Channel precoding with small envelope variations for π=4-QPSK and MSK over frequency-selective slow fading channels

Abstract

Abstract-This paper presents channel precoding schemes to combat intersymbol interference (ISI) over a frequency-selective slow fading channel in wireless communication systems using 4 shifted quadrature phase-shift keying or minimum shift keying. Based on the dimension partitioning technique, the precoders predistort the phase of the transmitted symbol in the forward link to combat ISI, keeping the transmitted symbol amplitude constant. The proposed schemes can ensure the stability of the precoder even in equalizing a nonminimum-phase channel, combat ISI without increasing the complexity of portable unit receivers, and reduce the envelope variations of transmitted signals such that power-efficient nonlinear amplifiers can be used for the precoded signals without causing a significant undue distortion. Theoretical analysis and simulation results are presented to demonstrate the effectiveness of the proposed channel precoding schemes.Index Terms-Channel precoding, equalization, intersymbol interference (ISI), minimum shift keying (MSK), 4 shifted quadrature phase-shift keying ( 4-QPSK), slow frequency-selective fading.

Pre-Equalization of Continuous Phase Modulation for Multipath Fading Channels

“…TH-type precoding uses modulo-arithmetic operations to maintain the stability of the transmitter, whereas its application to the phase modulated waveforms results in large envelope fluctuations and destroys the spectral efficiency. The dimension partitioning techniques which are proposed for quadrature phase-shift keying (QPSK) in [9] and π/4-QPSK in [10] keep the signal amplitude constant and only allow the distortion of the signal phase for pre-equalization. In [10], dimension partitioning is also applied to minimum shift keying (MSK) because it can be represented as offset QPSK with halfsinusoid pulse shaping.…”

“…The dimension partitioning techniques which are proposed for quadrature phase-shift keying (QPSK) in [9] and π/4-QPSK in [10] keep the signal amplitude constant and only allow the distortion of the signal phase for pre-equalization. In [10], dimension partitioning is also applied to minimum shift keying (MSK) because it can be represented as offset QPSK with halfsinusoid pulse shaping. However, this type of pre-equalization is not applicable to other CPM schemes in general since they cannot be represented by square signal constellations.…”

“…For this purpose, a time-division duplex system is considered where the transmitter and the receiver operate alternately in the same frequency band. Then, by assuming slow fading, channel information that is obtained from the received packets is used to equalize the transmitted packets, as in [9] and [10]. The proposed scheme depends on the approximation of CPM signals by using the nonsymmetric non-orthogonal exponential expansion (nSnOEE) in [14].…”

“…The proposed method requires that the ISI on a symbol interval only depends on the past symbols, as in [9], [10]. Therefore, it is assumed that τ l − τ 0 ≥ T for l = 1, .…”

“…For simplicity, it is assumed that τ 0 = 0 in the rest of the paper. Furthermore, channel information is assumed to be available at the transmitter, as described in [9], [10].…”