performance - P FA vs. E s/n 0, L UW =48, ν =0.15 (c) NCPDI DPDI -Span DPDI. n-span DPDI. (Lpdi-1)-Span DPDI Σ Timing Error Standard Deviation MCRB - L0=48 Nhps=, v=0.0 Nhps=, v=0.15 Nhps=4, v=0.0 Nhps=4, v=0.15 Fig. 3. UW Detector Block Diagrams : (a) NCPDI (Non Coherent - Post Detection Integration) detector; (b) DPDI (Differential - Post Detection Integration) detector; (c) GPDI (Generalized - Post Detection Integration) detector. 1.E-0 0 4 6 8 10 1 14 16 Fig. 6. Integrated timing performance - RMSE vs. E s/n 0, L 0 = 48, B AAF =1/T, ν = {0.0, 0.15} 153