| The ENCAP $4^{N}$ (ENCoded Amplitude and Phase $4^{N}$) [1], related with a vast class of OQPSK (Offset Quadri-Phase Shift Keying) type signals, can be advantageous when is important to achieve good tradeoffs between spectral efficiency and envelope fluctuations when a nonlinear amplification is employed.
This paper presents a simplified representation of FQPSK (Feher-Patented Quadrature-Phase Shift Keying)[2], showing the potential improvement in power efficiency. It is also demonstrated that the power efficiency it is achieved without sacrifice of spectral compactness.
Usually, the coding rule for ENCAP $4^{N}$ format is based on the complex envelope decomposition in pulses with bit duration T, directly related to the $4^{N}$ generating functions set. In this paper, it is proposed a new interpretation based in this signal format that results in a new coding rule, based on a complex envelope description as function of pulses with duration 2T. The signal, in accordance with the foregoing coding rule, can be viewed as a trellis coded modulation with $2^{2N+2}$ states and pulses shapes, the optimum receiver will employ a Viterbi algorithm, with $2^{2N+2}$ states and a bank filter with $2^{2N}$ matched filters for each possible pulse shape.
Also, exploring the equivalence between the ENCAP-OQPSK format and the analytical representation of non-linear OQPSK signals is presented an equivalent signal format, allowing a simplified description for these signals. As consequence, the transmitter and receiver structures are simplified. The decoding process is now based on a trellis with $2^{2N}$ states, and the number of pulse is reduced by a factor of 4. Therefore, our approach allows a significant reduction on the receiver complexity, since the filters bank structure only needs $2^{2N}$ matched filters.
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