Turbo Embedded Estimation with imperfect Phase/Frequency Recovery

Transcription

1 Turbo mbedded stimation with imerfect Phase/Frequency ecovery Stefano Cioni, Giovanni. Corazza, Alessandro Vanelli Coralli niversity of ologna Deartment of lectronics, Comuter Science, and Systems D..I.S. - ACS Via V.Toffano, 2/ ologna, Italy Phone: Fax: {scioni,gecorazza,avanelli}@deis.unibo.it Abstract In recent years large scientific interest has been devoted to joint data decoding and arameter estimation techniques. In this aer, iterative turbo decoding joint to channel frequency and hase estimation is roosed. The hase and frequency estimator is embedded into the structure of the turbo decoder itself, taing into consideration both turbo interleaving and uncturing. esults show that the roosed technique outerforms conventional aroaches both in terms of detection caabilities and imlementation comlexity. I. INTODCTION The remarable erformance of turbo codes [1] has caused widesread emloyment of this technique in communication systems oening new challenges in wideband digital receivers. Some stimulating alications stem from the future broadband satellite systems which aim at roviding multimedia services to low cost and ower-limited user terminals. This tas can be achieved by imlementing erformant and robust regenerative rocessing techniques in order to achieve high quality of service (QoS) at low signal-to-noise ratio (SN). fficient coding schemes have to be used, such as turbo codes, but several imairments must be counteracted. In this framewor, the instability of the transmitter, receiver and on-board oscillators are addressed. The frequency offset and hase jitter due to oscillator imerfections are some of the imairments that can not be neglected. In articular, the channel hase can be estimated exloiting the resence of the turbo decoder and taing all advantages from the soft information rovided by the iterative decoding rocess. In [2] and [3] different aroaches to joint channel estimation and iterative decoding are roosed. All share a common idea: an external channel estimator which firstly rovides the coarse estimation, then exloits the soft a osteriori robability (APP) This wor has been suorted in art by the uroean IST roject SATIN (IST ) achieved by the turbo decoders to refine the estimates. Indeed, in the scientific literature, the term joint iterative estimation is commonly referred to the external iterative loo between the maximum a osteriori (MAP) decoder and the channel arameter estimator. On the other hand, as in Per-Survivor Processing (PSP) [4], it is ossible to embed the estimation of all unnown channel arameters in the search algorithm itself (e.g., the Viterbi algorithm (VA)) thus really joining arameter estimation and data detection. In this aer, an integrated technique for PSK modulation in which estimation is carried inside the turbo decoder is roosed: this is identified as turbo embedded estimation (T). It shall be noted that recently [5] a similar technique has been roosed for QPSK using different aroaches for metric comutation in hase estimation. Here, we consider a different aroach for metric comutation and we wor with smaller size acets. In the aer, T is comared with an external iterative technique and benchmared with AWGN erformance. esults show that T not only offers suerior and robust erformance versus the conventional segregated architectures in many challenging environments, but that, contrary to the PSP case, it is also less comlex than the other roosed schemes in terms of the number of comutational comlexity. The article is organized as follows. Section 2 contains the descrition of the system model. Section 3 contains the descrition of the external channel estimation joint to the iterative turbo rocess, while the roosed embedded aroach is reorted in Section 4. Finally, Section 5 reorts the numerical results, while Section 6 summarizes the conclusions. II. SYSTM MODL In Fig. 1 the encoder bloc diagram is deicted. The turbo encoder, consisting of two recursive systematic /03/$ I 2385

