Soft Decision GMSK Demodulator

This model shows 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 uses the bit error rates for the two paths to illustrate that the soft decision receiver performs better. This is to be expected, because soft decisions enable the system to retain more information from the demodulation operation to use in the decoding operation.

Structure of the Example

The example model, doc_gmsk_soft_decision, transmits and receives a coded GMSK signal.

The key components are:

  • A Bernoulli Binary Generator block, which generates binary numbers.

  • A Convolutional Encoder block, which encodes the binary numbers using a rate 1/2 convolutional code.

  • A GMSK modulator section, which computes the logical difference between successive bits and modulates the result using the GMSK Modulator Baseband block.

  • A GMSK soft demodulator section that implements the detector design proposed in [1], called a serial receiver. This section of the model produces a noisy bipolar signal. The section labeled Soft Decisions uses an eight-region partition in the Quantizing Encoder block to prepare for 3-bit soft-decision decoding using the Viterbi Decoder block. The section labeled Hard Decisions uses a two-region partition to prepare for hard-decision Viterbi decoding. Using a two-region partition here is equivalent to having the demodulator make hard decisions. In each decoding section, a Delay block aligns codeword boundaries with frame boundaries so that the Viterbi Decoder block can decode properly. This is necessary because the combined delay of other blocks in the system is not an integer multiple of the length of a codeword.

  • A pair of Error Rate Calculation blocks, as well as Display blocks that show the BER for the system with each type of decision.

The Serial GMSK Receiver

The serial GMSK receiver is based on the fact that GMSK can be represented as a combination of amplitude pulses [2] - [3], and can, therefore, be demodulated with a matched filter. The GMSK waveform used in this model has a BT product of 0.3 and a frequency pulse length of 4 symbols. As such, it can be represented by eight different amplitude pulses, which are shown in Figure 2 of [3]. The matched filter in this model uses only the largest pulse of the eight, because of its simplicity of implementation. That same simplicity, however, yields BER performance that is inferior to the more traditional Viterbi-based demodulator.

Results and Displays

The example model includes these visualizations to illustrate its performance:

  • The Display blocks illustrate that the soft decision receiver performs better (that is, has a smaller BER) than the hard decision receiver.

  • The Tx Signal window shows the scatter plot of the signal before the AWGN channel.

  • The Rx Signal window shows the scatter plot of the signal after the AWGN channel.

  • The Freq Response window shows the frequency response of the GMSK signal before and after the AWGN channel.

  • The Decision Levels window shows, in yellow, the various soft decision levels in the top plot and the binary hard decisions in the bottom plot. This window also indicates, in blue, when errors occur.


[1] Bjerke, B., J. Proakis, M. Lee, and Z. Zvonar, "A Comparison of GSM Receivers for Fading Multipath Channels with Adjacent- and Co-Channel Interference," IEEE J. Select. Areas Commun., Nov. 2000, pp. 2211-2219.

[2] Laurent, Pierre, "Exact and Approximate Construction of Digital Phase Modulations by Superposition of Amplitude Modulated Pulses (AMP)," IEEE Trans. Comm., Vol. COM-34, No. 2, Feb. 1986, pp. 150-160.

[3] Jung, Peter, "Laurent's Representation of Binary Digital Continuous Phase Modulated Signals with Modulation index 1/2 Revisited", IEEE Trans. Comm., Vol. COM-42, No. 2/3/4, Feb./Mar./Apr. 1994, pp. 221-224.