Explanation of concept of MLSD algorithm

1. PONDICHERRY UNIVERSITY
DEPARTMENT OF ELECTRONICS
MAXIMUM LIKELIHOOD SEQUENCE
DETECTION ALGORITHM
By:
DEEPANSHU KAUSHAL
M.TECH(ECE/SEM 1)
REG NO:15304004

2. INTRODUCTION
Symbol Intervals interdependent for modulation systems with
memory.
Used for detection of Modulation Systems with memory.

3. OPTIMUM DETECTION RULE
Modulation schemes with memory represented as FSM drawn in
Trellis form.
For symbol interval ‘K’, each path in trellis represents one complete
message signal.
MLSD algorithm selects path with minimum equivalent distance
from the transmitted message.

5. WORKING OF MLSD ALGORITHM
 Considering PAM signal represented as L=1 NRZ-I sequence

6. TRELLIS FOR NRZI SIGNAL

7. Consider the message content at S0 as (0,0) and (1,1) and at S1 as
(0,1) and (1,0).
The trellis path for corresponding messages are
S0 (0,0) (1,1)
S1 (0,1) (1,0)
At t=2T
NODE INFORMATION BITS SIGNAL POINTS
S0 (0,0) (−√Eb,−√Eb)
(1,1) (√Eb,−√Eb)
S1 (0,1) (−√Eb,√Eb)
(1,0) (√Eb,√Eb)

8. Assume D represents equivalent distance and r1 & r2 represent
estimated message at receiver.

9. Each of equivalent distance is compared with s(t) and minimum
distance is considered to be actual data transmitted.
Assuming (0,0) and (0,1) is the data matching with transmitted data,
therefore at t=3T, the third data i.e. r3 is estimated based on
previous data.

10. All the above data are estimated in such a way that it retains the
same state.
This process of estimating the correct path through trellis is termed
as Viterbi algorithm.
This algorithm reduces complexity at each stage by a factor of two.

11. THANK YOU