GMSK Modulator Baseband

Modulate signal using Gaussian minimum shift keying method

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Libraries:
Communications Toolbox / Modulation / Digital Baseband Modulation / CPM

Description

The GMSK Modulator Baseband block modulates an input signal using the Gaussian minimum shift keying (GMSK) method. The output is a baseband representation of the modulated signal. For more information about the modulation and the filtering applied, see Algorithms.

Examples

Compare GMSK and MSK Signals in Simulink

The cm_gmsk_vs_msk model compares Gaussian minimum shift keying (GMSK) and minimum shift keying (MSK) modulation schemes.

The Random Integer Generator block provides a source of uniformly distributed random integers in the range [0, M-1], where M is the constellation size of the GMSK or MSK signal. The Unipolar to Bipolar Converter block maps a unipolar input signal to a bipolar output signal consisting of integers between -(M-1) and +(M-1). The bipolar data is routed to separate paths. The top path applies GMSK modulation by using the GMSK Modulator Baseband block. The bottom path applies MSK modulation by using the MSK Modulator Baseband block. Noise is added to both the GMSK and MSK signals by using AWGN Channel blocks. The Eye Diagram blocks are used to visualize eye diagrams of both signals.

The eye diagrams show the similarity between the GMSK and MSK signals when you set the initial pulse length of the GMSK Modulator Baseband block to 1.

To view the difference that a partial response modulation has on the eye diagram, set the initial pulse length in the GMSK modulator to 5. The increased pulse length results in an increase in the number of paths, showing that the CPM waveform depends on values of the previous symbols as well as the present symbol. Plot the eye diagram of the GMSK signal.

If you change the initial pulse length to an even number, such as 4, you should set the initial phase offset of the GMSK modulator to pi/4 and the offset argument of the eye diagram to 0 for a better view of the modulated signal. To more clearly view the Gaussian pulse shape, you must use scopes that enable you to view the phase of the signal, as described in the View CPM Phase Tree Using Simulink example.

Demodulate GMSK Signal in Simulink

Demodulate a GMSK-modulated signal impaired by AWGN and compute the bit error rate.

The cm_gmsk_mod_demod model generates random Bernoulli distributed binary data and then applies GMSK modulation to frames data. The GMSK-modulated signal passes through an AWGN channel and then is demodulated by using the GMSK method. The bit error rate is calculated on frames of data.

The Error Rate Calculation block has the receive delay set to the value of the traceback depth used by the GMSK Baseband Demodulator block. The model uses the Find Delay block to confirm the delay equals the value of the traceback depth.

Transmit to receive delay is 16 symbols.
BER = 8.3934e-05

Combine QPSK and GMSK Signals Using Simulink

Combine two 60 KHz frequency bands adjacent to each other.

Run the model to explore how combining the frames affects the signals. The model frequency shifts and combines frames of QPSK and GMSK baseband modulated signals. A spectrum analyzer displays the individual and combined signals.

Extended Examples

Soft Decision GMSK Demodulator

A system that includes convolutional coding and GMSK modulation. The receiver in this model includes two parallel paths, one that uses soft decisions and another that uses hard decisions. The model computes bit error rates for the two paths to illustrate that the soft decision receiver performs better. The performance advantage for soft decision reception over hard decision reception is expected because soft decisions enable the system to retain more information from the demodulation operation to use in the decoding operation.

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Correct Misalignment of Interleaved Words Due to Demodulation

In communications systems, you can use techniques such as interleaving to protect against burst errors. Interleaving is a process that rearranges the order of data bits or symbols. The effectiveness of interleaving depends on the precise alignment of data words prior to this process. This example shows how to correct for the misalignment of codewords due to delays incurred in digital demodulation, when performing deinterleaving and outer block decoding.

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Ports

Input

In — Input signal

scalar | column vector

Input signal, specified as a scalar or column vector. For more information, see Integer-Valued Signals and Binary-Valued Signals.

This port is unnamed on the block.

Data Types: double | Boolean | int8 | int16 | int32

Output

Out — GMSK-modulated baseband signal

column vector

GMSK-modulated baseband signal, returned as a column vector. Use the Output data type parameter to specify the output data type. The modulated output symbols are oversampled by the Samples per symbol parameter value. For information on the processing rates, see Single-Rate Processing and Multirate Processing.

This port is unnamed on the block.

Data Types: double | single

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Input type — Integer or group-of-bits input indicator

Integer (default) | Bit

Integer or group-of-bits input indicator, specified as Integer or Bit.

• Set this parameter to Integer to input data as integers.

• Set this parameter to Bit to input data as bits.

For more information, see Integer-Valued Signals and Binary-Valued Signals.

BT product — Product of bandwidth and symbol time of Gaussian pulse shape

.3 (default) | positive scalar

Product of the bandwidth and symbol time of the Gaussian pulse shape, specified as a positive scalar. For more details, see Algorithms.

