Incompatibility Of Trellis-Based NonCoherent SOQPSK Demodulators For Use In FEC Applications. Erik Perrins

Transcription

1 AFFTC-PA Inompatibility Of Trellis-Based NonCoherent SOQPSK Demodulators For Use In FEC Appliations A F F T C Erik Perrins AIR FORCE FLIGHT TEST CENTER EDWARDS AFB, CA 12 MARCH 2012 Approved for publi release; distribution is unlimited. AIR FORCE FLIGHT TEST CENTER EDWARDS AIR FORCE BASE, CALIFORNIA AIR FORCE MATERIEL COMMAND UNITED STATES AIR FORCE

2 REPORT DOCUMENTATION PAGE Form Approved OMB No Publi reporting burden for this olletion of information is estimated to average 1 hour per response, inluding the time for reviewing instrutions, searhing existing data soures, gathering and maintaining the data needed, and ompleting and reviewing this olletion of information. Send omments regarding this burden estimate or any other aspet of this olletion of information, inluding suggestions for reduing this burden to Department of Defense, Washington Headquarters Servies, Diretorate for Information Operations and Reports ( ), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA Respondents should be aware that notwithstanding any other provision of law, no person shall be subjet to any penalty for failing to omply with a olletion of information if it does not display a urrently valid OMB ontrol number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 12/03/ TITLE AND SUBTITLE 2. REPORT TYPE Tehnial Paper 3. DATES COVERED (From - To) Feb 12 Ot 12 5a. CONTRACT NUMBER Inompatibility Of Trellis-Based NonCoherent SOQPSK Demodulators For Use In FEC Appliations 6. AUTHOR(S) Erik Perrins 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) AND ADDRESS(ES) Department of Eletrial Engineering & Computer Siene University of Kansas, Lawrene, KS b. GRANT NUMBER 5. PROGRAM ELEMENT NUMBER 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 8. PERFORMING ORGANIZATION REPORT NUMBER AFFTC-PA SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) Tom Young, EA Air Fore Flight Test Center Edwards AFB CA SPONSOR/MONITOR S ACRONYM(S) N/A 11. SPONSOR/MONITOR S REPORT NUMBER(S) 12. DISTRIBUTION / AVAILABILITY STATEMENT Approved for publi release A: distribution is unlimited. 13. SUPPLEMENTARY NOTES CA: Air Fore Flight Test Center Edwards AFB CA CC: ABSTRACT This paper examines the ompatibility/inompatibility of trellis-based nonoherent shaped offset quadrature phase shift keying (SOQPSK) demodulators for use in forward error orretion (FEC) appliations. The nonoherent demodulators are of the type given in [1, 2]. These demodulators do not expliitly estimate and trak the phase offset in the reeived signal, as is done by a oherent demodulator. Instead, they have impliit phase estimators assoiated with eah state (survivor) in the trellis. We show, however, that these impliit phase estimators still lok onto the arrier phase, in a manner similar to that of a oherent demodulator. Furthermore, beause of the extremely low signal-to-noise ratio (SNR) in FEC appliations, the phase lok sometimes slips by 180 degrees, whih auses the demodulator output symbols to be inverted. We show that this is a relatively minor problem for a serially onatenated onvolutional ode (SCCC), mainly beause the SCCC system uses differential enoding and this enoding is immune to 180 degree phase shifts. On the other hand, a low density parity hek (LDPC) oded system does not use differential enoding. Thus, in LDPC systems the 180 degree phase shift proves to be quite atastrophi. The solution to this problem is to adjust the forgetting fator parameter of the nonoherent detetor to a value that yields a tighter phase lok. However, this diminishes the nonoherent nature of the demodulator. Therefore, another way of stating our onlusion is that oherent demodulators should be used in FEC appliations, espeially those using LDPC odes. In the end, while disappointing, this onlusion does not ome as a major surprise, beause one would not expet nonoherent demodulation to be appliable when differential enoding is not used. 15. SUBJECT TERMS forward error orretion (FEC), serially onatenated onvolutional ode (SCCC), low signal-to-noise ratio (SNR), telemetry, spetrum 16. SECURITY CLASSIFICATION OF: Unlassified a. REPORT Unlassified b. ABSTRACT Unlassified 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES. THIS PAGE Unlassified None 7 19a. NAME OF RESPONSIBLE PERSON 412 TENG/EN (Teh Pubs) 19b. TELEPHONE NUMBER (inlude area ode) Standard Form 298 (Rev. 8-98) Presribed by ANSI Std. Z39.18

