Abstract: A method at a receiver comprises receiving a signal conveying symbols at respective positions within a clock cycle, the symbols comprising a data set consisting of data symbols and a pilot set consisting of pilot symbols; determining detected phases of the symbols based on the signal; generating first phase estimates based on the detected phases of a subset of the pilot set, and reference phases of the subset of the pilot set, the first phase estimates being associated with the positions of the pilot set; and generating second phase estimates based on the detected phases of the pilot set, reference phases of the pilot set, and the first phase estimates, the second phase estimates being associated with the positions of the pilot set and of at least a subset of the data set; and applying rotations to the detected phases of the symbols based on the second phase estimates.

Abstract: Upon receiving a communications signal conveying symbols at a symbol period T, a receiver applies filter coefficients to a digital representation of the communications signal, thereby generating filtered signals having a shape in the frequency domain characterized by a bandwidth expansion factor ?, where components of the filtered signals correspond to angular frequencies ? = - ? ? ( 1 + ? ) T ? ? … - ? ? ( 1 - ? ) T , + ? ? ( 1 - ? ) T ? ? … + ? ? ( 1 + ? ) T . The receiver calculates first-order components from a first phase derivative of the components at a first differential distance, second-order components from a second phase derivative of the first-order components at a second differential distance, and composite second-order components from an average of the second-order components over multiple time intervals.

Abstract: A receiver generates a stream of digital samples from an analog electrical signal that represents data conveyed to the receiver over a communication channel, where the stream of digital samples comprises current samples corresponding to a current timepoint, previous samples corresponding to a timepoint earlier than the current timepoint, and subsequent samples corresponding to a timepoint later than the current timepoint. The receiver generates previous, current, and subsequent phase offset signals based on the previous, current, and subsequent samples, respectively. The receiver uses the previous phase offset signal to adjust clock frequency and clock phase of the current samples, thereby resulting in current adjusted samples. The receiver adjusts clock phase of the current adjusted samples based on any one of the previous, current, and subsequent phase offset signals. In some examples, receiver adjusts the clock phase of the current adjusted samples based on the subsequent phase offset signal.

Abstract: A method at a receiver comprises receiving a signal conveying symbols at respective positions within a clock cycle, the symbols comprising a data set consisting of data symbols and a pilot set consisting of pilot symbols; determining detected phases of the symbols based on the signal; generating first phase estimates based on the detected phases of a subset of the pilot set, and reference phases of the subset of the pilot set, the first phase estimates being associated with the positions of the pilot set; and generating second phase estimates based on the detected phases of the pilot set, reference phases of the pilot set, and the first phase estimates, the second phase estimates being associated with the positions of the pilot set and of at least a subset of the data set; and applying rotations to the detected phases of the symbols based on the second phase estimates.

Abstract: A receiver generates a stream of digital samples from an analog electrical signal that represents data conveyed to the receiver over a communication channel, where the stream of digital samples comprises current samples corresponding to a current timepoint, previous samples corresponding to a timepoint earlier than the current timepoint, and subsequent samples corresponding to a timepoint later than the current timepoint. The receiver generates previous, current, and subsequent phase offset signals based on the previous, current, and subsequent samples, respectively. The receiver uses the previous phase offset signal to adjust clock frequency and clock phase of the current samples, thereby resulting in current adjusted samples. The receiver adjusts clock phase of the current adjusted samples based on any one of the previous, current, and subsequent phase offset signals. In some examples, receiver adjusts the clock phase of the current adjusted samples based on the subsequent phase offset signal.

Abstract: An apparatus comprises a frequency accumulator to produce a frequency ramp, and a symbol modulator to receive symbols and to add to the frequency ramp frequency offsets representative of the symbols, to produce a modulated frequency ramp for a modulated chirp. The apparatus includes a spreading factor controller to control a roll-over rate of the modulated frequency ramp responsive to spreading factor and frequency bandwidth control signals, to control a spreading factor and a frequency bandwidth of the modulated chirp. The apparatus includes a center frequency controller to control a center frequency of the modulated frequency ramp responsive to a center frequency control signal. The apparatus includes a phase accumulator to accumulate frequency samples of the modulated frequency ramp to produce phase samples corresponding to the modulated chirp, and a vector rotator to rotate the phase samples based on an input vector to produce a modulated chirp.

Abstract: Upon receiving a communications signal conveying symbols at a symbol period T, a receiver applies filter coefficients to a digital representation of the communications signal, thereby generating filtered signals characterized by a substantially raised cosine shape in the frequency domain with a roll-off factor ?, where components of the filtered signals correspond to angular frequencies ? = - ? ? ( 1 + ? ) T ? … - ? ? ( 1 - ? ) T , + ? ? ( 1 - ? ) T ? … + ? ? ( 1 + ? ) T . The receiver calculates first-order components from a first phase derivative of the components at a first differential distance, second-order components from a second phase derivative of the first-order components at a second differential distance, and composite second-order components from an average of the second-order components over multiple time intervals.

