In this paper, we present an algorithm based on the Hidden Markov Models (HMM) theory to solve the problem of blind channel estimation and sequence detection in mobile digital communications. The environment in which the algorithm is tested is the Paneuropean Mobile Radio System, also known as GSM. In this system, a large part in each burst is devoted to allocate a training sequence used to obtain a channel estimate. The algorithm presented would not require this sequence, and that would imply an increase of the system capacity. Performance, evaluated for standard test channels, is close to that of non-blind algorithms.Peer ReviewedPostprint (published version

Antón Haro, Carles

Rodríguez Fonollosa, Javier

Rodríguez Fonollosa, José Adrián

English

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APPLICATION OF HIDDEN MARKOV MODELS TO BLINDCHANNEL ESTIMATION AND DATA DETECTION IN A GSMENVIRONMENTCarles Antón-Haro, José A. R. Fonollosa and Javier R. Fonollosa.Dpt. of  Signal Theory and Communications. Universitat Politècnica de Catalunya.c/ Gran Capità s/n. 08034 Barcelona (SPAIN)Tel: +34-3-4016454, Fax: +34-3-4016447, e-mail: carles@gps.tsc.upc.esABSTRACT  In this paper, we present an algorithm based on the HiddenMarkov Models (HMM) theory to solve the problem ofblind channel estimation and sequence detection in mobiledigital communications. The environment in which thealgorithm is tested is the Paneuropean Mobile RadioSystem, also known as GSM. In this system, a large part ineach burst is devoted to allocate a training sequence used toobtain a channel estimate. The algorithm presented wouldnot require this sequence, and that would imply an increaseof the system capacity. Performance, evaluated for standardtest channels, is close to that of non-blind algorithms.1. INTRODUCTIONIt is well known that no high-speed band-limited digitalcommunication can be carried out without the help of anequalizer. Conventional approaches to the adjustment ofthis equalizer require the transmission of a trainingsequence (i.e. known a priori by the receiver and thetransmitter), which provides an accurate initial estimate forthe equalizer taps; afterwards, slighter adjustments can bemade on a decision directed (DD) basis to adapt this firstestimate to the, almost always, changing environment. Ofcourse, the transmission of these training sequences, whenpossible, brings down the capacity of the system. For thatreason, there is an increasing interest around blindequalizers [1,2,3] which deal with the problem of theadjustment without training sequences (i.e. blindly).In [3], an Estimation-Modification (EM) Viterbi-basedalgorithm is proposed to perform jointly a MaximumLikelihood (ML) channel estimation and sequencedetection. However, modeling the received signal as aHMM allows us to make use of the complete theorydeveloped for these models. For example, the Baum&Welch(BW) algorithm was proposed in [7] to estimate theparameters of the channel and the characteristics of themodulation. This algorithm is known to lead, at least, to alocal maximum of the likelihood function [4], what is notguaranteed by the Viterbi algorithm. In this paper, severalmodifications to this previously proposed algorithm areintroduced to deal with mobile radio channels. This work was supported by the Comissionat per a les Universitats i Recerca(Generalitat de Catalunya).2. OVERVIEW OF THE GSM SYSTEMThe whole GSM system is specified in the ETSI (EuropeanTelecommunication Standards Institute) recommendations.We are not concerned in a full study of it, but in thosepoints related to the transmission subsystem.2.1 Transmission SubsystemThe GSM system operates in the 900 MHz band. Aconstant-envelope Gaussian Minimum Shift Keying(GMSK) modulation scheme with a relative bandwidth(BT) equal to 0.3 is used, due to its good spectral properties.The access strategy