3 INCOMPATIBILITY OF TRELLIS-BASED NONCOHERENT SOQPSK DEMODULATORS FOR USE IN FEC APPLICATIONS Erik Perrins Department of Eletrial Engineering & Computer Siene University of Kansas Lawrene, KS INTRODUCTION This paper examines the ompatibility/inompatibility of trellis-based nonoherent shaped offset quadrature phase shift keying (SOQPSK) demodulators for use in forward error orretion (FEC) appliations. The nonoherent demodulators are of the type given in [1, 2]. These demodulators do not expliitly estimate and trak the phase offset in the reeived signal, as is done by a oherent demodulator. Instead, they have impliit phase estimators assoiated with eah state (survivor) in the trellis. We show, however, that these impliit phase estimators still lok onto the arrier phase, in a manner similar to that of a oherent demodulator. Furthermore, beause of the extremely low signal-to-noise ratio (SNR) in FEC appliations, the phase lok sometimes slips by 180 degrees, whih auses the demodulator output symbols to be inverted. We show that this is a relatively minor problem for a serially onatenated onvolutional ode (SCCC), mainly beause the SCCC system uses differential enoding and this enoding is immune to 180 degree phase shifts. On the other hand, a low density parity hek (LDPC) oded system does not use differential enoding. Thus, in LDPC systems the 180 degree phase shift proves to be quite atastrophi. The solution to this problem is to adjust the forgetting fator parameter of the nonoherent detetor to a value that yields a tighter phase lok. However, this diminishes the nonoherent nature of the demodulator. Therefore, another way of stating our onlusion is that oherent demodulators should be used in FEC appliations, espeially those using LDPC odes. In the end, while disappointing, this onlusion does not ome as a major surprise, beause one would not expet nonoherent demodulation to be appliable when differential enoding is not used. SYSTEM MODEL The transmitter and reeiver models are shown in Figures 1 and 2, respetively. The transmitter onsists of a FEC enoder followed by the SOQPSK modulator. The reeiver onsists of a soft-output SOQPSK demodulator followed by a FEC deoder. All of these modules are fully desribed in our related paper [3], exept for the nonoherent demodulator that we now desribe. The oherent demodulator uses trellis metris given by { } Re e j ˆφe jθ n 1 (n+1)ts nt s r(t)e jπαnq(t nts) dt. (1) 1

4 u s(t; ) u FEC SOQPSK Enoder Modulator Figure 1: Transmitter Model. r(t) ĉ û SOQPSK FEC u Demodulator Deoder Figure 2: Reeiver Model. The reeived signal, r(t), ontains an unknown phase offset, φ. Although the above expression is quite intriate, it onsists of three main parts: the mathed filtering (MF) operation (i.e. the integral), the phase state orretion (i.e. the fator e jθ n 1 j ), and the orretion for the arrier phase offset (i.e. the fator e ˆφ), where ˆφ is the estimated phase offset. The oherent demodulator expliitly estimates this phase via some means, suh as a phase-loked loop (PLL). In the ase of perfet phase orretion we have ˆφ = φ. In the ase of the nonoherent demodulator, a omplex-valued phase referene, Q n, is assoiated with eah state in the trellis at time step n. This impliit phase estimate is used to orret the phase of the metris that branh out from state s in the trellis. Thus the trellis metris in the nonoherent demodulator beome { } Re Q n 1e jθ n 1 (n+1)ts nt s r(t)e jπαnq(t nts) dt where ( ) denotes the omplex onjugate. When the soft-ouput Viterbi algorithm (SOVA) determines the surviving branh at eah ending state, it then updates impliit phase referene via the operation ( ) Q n = aq n 1 + (1 a) e jθ n 1 (n+1)ts nt s r(t)e jπαnq(t nts) dt where 0 a 1 is the forgetting fator. The ingredients in this update are the past information, saled by a, and the information from the urrent time step, saled by 1 a. When a is small, the phase referene update plaes more weight on the urrent time step (beause the fator 1 a is large) and plaes less weight on (i.e. forgets) the past referene Q n 1 (s S (e 1 )). As a 1, the phase referene update essentially ignores the information from the urrent time step and relies almost entirely on the past information. When a = 1, the phase referene is no longer updated, and (2) is essentially the same as the oherent ase (assuming perfet phase orretion). (2) (3) IMPLICIT PHASE LOCK AND 180 DEGREE PHASE SLIP Although the nonoherent reeiver does not expliitly produe a phase estimate, ˆφ, a arrier phase estimate and arrier phase traking is impliit in Q n. During the signal aquisition proess, the reeiver must resolve the time boundary between the transmitted symbols (i.e., symbol timing reovery). Then, for SOQPSK, the reeiver imposes its own starting point for even/odd symbol indexes. One this is 2