2 convolutional (SC) encoders and an interleaver, has code rate r = 1/3 and constraint length ν. The information bit sequence {d } is organized in acets of length N and feeds the turbo encoder roducing the systematic sequences {x s }, and the arity chec sequence {x1 } and {x 2 }. In the turbo encoder, the uncturing bloc is introduced to reduce the effective encoder rate to r =1/2. A multilexer taes alternatively the systematic and the unctured arity chec sequence {x } and feeds a PSK maer, which yields the symbol sequence {A }, with average energy s = { A 2 } =1. At the beginning of each acet a reamble of N re nown symbols may be included to ease initial arameter acquisition in the receiver section. In Fig. 2 the receiver bloc diagram is reorted. Assuming negligible filter distortion, symbol rate samling, and erfect timing recovery in the digital receiver, the comlex samles at the outut of the matched filter can be exressed as: = A e j(2π ft+φ ) + n (1) where n is the comlex AWGN rocess whose indeendent in hase and quadrature comonent samles have identical variance N 0 /2, ft reresents the residual carrier frequency offset, due to local oscillator mismatch and doler shift, normalized to the code symbol rate and φ accounts for the hase noise introduced by the fluctuations in the signal source and local oscillators within the transmitter and the receiver. The frequency offset ft is assumed to be deterministic and constant during the transmission of each data acet, whereas the hase sequence φ is modeled as a Wiener random rocess characterized by zero mean Gaussian indeendent increments with a standard deviation σ φ [4]. The bloc diagram of Fig. 2 encomasses both external (dashed bloc) and embedded angle estimation. The carrier frequency offset estimate, ˆfT, is given by the Luise&eggianini (L&) algorithm [6] which feeds both the external hase estimator and the initial hase acquisition bloc for T algorithm. The L& algorithm oerates on the nown reamble symbols. After angle equalization, the demultilexer restores the three decoding sequences, (y s,y1,y2 ) that feed the turbo decoder. III. XTNAL STIMATION In the external aroach, hase estimation is imlemented iteratively using the APP reliability given by the turbo decoder. Intuitively, this iterative technique gives advantages with resect to a hard feedbac, since a more reliable information imroves the hase estimator erformance. In this aer, a sliding window feedforward hase estimator based on the Viterbi&Viterbi (V&V) algorithm [7] is adoted. To avoid biased estimation, only the estimate associated with the symbol centered on the sliding window is used. A hybrid data aided/non data aided (DA/NDA) hase estimator is used in the first iteration to comensate for the absence of decoder outut. In the successive iterations a weighted decision directed (WDD) aroach is then ursued. A. Hybrid DA/NDA hase estimation The window taes into account an even number L of the total 2N + N re received symbols. The window size L is assumed to be larger than the number of reamble symbols N re, i.e., L>N re. Therefore the nown symbols {d i } within the sliding window are used to obtain the DA estimate ˆθ DA () =arg N re 1 i=max[0, L/2] i e j ˆfT d i (2) whereas the V&V is alied to the unnown symbols obtaining the NDA estimate ˆθ NDA ()= 1 min[+l/2,2n+n re] 2 arg i e j2arg{ie j ˆfT } i=max[n re, L 2 ] (3) xloiting the hase correlation introduced by the Wiener rocess, the hase ambiguity associated with the V&V (i.e., [0,π]) is resolved by choosing the hase value nearest to the receding estimate, ˆθNDA ( 1). The overall hase estimate for the -th symbol is then obtained by a weighted average of the DA and NDA estimates as ˆθ DA/NDA ()= N i re ˆθ DA ()+(L N i re) ˆθ NDA () L with N i re being the number of reamble symbols within the current sliding window. It is worthwhile noting that as the window reaches the end of the bloc, it is not ossible to slide it further, thus for the last L/2 symbols the same hase estimate, ˆθ NDA (2N + N re L/2 1) is used.. WDD hase estimation After the decoding rocess, the soft information of the second decoder, Λ 2 (d ), for all transmitted symbols can be exloited for hase estimation. The simlest idea is to adot the ML formula weighted by data reliability, so that fed bac symbols with high reliability drive the hase 2386

3 estimator more than the less reliable ones. Accordingly, the hase estimate equation becomes: { } ˆθ WDD ()=arg i e j ˆfT ˆdi i (4) i ω where ˆd i is the hard decision value or the sign of Λ 2 (d i ), i is the reliability for the received symbols related to the module of Λ 2 (d i ) through the transformation: i { 1 for i =0, 1,...N re 1 1 e Λ2(di) else and ω is the index set of the window symbols. IV. TO MDDD STIMATION xloiting the PSP exerience [4], a new iterative estimation algorithm joint to turbo decoding is roosed herein. As in PSP, the channel estimator is integrated into the MAP algorithm. The aim is to tae all the advantages deriving from joint arameter estimation and turbo decoding rocesses. In this case the estimation rocess shall be embedded into the CJ algorithm [8] instead of the VA