Generation of balanced quadrature phase shift keyed sequences through guided scrambling

Balanced codes (also called DC-free codes) are widely used in binary communication systems to increase the likelihood of accurate symbol recovery with practical demodulators. Guided scrambling (GS) is recognised as a viable approach to efficiently generate DC-free binary sequences. In this study the authors extend the use of GS to generate balanced sequences of quadrature phase shift keyed (QPSK) symbols by using arithmetic from the ring of polynomials defined over the Galois field of four elements. In addition to ensuring adequate timing information and consistent decision thresholds to improve the performance of practical demodulators, balanced encoding of QPSK symbol sequences creates a null at DC in the spectrum of the equivalent complex baseband signal. This corresponds to a null at the centre frequency of the bandpass QPSK signal that enables the insertion of a pilot tone and avoidance of narrowband interference without filtering or distortion of the signal. The authors outline sufficient conditions for the generation of balanced GS QPSK sequences, and based upon these conditions the authors recommend scrambling polynomials and quotient selection criteria. The authors then present analytical and simulation results that confirm the generation of balanced sequences using this approach.