5 Phase (degrees) Q n Symbol index (n) Figure 3: Angle of the nonoherent phase referene over the duration of one ode word. In the middle of the ode word, the phase referene slips from one lok point to the other. aomplished, there are two possible phase alignments with SOQPSK one being 180 degrees apart from the other and the phase estimate of the reeiver will lok onto one of these phase alignments. All of this is true whether the arrier phase is impliitly or expliitly estimated. We onsider the nonoherent demodulator with a = 7/8, operating with a rate 2/3 FEC ode and a bit-energy-to-noise ratio in the range of E b /N 0 = 2 to 4 db. Beause of the oding rate, the symbol-energyto-noise ratio, E s /N 0, is diminished by 10 log 10 (2/3) = 1.76 db, and thus we have E s /N 0 = 0.24 to 2.24 db. The demodulator has the task of synhronizing with respet to the oded symbols, and thus the low value of E s /N 0 makes synhronization more hallenging. Figure 3 shows the angle of the impliit nonoherent phase referene (in degrees) over the duration of one 6144-symbol ode word. Initially, the phase referene is loked onto a value of +90 degrees. Near the middle of the ode word, the noise auses the phase referene to slip to the opposite alignment point of 90 degrees. This auses the bits before and after the phase slip to be inverted with respet to eah other. At these low SNRs, the phase slips our a few perent of the time. If the FEC ode is LDPC, the deoder has no way to deal with the inverted bits other than to treat them as errors and thus the deoder is overwhelmed. This is evident by the LDPC BER urve shown in Figure 4. Beause the rate of ourrene for the phase slips dereases slowly as E b /N 0 inreases, the BER urve is dominated by errors arising from the phase slips and does not exhibit the desired waterfall harateristi that is typial of LDPC odes. For SCCC, the phase slips do not present muh of a problem beause they are orreted by the differential deoder with only a minor hiup (i.e. two errors). Thus, the SCCC BER urve in Figure 4 drops off quikly in the waterfall fashion. The performane of the two FEC deoders is illustrated in a different way in Figure 5. This figure shows the perentage of phase slips that ultimately lead to deoded bit errors. In the ase of LDPC, essentially all phase slips result in deoded bit errors; the only non-error phase slips are those rare instanes where the phase slip ours at the end of the transmitted ode word and the number of inverted bits is small enough that the LDPC deoder is not ompletely overwhelmed. The situation is very different for SCCC. For E b /N 0 < 2.5 db, essentially all phase slips result in deoded bit errors. For 2.5 < E b /N 0 < 3.5 db, the perentage drops beause the SCCC deoder is better able to orret the two additional errors indued by the phase shift. For E b /N 0 > 3.5 db, the two 3

6 BER LDPC SCCC E b /N 0 [db] Figure 4: BER results for LDPC and SCCC when paired with a nonoherent demodulator Perentage LDPC SCCC E b /N 0 [db] Figure 5: The perentage of phase slips that ultimately lead to deoded bit errors. In the ase of LDPC, essentially all phase slips result in deoded bit errors. In the ase of SCCC, as E b /N 0 inreases, the SCCC deoder is better able to orret the phase slip errors and at some point the phase slips no longer ontribute to the BER. 4

7 additional errors indued by the phase shift are always orreted by the deoder and the phase shifts no longer ontribute to the BER. DISCUSSION AND CONCLUSIONS In the examples above, a value of a = 7/8 was used for the forgetting fator. Seleting a value even loser to 1.0 will redue the rate of phase slips, but at the ost of making the demodulator less able to adapt (i.e. slower to aquire the signal). This is, in fat, the same tradeoff that exists in a PLL-based phase traking system: a narrower loop bandwidth results in a tighter lok at the expense of a longer aquisition time. Beause the nonoherent phase referene requires implementation omplexity [in the form of multipliations in (2) and the update in (3)] and beause the nonoherent harateristi is minimal due to a 1, our onluding reommendation is that nonoherent demodulators should not be used in FEC appliations, espeially those using LDPC odes. Our related paper [3] shows that simple-yet-robust symbol-by-symbol (SxS) demodulators yield strong BER performane at a fration of the omplexity of trellis-based demodulators. Thus, there are other more promising tehnologies available for FEC appliations. ACKNOWLEDGEMENT This projet is funded by the Test Resoure Management Center (TRMC) Test and Evaluation/Siene & Tehnology (T&E/S&T) Program through the U.S. Army Program Exeutive Offie for Simulation, Training and Instrumentation (PEO STRI) under Contrat No. W900KK-11-C REFERENCES [1] R. Shober and W. H. Gerstaker, Metri for nonoherent sequene estimation, Eletron. Lett., vol. 35, pp , De [2] A. Syed and E. Perrins, Comparison of nonoherent detetors for SOQPSK and GMSK in phase noise hannels, in Pro. Int. Telemetering Conf., (Las Vegas, NV), Ot [3] E. Perrins, System design for FEC in aeronautial telemetry, in Pro. Int. Telemetering Conf., (San Diego, CA), Ot