Abstract: An apparatus comprises a frequency accumulator to produce a frequency ramp, and a symbol modulator to receive symbols and to add to the frequency ramp frequency offsets representative of the symbols, to produce a modulated frequency ramp for a modulated chirp. The apparatus includes a spreading factor controller to control a roll-over rate of the modulated frequency ramp responsive to spreading factor and frequency bandwidth control signals, to control a spreading factor and a frequency bandwidth of the modulated chirp. The apparatus includes a center frequency controller to control a center frequency of the modulated frequency ramp responsive to a center frequency control signal. The apparatus includes a phase accumulator to accumulate frequency samples of the modulated frequency ramp to produce phase samples corresponding to the modulated chirp, and a vector rotator to rotate the phase samples based on an input vector to produce a modulated chirp.

Abstract: An apparatus comprises a frequency accumulator to produce a frequency ramp, and a symbol modulator to receive symbols and to add to the frequency ramp frequency offsets representative of the symbols, to produce a modulated frequency ramp for a modulated chirp. The apparatus includes a spreading factor controller to control a roll-over rate of the modulated frequency ramp responsive to spreading factor and frequency bandwidth control signals, to control a spreading factor and a frequency bandwidth of the modulated chirp. The apparatus includes a center frequency controller to control a center frequency of the modulated frequency ramp responsive to a center frequency control signal. The apparatus includes a phase accumulator to accumulate frequency samples of the modulated frequency ramp to produce phase samples corresponding to the modulated chirp, and a vector rotator to rotate the phase samples based on an input vector to produce a modulated chirp.

Abstract: An apparatus comprises a frequency accumulator to produce a frequency ramp, and a symbol modulator to receive symbols and to add to the frequency ramp frequency offsets representative of the symbols, to produce a modulated frequency ramp for a modulated chirp. The apparatus includes a spreading factor controller to control a roll-over rate of the modulated frequency ramp responsive to spreading factor and frequency bandwidth control signals, to control a spreading factor and a frequency bandwidth of the modulated chirp. The apparatus includes a center frequency controller to control a center frequency of the modulated frequency ramp responsive to a center frequency control signal. The apparatus includes a phase accumulator to accumulate frequency samples of the modulated frequency ramp to produce phase samples corresponding to the modulated chirp, and a vector rotator to rotate the phase samples based on an input vector to produce a modulated chirp.

Abstract: In a digital communication system there is provided a method for OFDM channel estimation that jointly considers the effects of coarse timing error and multipath propagation. The method uses an iterative channel estimation technique, which considers the practical scenario of fractional timing error and non-sample space echo delays. The method does not require channel state information such as second-order statistic of the channel impulse responses or the noise power. Moreover, timing error can be conveniently obtained with the proposed technique. Simulation shows that, when comparing OFDM channel estimation techniques under DOCSIS 3.1 realistic channel conditions, the proposed algorithm significantly outperforms conventional methods.

Abstract: In a digital communication system there is provided a method for OFDM channel estimation that jointly considers the effects of coarse timing error and multipath propagation. The method uses an iterative channel estimation technique, which considers the practical scenario of fractional timing error and non-sample space echo delays. The method does not require channel state information such as second-order statistic of the channel impulse responses or the noise power. Moreover, timing error can be conveniently obtained with the proposed technique. Simulation shows that, when comparing OFDM channel estimation techniques under DOCSIS 3.1 realistic channel conditions, the proposed algorithm significantly outperforms conventional methods.

Abstract: In a digital communication system there is provided a method for OFDM channel estimation that jointly considers the effects of coarse timing error and multipath propagation. The method uses an iterative channel estimation technique, which considers the practical scenario of fractional timing error and non-sample space echo delays. The method does not require channel state information such as second-order statistic of the channel impulse responses or the noise power. Moreover, timing error can be conveniently obtained with the proposed technique. Simulation shows that, when comparing OFDM channel estimation techniques under DOCSIS 3.1 realistic channel conditions, the proposed algorithm significantly outperforms conventional methods.

Abstract: In a digital communication system there is provided a method for OFDM channel estimation that jointly considers the effects of coarse timing error and multipath propagation. The method uses an iterative channel estimation technique, which considers the practical scenario of fractional timing error and non-sample space echo delays. The method does not require channel state information such as second-order statistic of the channel impulse responses or the noise power. Moreover, timing error can be conveniently obtained with the proposed technique. Simulation shows that, when comparing OFDM channel estimation techniques under DOCSIS 3.1 realistic channel conditions, the proposed algorithm significantly outperforms conventional methods.