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function [ rx_burst METRIC] = viterbi_detector(SYMBOLS,NEXT,PREVIOUS,START,STOPS,Y,Rhh)
%
% VITERBI_DETECTOR:
% This matlab code does the actual detection of the
% received sequence. As indicated by the name the algorithm
% is the viterbi algorithm, which is a MLSE. At this time
% the approch is to use Ungerboecks modified algorithm, and
% to return hard output only.
%
% SYNTAX: [ rx_burst ]
% =
% viterbi_detector(SYMBOLS,NEXT,PREVIOUS,START,STOPS,Y,Rhh)
%
% INPUT: SYMBOLS: The table of symbols corresponding the the state-
% numbers. Format as made by make_symbols.m
% NEXT: A transition table containing the next legal
% states, as it is generated by the code make_next.m
% PREVIOUS: The transition table describing the legal previous
% states as generated by make_previous.m
% START: The start state of the algorithm.
% STOPS: The legal stop states.
% Y: Complex baseband representation of the matched
% filtered and down converted received signal, as it
% is returned by mf.m
% Rhh: The autocorrelation as estimated by mf.m
%
% OUTPUT: rx_burst: The most likely sequence of symbols.
%
% SUB_FUNC: make_increment
%
% WARNINGS: None.
%
% TEST(S): Tested with no noise, perfect syncronization, and channel
% estimation/filtering. (Refer to viterbi_ill.m)
%
% AUTOR: Jan H. Mikkelsen / Arne Norre Ekstrøm
% EMAIL: hmi@kom.auc.dk / aneks@kom.auc.dk
%
% $Id: viterbi_detector.m,v 1.7 1997/11/18 12:41:26 aneks Exp $
% KNOWLEDGE OF Lh AND M IS NEEDED FOR THE ALGORITHM TO OPERATE
%
[ M , Lh ] = size(SYMBOLS);
% THE NUMBER OF STEPS IN THE VITERBI
%
STEPS=length(Y);
% INITIALIZE TABLES (THIS YIELDS A SLIGHT SPEEDUP).
%
METRIC = zeros(M,STEPS);
SURVIVOR = zeros(M,STEPS);
% DETERMINE PRECALCULATABLE PART OF METRIC
%
INCREMENT=make_increment(SYMBOLS,NEXT,Rhh);
%INCREMENT
% THE FIRST THING TO DO IS TO ROLL INTO THE ALGORITHM BY SPREADING OUT
% FROM THE START STATE TO ALL THE LEGAL STATES.
%
PS=START;
% NOTE THAT THE START STATE IS REFERRED TO AS STATE TO TIME 0
% AND THAT IT HAS NO METRIC.
%
S=NEXT(START,1);
METRIC(S,1)=real(conj(SYMBOLS(S,1))*Y(1))-INCREMENT(PS,S);
SURVIVOR(S,1)=START;
S=NEXT(START,2);
METRIC(S,1)=real(conj(SYMBOLS(S,1))*Y(1))-INCREMENT(PS,S);
SURVIVOR(S,1)=START;
PREVIOUS_STATES=NEXT(START,:);
% MARK THE NEXT STATES AS REAL. N.B: COMPLEX INDICATES THE POLARITY
% OF THE NEXT STATE, E.G. STATE 2 IS REAL.
%
COMPLEX=0;
for N = 2:Lh,
if COMPLEX,
COMPLEX=0;
else
COMPLEX=1;
end
STATE_CNTR=0;
for PS = PREVIOUS_STATES,
STATE_CNTR=STATE_CNTR+1;
S=NEXT(PS,1);
METRIC(S,N)=METRIC(PS,N-1)+real(conj(SYMBOLS(S,1))*Y(N))-INCREMENT(PS,S);
SURVIVOR(S,N)=PS;
USED(STATE_CNTR)=S;
STATE_CNTR=STATE_CNTR+1;
S=NEXT(PS,2);
METRIC(S,N)=METRIC(PS,N-1)+real(conj(SYMBOLS(S,1))*Y(N))-INCREMENT(PS,S);
SURVIVOR(S,N)=PS;
USED(STATE_CNTR)=S;
end
PREVIOUS_STATES=USED;
end
% AT ANY RATE WE WILL HAVE PROCESSED Lh STATES AT THIS TIME
%
PROCESSED=Lh;
% WE WANT AN EQUAL NUMBER OF STATES TO BE REMAINING. THE NEXT LINES ENSURE
% THIS.
