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Equalize linearly modulated signal using Viterbi algorithm


y = mlseeq(x,chcffs,const,tblen,opmode)
y = mlseeq(x,chcffs,const,tblen,opmode,nsamp)
y = mlseeq(...,'rst',nsamp,preamble,postamble)
y = mlseeq(...,'cont',nsamp,... init_metric,init_states,init_inputs)
[y,final_metric,final_states,final_inputs] = ... mlseeq(...,'cont',...)


y = mlseeq(x,chcffs,const,tblen,opmode) equalizes the baseband signal vector x using the Viterbi algorithm. chcffs is a vector that represents the channel coefficients. const is a complex vector that lists the points in the ideal signal constellation, in the same sequence that the system's modulator uses. tblen is the traceback depth. The equalizer traces back from the state with the best metric. opmode denotes the operation mode of the equalizer; the choices are described in the following table.

Value of opmodeTypical Usage
'rst'Enables you to specify a preamble and postamble that accompany your data. The function processes x independently of data from any other invocations of this function. This mode incurs no output delay.
'cont'Enables you to save the equalizer's internal state information for use in a subsequent invocation of this function. Repeated calls to this function are useful if your data is partitioned into a series of smaller vectors that you process within a loop, for example. This mode incurs an output delay of tblen symbols.

y = mlseeq(x,chcffs,const,tblen,opmode,nsamp) specifies the number of samples per symbol in x, that is, the oversampling factor. The vector length of x must be a multiple of nsamp. When nsamp > 1, the chcffs input represents the oversampled channel coefficients.

Preamble and Postamble in Reset Operation Mode

y = mlseeq(...,'rst',nsamp,preamble,postamble) specifies the preamble and postamble that you expect to precede and follow, respectively, the data in the input signal. The vectors preamble and postamble consist of integers between 0 and M-1, where M is the order of the modulation, that is, the number of elements in const. To omit a preamble or postamble, specify [].

When the function applies the Viterbi algorithm, it initializes state metrics in a way that depends on whether you specify a preamble and/or postamble:

  • If the preamble is nonempty, the function decodes the preamble and assigns a metric of 0 to the decoded state. If the preamble does not decode to a unique state (that is, if the length of the preamble is less than the channel memory), the decoder assigns a metric of 0 to all states that can be represented by the preamble. The traceback path ends at one of the states represented by the preamble.

  • If the preamble is unspecified or empty, the decoder initializes the metrics of all states to 0.

  • If the postamble is nonempty, the traceback path begins at the smallest of all possible decoded states that are represented by the postamble.

  • If the postamble is unspecified or empty, the traceback path starts at the state with the smallest metric.

Additional Syntaxes in Continuous Operation Mode

y = mlseeq(...,'cont',nsamp,... init_metric,init_states,init_inputs) causes the equalizer to start with its state metrics, traceback states, and traceback inputs specified by init_metric, init_states, and init_inputs, respectively. These three inputs are typically the extra outputs from a previous call to this function, as in the syntax below. Each real number in init_metric represents the starting state metric of the corresponding state. init_states and init_inputs jointly specify the initial traceback memory of the equalizer. The table below shows the valid dimensions and values of the last three inputs, where numStates is ML-1, M is the order of the modulation, and L is the number of symbols in the channel's impulse response (with no oversampling). To use default values for all of the last three arguments, specify them as [],[],[].

Input ArgumentMeaningMatrix SizeRange of Values
init_metricState metrics1 row, numStates columnsReal numbers
init_statesTraceback statesnumStates rows, tblen columnsIntegers between 0 and numStates-1
init_inputsTraceback inputsnumStates rows, tblen columnsIntegers between 0 and M-1

[y,final_metric,final_states,final_inputs] = ... mlseeq(...,'cont',...) returns the normalized state metrics, traceback states, and traceback inputs, respectively, at the end of the traceback decoding process. final_metric is a vector with numStates elements that correspond to the final state metrics. final_states and final_inputs are both matrices of size numStates-by-tblen.


The example below illustrates how to use reset operation mode on an upsampled signal.

% Use 2-PAM.
M = 2; hMod = comm.PAMModulator(M); hDemod = comm.PAMDemodulator(M);
hChan = comm.AWGNChannel('NoiseMethod', 'Signal to noise ratio (SNR)', ...
const = step(hMod,(0:M-1)'); % PAM constellation
tblen =  10; % Traceback depth for equalizer
nsamp = 2; % Number of samples per symbol

msgIdx = randi([0 M-1],1000,1); % Random bits
msg = upsample(step(hMod,msgIdx),nsamp); % Modulated message
chcoeffs = [.986; .845; .237; .12345+.31i]; % Channel coefficients
chanest = chcoeffs; % Channel estimate
hMLSEE = comm.MLSEEqualizer('TracebackDepth',tblen,...
    'Channel',chanest, 'Constellation',const, 'SamplesPerSymbol', nsamp);
filtmsg = filter(chcoeffs,1,msg); % Introduce channel distortion.
msgRx = step(hChan,filtmsg); % Add Gaussian noise.
msgEq = step(hMLSEE,msgRx); % Equalize.
msgEqIdx = step(hDemod,msgEq); % Demodulate.
%Calculate BER
hErrorCalc = comm.ErrorRate;
berVec  = step(hErrorCalc, msgIdx, msgEqIdx);
ber  = berVec(1)
nerrs = berVec(2)

The output is shown below. Your results might vary because this example uses random numbers.

nerrs =


ber =


The example in Example: Continuous Operation Mode illustrates how to use the final state and initial state arguments when invoking mlseeq repeatedly.

The example in Use a Preamble in MATLAB illustrates how to use a preamble.


[1] Proakis, John G., Digital Communications, Fourth Edition, New York, McGraw-Hill, 2001.

[2] Steele, Raymond, Ed., Mobile Radio Communications, Chichester, England, John Wiley & Sons, 1996.

Introduced before R2006a

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