The present disclosure provides a method implemented in a wireless communication device for estimating a frequency offset between a carrier frequency of a received signal and a frequency of a local oscillator as well as the wireless communication device. The method comprises determining a plurality of phase change candidates for a phase change between a data symbol and a first reference symbol in the signal. The method further comprises generating a collection of constellation symbols from the data symbol and rotating the collection of constellation symbols by the plurality of phase change candidates. Then, one of the phase change candidates corresponding to one of the rotated collections of constellation symbols is selected in such a manner that said one of the rotated collections of constellation symbols matches a set of constellation points best. Next, the frequency offset is determined based on the selected phase change candidate.

A transceiver includes a receive circuit configured to receive an incoming signal and recover a reference signal at a reference frequency from the incoming signal. The incoming signal is a wireless packet. A first oscillator generates a signal at a set of predetermined frequencies. A first phase lock loop (PLL) interfaced with the first oscillator. The first PLL is configured to adjust a first oscillator frequency of the first oscillator based on an incoming frequency of the incoming signal using the reference frequency. A transmit circuit includes a second oscillator configured to generate a carrier signal at a predetermined frequency and a modulator configured to modulate data over the carrier signal at the predetermined frequency. The transmit circuit includes a second PLL interfaced with the second oscillator that sets the second oscillator to generate the carrier signal at the predetermined frequency using the reference signal. The transmit circuit transmits the modulated carrier signal.

The present disclosure provides a method implemented in a wireless communication device for estimating a frequency offset between a carrier frequency of a received signal and a frequency of a local oscillator as well as the wireless communication device. The method comprises determining a plurality of phase change candidates for a phase change between a data symbol and a first reference symbol in the signal. The method further comprises generating a collection of constellation symbols from the data symbol and rotating the collection of constellation symbols by the plurality of phase change candidates. Then, one of the phase change candidates corresponding to one of the rotated collections of constellation symbols is selected in such a manner that said one of the rotated collections of constellation symbols matches a set of constellation points best. Next, the frequency offset is determined based on the selected phase change candidate.

Constant-envelope phase-optimized transmission methods and apparatus are disclosed. An example method includes determining initial values of modulation phases in a first quadrant, the modulation phases associated with binary codes to be transmitted; and optimizing the initial values to second values to enable a product of an objective function to be within a threshold value.