%
if ~COMPLEX,
COMPLEX=1;
PROCESSED=PROCESSED+1;
N=PROCESSED;
for S = 2:2:M,
PS=PREVIOUS(S,1);
M1=METRIC(PS,N-1)+real(conj(SYMBOLS(S,1))*Y(N)-INCREMENT(PS,S));
PS=PREVIOUS(S,2);
M2=METRIC(PS,N-1)+real(conj(SYMBOLS(S,1))*Y(N)-INCREMENT(PS,S));
if M1 > M2,
METRIC(S,N)=M1;
SURVIVOR(S,N)=PREVIOUS(S,1);
else
METRIC(S,N)=M2;
SURVIVOR(S,N)=PREVIOUS(S,2);
end
end
end
% NOW THAT WE HAVE MADE THE RUN-IN THE REST OF THE METRICS ARE
% CALCULATED IN THE STRAIGHT FORWARD MANNER. OBSERVE THAT ONLY
% THE RELEVANT STATES ARE CALCULATED, THAT IS REAL FOLLOWS COMPLEX
% AND VICE VERSA.
%
N=PROCESSED+1;
while N <= STEPS,
for S = 1:2:M-1,
PS=PREVIOUS(S,1);
M1=METRIC(PS,N-1)+real(conj(SYMBOLS(S,1))*Y(N)-INCREMENT(PS,S));
PS=PREVIOUS(S,2);
M2=METRIC(PS,N-1)+real(conj(SYMBOLS(S,1))*Y(N)-INCREMENT(PS,S));
if M1 > M2,
METRIC(S,N)=M1;
SURVIVOR(S,N)=PREVIOUS(S,1);
else
METRIC(S,N)=M2;
SURVIVOR(S,N)=PREVIOUS(S,2);
end
end
N=N+1;
for S = 2:2:M,
PS=PREVIOUS(S,1);
M1=METRIC(PS,N-1)+real(conj(SYMBOLS(S,1))*Y(N)-INCREMENT(PS,S));
PS=PREVIOUS(S,2);
M2=METRIC(PS,N-1)+real(conj(SYMBOLS(S,1))*Y(N)-INCREMENT(PS,S));
if M1 > M2,
METRIC(S,N)=M1;
SURVIVOR(S,N)=PREVIOUS(S,1);
else
METRIC(S,N)=M2;
SURVIVOR(S,N)=PREVIOUS(S,2);
end
end
N=N+1;
end
% HAVING CALCULATED THE METRICS, THE MOST PROBABLE STATESEQUENCE IS
% INITIALIZED BY CHOOSING THE HIGHEST METRIC AMONG THE LEGAL STOP
% STATES.
%
BEST_LEGAL=0;
for FINAL = STOPS,
if METRIC(FINAL,STEPS) > BEST_LEGAL,
S=FINAL;
BEST_LEGAL=METRIC(FINAL,STEPS);
end
end
% UNCOMMENT FOR TEST OF METRIC
%
% METRIC
% BEST_LEGAL
% S
% pause
% HAVING FOUND THE FINAL STATE, THE MSK SYMBOL SEQUENCE IS ESTABLISHED
%
IEST(STEPS)=SYMBOLS(S,1);
N=STEPS-1;
while N > 0,
% if(N>STEPS-40),
% previo=ceil(S/2)
% end
S=SURVIVOR(S,N+1);
IEST(N)=SYMBOLS(S,1);
N=N-1;
end
% THE ESTIMATE IS NOW FOUND FROM THE FORMULA:
% IEST(n)=j*rx_burst(n)*rx_burst(n-1)*IEST(n-1)
% THE FORMULA IS REWRITTEN AS:
% rx_burst(n)=IEST(n)/(j*rx_burst(n-1)*IEST(n-1))
% FOR INITIALIZATION THE FOLLOWING IS USED:
% IEST(0)=1 og rx_burst(0)=1
%
rx_burst(1)=IEST(1)/(j*1*1);
for n = 2:STEPS,
rx_burst(n)=IEST(n)/(j*rx_burst(n-1)*IEST(n-1));
end
% rx_burst IS POLAR (-1 AND 1), THIS TRANSFORMS IT TO
% BINARY FORM (0 AND 1).
%
rx_burst=(rx_burst+1)./2;
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