is TDMA with 8 timeslots per carrier.At the chosen bit rate (270.8 kb/s), multipath propagationleads to deep fades and to uncontrolled IntersymbolInterference (ISI). Besides, receiver's mobile nature allowsDoppler effect to show up. As depicted in Fig. 1, eachtimeslot in Normal Bursts reserves its 26 central bits to hosta sounding sequence. This sequence is used at the receiverto obtain an estimate of the channel impulse response(CIR). This information is then used by the detector (i.e. aMLSE-type) to perform data detection. In contrast, a blindequalizer would make this sequence unnecessary, so thatmore voice channels could be allocated instead.          1  T D M A  fram e = 8 tim es lots  1        2        3       4        5      6        7       8   tail     m essage      sounding s eq    m ess age      tail   guard    3            58                   26                   58            3      8 .25           1 tim es lot =  156.25 bitsFig. 1: TDMA frame and Normal Burst structure in GSM system2.2 Channel ModelsIn order to provide identical test conditions for differentimplementations of the GSM system, a set of 12-echo and6-echo propagation models, corresponding to typicalscenarios were defined by the ETSI (see Fig. 2) [5]. Delayspreads for different signal reflections are comprised among0.5μs in the Rural Area (RA) channel - the least hostile interms of ISI -, and 17.5μs for the Hilly Terrain (HT) one.Taking into account the bit interval duration (3.60 μs), weobserve that channel memory is up to 4 symbols. Forreliable communication, the uncontrolled ISI introduced bythe channel as well as that introduced deliberately by thepartial response modulator [6], have to be removed by thechannel equalizer.Fig. 2: Some of the 6-echo propagation models defined in the ETSIrecommendation3. SIGNAL MODELAccording to section 2, the signal at the input of the BWdetector can be modeled as:[ ] [ ] [ ]x n n w n= +f( )s (1)where f(.) is a nonlinear function of the present state s[n],and w[n] denotes a sequence of zero-mean Gaussianvariables with variance σ2.Fig. 3: Transmission subsystem.Note that: (1) the GMSK modulator is nonlinear, and (2)both the modulator and the channel contribute to the systemmemory. Assuming a linear model for the channel, f can beexpressed as:[ ]( ) [ ] [ ] [ ] [ ]f s n h i d n i h iiLn iiLc c= − ==−⋅ −=−∑ ∑0101e jφ (2)where h and d are the baseband equivalences for h0 and d0.For a modulation index equal to 0.5, φ[n] states as:[ ] [ ] [ ] [ ]φ π θn q r a n r nr RR= − +=−∑ (3)where q[r]∈[0,0.5] are the weights corresponding to the(sampled) gaussian-shaping pulse, and θ[n]∈{0,π/2,π,3π/2}accounts for the accumulated phase at instant n. Now weconclude that the number of transmitter symbols involved ina single observation at the receiver is given by:L L L R Lm c c= + − = + + −1 2 1 1( ) (4)However, the amount of ISI produced by the GMSKmodulator for BT=0.3 can be neglected without significantperformance loss. Under this simplifying assumption, thatreduces significantly the number of states andcomputational complexity, we get that R=0 ⇒ L=Lc. Atthis point, we can model the observations as a probabilisticfunction of the state s[n]=(a[n],..,a[n-L+1],θ[n])T, obtaininga description of xD=(x[1],x[2],..,x[D])T as a first orderHMM with the following characteristics:1. Nr of states: N=4·2L. We denote individual states asS=(s1,...,sN)T and s[n] as the state at instant n.2. The probability density function conditioned to state j is:( )p f ,jx mj je m j Nj= = ≤ ≤−−121222σ πσ s (5)3. The state transition probability distribution is:{ }[ ] [ ]( )( )( )As s s s= ≤ ≤= + = = === =⎧⎨⎪⎩⎪−a i j Na P n nP s if s s k Lotherwiseijij j ij jkik, ,, , ..,( ) (11201 1)(6)      where sj(k)∈{-1,1} denotes the kth element in sj:s j j j jL Ts s s= ( , ,.., , )(1) ( ) ( )2 θ (7)4. THE BW ALGORITHMOnce the HMM is built, the BW algorithm