Pulse length (symbol intervals) — Length of frequency pulse shape

4 (default) | positive integer

Length of the frequency pulse shape, specified as a positive integer. This parameter represents the truncated frequency pulse length of the Gaussian pulse shape in symbol intervals.

Symbol prehistory — Data symbols used before start of simulation

1 (default) | -1 | vector

Symbol prehistory, specified as -1, 1, or a vector with elements equal to those values. This parameter defines the data symbols that the modulator uses before the block processes symbols, in reverse chronological order.

• A scalar value expands to a vector of length L_P – 1. L_P represents the pulse length, which is specified by the Pulse length (symbol intervals) parameter.

• For a vector, the length must be L_P – 1.

Phase offset (rad) — Initial phase offset

0 (default) | scalar

Initial phase offset of the modulated waveform in radians, specified as a scalar.

Samples per symbol — Number of samples per output symbol

8 (default) | positive integer

Number of samples per output symbol, specified as a positive integer. The number of samples per symbol represents the upsampling factor from input samples to output samples. For more information, see Signal Upsampling and Rate Changes.

Rate options — Block processing rate

Enforce single-rate processing (default) | Allow multirate processing

Block processing rate, specified as one of these options:

• Enforce single-rate processing — The input and output signals have the same sample time. The block implements the rate change by making a size change at the output when compared to the input. The output width equals the product of the number of symbols and the Samples per symbol parameter value.

• Allow multirate processing — The input and output signals have different sample times. The output sample time equals the symbol period divided by the Samples per symbol parameter value.

Output data type — Data type of output

double (default) | single

Data type of the output, specified as double or single.

Block Characteristics

Data Types	Boolean | double | integer | single
Multidimensional Signals	no
Variable-Size Signals	no

More About

Integer-Valued Signals and Binary-Valued Signals

This block accepts a scalar or column vector input signal. For a column vector input signal, the width of the output equals the product of the number of symbols and the value for the Samples per symbol parameter.

• When you set the Input type parameter to Integer, the block accepts bipolar values of –1 and 1.

• When you set the Input type parameter to Bit, the block accepts binary values of 0 and 1.

Single-Rate Processing

In single-rate processing mode, the input and output signals have the same port sample time. The block implicitly implements the rate change by making a size change at the output when compared to the input. In this mode, the input to the block can be multiple symbols. The output width equals the product of the number of input symbols and the Samples per symbol parameter value.

Multirate Processing

In multirate processing mode, the input and output signals have different port sample times. In this mode, the input to the block must be one symbol. The output sample time equals the symbol period divided by the Samples per symbol parameter value.

Group Delay

The group delay is the number of samples between the filter response start and the filter response peak. This block introduces a group delay equal to (L_P/2) ×N_SPS. The Pulse length (symbol intervals) parameter specifies the pulse length, L_P, and the Samples per symbol parameter specifies N_SPS using a reference of output sample periods. The traceback depth for the Viterbi algorithm at the receiver (demodulator) is specified by the Traceback depth parameter. In most cases, the traceback depth is larger than the group delay. The traceback depth of the demodulator determines the net delay effect.

Algorithms

GMSK Modulation

GMSK is a continuous phase (CPM) scheme with no phase discontinuities because the frequency changes occur at the carrier zero-crossing points. For more information, see [1]. For GMSK (and MSK), the frequency difference between the logical one and logical zero states is always equal to half the data rate. This difference can be expressed in terms of the modulation index. Specifically, an input symbol of 1 causes a phase shift of π/2 radians, which corresponds to a modulation index of 0.5. GMSK applies a Gaussian Pulse Shaping Filter.

Gaussian Pulse Shaping Filter

These equations define the frequency pulse shape of the Gaussian pulse shaping filter:

$$\begin{array}{c}g(t)=\frac{1}{2T}\left\{Q\left[2\pi B_b\frac{t-\frac{T}{2}}{\sqrt{\ln 2}}\right]-Q\left[2\pi B_b\frac{t+\frac{T}{2}}{\sqrt{\ln 2}}\right]\right\},\text{where}\\ Q(t)={\displaystyle {\int }_t^{\infty }\frac{1}{\sqrt{2\pi }}{e}^{-{\tau }^2/2}d\tau }\end{array}$$

B_b represents the bandwidth of the pulse and T is the symbol durations. Q(t) is the complementary cumulative distribution function.

The BT product parameter represents the bandwidth multiplied by time. Use this parameter to reduce the bandwidth at the expense of increased intersymbol interference. The Pulse length (symbol intervals) parameter measures the length of the Gaussian pulse shape in symbol intervals.

References

[1] Anderson, John B., Tor Aulin, and Carl-Erik Sundberg. Digital Phase Modulation. New York: Plenum Press, 1986.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a