as in PSP. In articular, a second order loo (SOL) tracing circuit is integrated in the CJ algorithm as reorted in Fig. 2. The embedded technique exloits the forward recursion to create the most robable received sequence. Indeed, remembering the definition for the α arameter [8], α i (m) = P {d = i, S = m 1}, it shall be noted that it reresents the robability associated with the state S = m conditioned by the first symbols. There is not a real ath between the different states inside the MAP decoder as a function of the time index, but observing α i (m) the most robable can be detected. The main stes of the turbo embedded estimation are: Ste 1: Most robable state detection At time in the forward recursion udating, α 1 i (m) αi (m), the state with the maximum value of robability among the M ossible states is searched. Ŝ max { m αi (m) } m M Ste 2: Most robable transition detection Knowing the most robable state at time, themost robable trellis transition can be chosen. Letting M be the set of ossible redecessors of Ŝ, this yields Ŝ max { m αi 1 (m) } m M Ste 3: Tracer udating Due to uncturing, only the systematic symbols, y s, can be used to udate the SOL. The SOL error signals of the systematic symbol at time can be comuted as [6]: e = Im [y s d ] e j ˆθ (5) ξ = ξ + δ(βe e 1 ) (6) where d is the bit ertaining to the most robable transition Ŝ Ŝ used for the sole urose of SOL udating. The variables δ and β are the loo gain arameters. To udate the hase estimate, it shall be noted that the next systematic symbol and its own arity chec symbol are two and three samling instants aart, resectively. Therefore, the hase values to derotate the symbols are: ˆθ +2 = ˆθ + ξ 2 (7) ˆθ +3 = ˆθ + ξ 3 (8) These hase estimates are used in the next γ robability evaluation for the forward recursion as follows ln[γ +2 ] = 2xs +2 ys +2 e j ˆθ +2 N 0 + 2x 1 +3 y1 +3 e j ˆθ +3 N 0 + AP +2 (9) where AP +2 is the a riori information of the current systematic symbol. Since, after hase correction the received symbols can be assumed uncorrelated, the bacward recursion does not change. Observing that only the first MAP decoder receives the systematic symbols in the same order in which they have been transmitted over the channel, this embedded estimation algorithm is not erformed by the second decoder. This one can only derotate its data inut, the interleaved systematic symbol ỹ s and the arity chec symbol y 2, with the hase estimate interleaved values received from the last iterative rocess erformed by the first decoder. Finally, to initialize the SOL inside the turbo decoder, hase and frequency acquisition is erformed over the nown reamble with the same DA algorithm used in the external iterative aroach. Accordingly ξ 0 = 2π ˆfT(N re 1) and ˆθ 0 = ˆθ DA (0). V. NMICAL SLTS In all simulations two identical SC encoders with constraint length ν =4, and generators g 0 (D) = (37) 8, g 1 (D) = (21) 8 are used. Puncturing is adoted and both encoders are terminated. The acet length is N = 1024, a square bloc interleaver is imlemented and 6 iterations are used in the decoding rocess. The carrier frequency offset ft {0.001, 0.01} and hase noise standard 2387

4 deviation σ φ = 1.0 degrees is considered. The sliding window length is set to L =70for the external estimation aroach. All the results are comared to the ideal erformance obtained nowing the channel arameters (). In Fig. 3 is reorted as a function of b /N 0, for ft =0.001 and σ φ =1.0 degrees in the case of N re =64. First of all, it shall be noted that a channel estimator is needed to achieve satisfactory erformance. Indeed, the term No stim, labels the case in which no frequency or hase estimation is erformed. It can be asserted that the system is totally unreliable. The second observation concerns the similar behaviour of the L& algorithm with resect to the No Acq technique. The term No Acq indicates that the L& estimation is not imlemented, therefore both the external and the embedded hase tracer exerience directly ft = without any comensation. This result confirms the reamble length selection. Finally, comaring the two roosed techniques, the external aroach loses about 0.4 d at = with resect to the T algorithm. In Fig. 4 is reorted as a function of b /N 0, for ft = 0.01, σ φ = 1.0 degrees and N re = 64. Interesting observations in favor of the T scheme can still be highlighted. First of all, it can be asserted that only T can achieve accetable detection erformance without any frequency offset acquisition. Anyway, with these channel conditions, frequency acquisition is strongly suggested. ven so, the external