gives us asolution to the problem of identificating the unknownparameters of the model: m=(m1...mN)T (or equivalentlyh=(h0...hLc-1)T), and σ2. A solution to the problem ofsequence detection is also obtained [4,7]. It is worth makinga point of the additional constraints than can be added as aresult of the assumption of a FIR model for the channel. Infact, after each reestimation for the parameters of themodel, it is possible to project them in the followingmanner [7] :   #m D D m= (8)where D=(d1,d2,.., dN)T is a NxLc matrix containing in itsrows all the possible Lc-tuples of the modulator consecutiveoutputs, di=(di(1)...di(Lc))T, corr esponding to the N differentstates of the system. D# denotes pseudoinverse. Otherwise,in two steps:      #h D mm D h==(9)That is to say, from m we can obtain a Least Squares (LS)estimate for the CIR in that timeslot.In conclusion, the whole algorithm states as follows:1. Estimation of m by means of the additional linearconstraint:   m Dh= (10)1. BW algorithm itself (see [7] for further details):• Compute the variable γi [n]  (i=1..N, n=1..D), thatis, the probability of being in state i at instant ngiven the whole sequence xD=(x[1],..,x[D])T and themodel.• Reestimation of the parameter set by means oftime averaging:[ ] [ ][ ]  ,mn x nni NiinLinL= ≤ ≤==∑∑γγ111 (11)[ ] [ ]   σ γ2 2111= −==∑∑Ln m x ni iiNnL(12)3. Estimation of h using again linear constraints.  #h D m= (13)4. Repeat steps 1..4 until convergence.5. Sequence detection:[ ] [ ]{ }â n max ni Ni=⎛⎝⎜ ⎞⎠⎟≤ ≤Ψ arg1 γ (14)where ψ(.) is a function that maps each state (i=1..N) ontothe present symbol.5. MODIFIED ALGORITHMHowever, when using the above algorithm in a GSMenvironment, some additional points should be considered:1. As seen before the original BW is a batch algorithm thatobtains a single averaged CIR estimate for everytimeslot (D symbols). Therefore, if the CIR variesrapidly a lot of errors will appear.2. For CIRs exhibiting large delay spreads, the number ofstates in the model (N) increases rapidly. However thenumber of states observed  in a timeslot period (D),remains constant. As a result, the variance in theestimation of some components in m increases. Thatintroduces a severe distortion in the CIR estimate and,in some cases, makes the algorithm unstable.The following strategies were followed, respectively, to copewith these problems:1. Splitting up timeslots in several subblocks producingdifferent CIR estimates in each. It is also possible todevelop recursive versions of the algorithm as the LMS-based one proposed in [7]. Nevertheless, better resultswere obtained by segmenting timeslots and applying thebatch-type BW algorithm in each.2. Substituting the LS estimation for h by a WeightedLeast Squares (WLS) estimation. That is:( )D D W D D WWLS H H# = −1 (15) where # denotes conjugate transpose. The weight matrixwas chosen to be:W =⎛⎝⎜⎜⎜⎞⎠⎟⎟⎟wwwN120 0000 0 . (16) where:[ ]w ni inL==∑γ1(17) In other words, if the estimate for mi  is not reliable,because that state was seldom observed (wi small), theerror committed in future reestimations of thatcomponent is not considered.With these modifications the algorithm performance wassignificantly improved.6. SIMULATION RESULTSThe above algorithm was tested for the channels describedin section 2.2. The parameters of the simulation were:• Sampling rate: 2 samples per symbol to compensatefor possible timing errors.• Initial parameters:  σ 2 =1,  h =[1,0,...,0]T• Subblocks/timeslot: Up to 4, for the RA250 channel.