estimation algorithm is not able to ee as close to the curve as the T aroach does. Indeed, at =3 10 3,thegainfor the embedded technique is in the order of d. Now, the frequency estimation sensibility with resect to the reamble length is analyzed. In the following examle, a reamble of N re =32symbols is considered. In this case, an error standard deviation of the residual frequency offset in the range is achieved. So, when frequency acquisition is erformed with ft = 0.001, the residual offset is slightly greater than the No Acq case. The new erformance is reorted as a function of b /N 0, for ft = and σ φ = 1.0 degrees in Fig. 5. The T algorithm is insensitive to the little frequency offset increment and the erformance is very close to the ideal carrier frequency and hase recovery. On the other hand, the external technique fails when the L& frequency estimation is imlemented, meaning that the hase ambiguity solution is very critical with resect to the frequency residual. The results of Fig. 6 can clarify this assertion. The external detection erformance as a function of the reamble length is reorted. Increasing reamble length from the original value N re =32u to N re = 64, the standard deviation of the residual frequency offset decreases down to As exected, the erformance with N re =64is comarable with the No Acq case and this validates the hyothesis. VI. CONCLSIONS In this aer, the roblem of iterative data detection and arameter estimation in low SN and time varying channel conditions has been addressed. In contrast to conventional external techniques, an iterative integrated concet has been analyzed and develoed: the turbo embedded estimation. T and external aroaches have been comared to extract erformance and comlexity trade-offs as a function of the channel conditions. To this aim, the detection caability of the two algorithms has been evaluated with carrier hase and frequency uncertainty due to oscillator non-ideality. All results have confirmed that T outerforms the conventional estimation aroach. The robustness of the embedded algorithm has been analyzed with resect to the residual frequency offset. On the contrary, the external hase aroach needs an increase in the nown reamble length to solve the hase ambiguity reliably. In conclusion, with resect to different channel environments, the new iterative roosal of arameter estimation joint to turbo decoding rocess is more reliable and less comlex than the techniques discussed in the literature. Stimulated by these satisfactory results, further develoments of T will be addressed in the challenging direction of more bandwidth efficient modulations and challenging channel conditions. FNCS [1] C. errou, A. Glavieux, and Thitimajshima, Near Shannon Limit rror-correcting Coding and Decoding: Turbo Codes, Proc. ICC, , May [2] C. Morlet, I. uret, and M. oucheret, A Carrier Phase stimator for Multi-media Satellite Payloads suited to SC Coding schemes, Proc. ICC, , [3] W. Oh and K. Cheun, Joint Decoding and Carrier Phase ecovery Algorithm for Turbo Codes, I Comm. Lett., vol. 5, no. 9, , Se [4] A. Vanelli-Coralli, P. Salmi, S. Cioni, G. Corazza, and A. Polydoros, A Performance eview of PSP for joint Phase/Frequency and Data stimation in Future roadband Satellite Networs, I J. Selected Areas Comm., vol. 19, no. 12, , Dec [5] A. Anastasooulos and K. Chugg, Adative Iterative Detection for Phase Tracing in Turbo-Coded System, I Trans. Comm., vol. 49, no. 12, , Dec [6]. Mengali and A. D Andrea, Synchronization Techniques for Digital eceivers. Plenum, [7] A. Viterbi and A. Viterbi, Nonlinear stimation of PSK-modulated Carrier Phase with Alication to urst Digital Transmission, I Trans. Inform. Theory, vol. 29, , July [8] L. ahl, J. Coce, F. Jeline, and J. aviv, Otimal Decoding of Linear Codes for minimizing symbol error rate, I Trans. Inform. Theory, vol. 20, , Mar

5 d s x Π d ~ SC1 SC2 x 1 x 2 P N C T x M X MOD A Fig. 1. Transmission bloc diagram A e j 2π ft+φ ) ( w ' MF L& Phase stim. j fˆt e θˆ Λ 2 ( d ) D M X s y y 1 y 2 TO DC PLL dˆ NoAcq - T NoAcq - xternal Preamble Acq. ξ,θˆ L& - T L& - xternal Fig. 2. Digital receiver bloc diagram. b /N 0 (d) Fig. 5. vs. b /N 0 with ft =0.001, σ φ =1.0 degrees, and N re =32. No stim NoAcq - T NoAcq - xternal L& - T L& - xternal b /N 0 (d) Fig. 3. vs. b /N 0 with ft =0.001, σ φ =1.0 degrees, and N re = NoAcq L& - Nre= L& - Nre= L& - Nre= NoAcq - T NoAcq - xternal L& - T L& - xternal b /N 0 (d) b /N 0 (d) Fig. 6. xternal erformance vs. different reamble length, with ft =0.001 and σ φ =1.0 degrees. Fig. 4. vs. b /N 0 with ft =0.01, σ φ =1.0 degrees, and N re =