• Speed of the mobiles: From 50 to 250 km/h.Fig. 4: Tracking for the first tap of the CIR vs time in amplitude and phasewhen each timeslot is segmented in subblocks (Test channel: RA250).Fig. 5: Comparative performance for different test channels and speed of themobiles: RA250 (+), RA100 (o), HT100 (x),   TU50 (*).In Fig. 4 tracking properties are shown. As mentioned insection 5, we observe that the channel estimate for eachsubblock is an average of that really observed. Due to CIRrapid variations, 4 subblocks are required in this case.Performance compared with that exhibited by theViterbi-based receiver proposed in [8,9] for different Eb/Noratios, is shown in Fig. 5. It is clear how close performanceis for both receivers. However, the comparison is notstraightforward in the case of RA channels. The reason isthat in the reference paper, [8], Rayleigh statistics wereassumed for all the echoes, whereas, in our study andaccording to the ETSI recommendations, a Rice pdf isconsidered for the first one. It is equivalent to admit a directline of sight,  what is far more realistic in such scenarios.In the case of HT channel, it is also important to pointout that such a satisfactory behaviour is a directconsequence of including the Weighting Matrix.7. CONCLUSIONSA BW-based algorithm for blind sequence detection andchannel estimation has been presented. Performance,evaluated in a very concrete environment (the GSMsystem), is close to that achieved by non-blind equalizers.However, the most important drawback of the algorithm isits high computational burden.Future work is concerned about reducing thecomputational complexity of the algorithm, as well asdeveloping recursive (and consequently adaptive) versionsof it, suitable for this scenario. It is also being studied thepossibility of including the time-varying nature of theparameters of the model in the batch BW framework.REFERENCES[1] J. Proakis and C.L. Nikias, “Blind Equalization”, Proc. SPIE AdaptiveSignal Processing 1991, Vol. 1565, pp. 76-87, 1991.[2] John Shynk et al., “A Comparative Performance Study of Several BlindEqualization Algorithms”, Proc. SPIE Adaptive Signal Processing 1991,Vol. 1565, pp. 102-117, 1991.[3] M. Ghosh and C.L. Weber, “Maximum Likelihood Blind Equalization”,Proc. SPIE Adaptive Signal Processing 1991, Vol. 1565, pp. 188-195,1991.[4] L. Rabiner, “A Tutorial on Hidden Markov Models and SelectedApplications in Speech Recognition”, Proc. IEEE, Vol. 77, No. 2, pp. 257-286, February 1989.[5] R. Steele, “Mobile Radio Communications”, Pentech Press Publishers,London 1992.[6] T. Aulin and C.W. Sundberg, “Continuous Phase Modulations (Parts I andII)”, IEEE  Trans. on Comm., Vol COM-29, No.3, pp. 196-225, 1981.[7] José A.R. Fonollosa and J. Vidal, “Application of Hidden Markov Modelsto Blind Channel Characterization and Data Detection”, Proc. IEEE Int. Conf.Accoust. Speech and Signal Processing, Australia, pp.185-188, April 1994.[8] R. d’Avella, L. Moreno and M. Sant’Agostino, “An Adaptive MLSEReceiver for TDMA Digital Mobile Radio”, IEEE J. on Selected Areas inComm., Vol. 7, No. 1, pp. 122-129, Jan. 1989.[9] G. Ungerboeck, “Adaptive Maximum-Likelihood Receiver for CarrierModulated Data Transmission Systems”, IEEE Trans. on Comm., Vol. COM-22, No. 5, pp. 856-864, May 1974.

Application of hidden markov models to blind channel estimation and data detection in a gsm environment

In this paper, we present an algorithm based on the Hidden Markov Models (HMM) theory to solve the problem of blind channel estimation and sequence detection in mobile digital communications. The environment in which the algorithm is tested is the Paneuropean Mobile Radio System, also known as GSM. In this system, a large part in each burst is devoted to allocate a training sequence used to obtain a channel estimate. The algorithm presented would not require this sequence, and that would imply an increase of the system capacity. Performance, evaluated for standard test channels, is close to that of non-blind algorithms.Peer Reviewe

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Application of hidden markov models to blind channel estimation and data detection in a gsm environment

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