An equalizer includes: a channel estimator configured to generate a set of time-domain channel coefficients based on a receive signal; a frequency-domain transformer configured to generate a set of frequency-domain channel coefficients based on a frequency transform of the set of time-domain channel coefficients; an equalizer coefficient generator configured to generate a set of frequency-domain equalizer coefficients based on the set of frequency-domain channel coefficients; a time-domain transformer configured to generate a set of time-domain equalizer coefficients based on a time transform of the set of frequency-domain equalizer coefficients; and a filter configured to filter the receive signal based on a filter function that is based on the set of time-domain equalizer coefficients.

An apparatus may include a circuit configured to receive first and second samples of an underlying data from respective first and second sample periods and which correspond to respective first and second sensors, a phase control value may have first and second values during respective first and second sample periods. The phase control value may be a control value for a sample clock signal. The circuit may also determine a difference in the phase control value between the first value and the second value. The circuit may then digitally interpolate the first and second samples to produce a phase shifted first and second samples where the digital interpolation of at least one of the first and second samples mat be at least in part based on the difference in the phase control value to compensate for a phase misalignment between the first sample and the second sample.

An apparatus can include a circuit configured to process an input signal using a set of channel parameters. The circuit can produce, using a first adaptation algorithm, a first set of channel parameters for use by the circuit as the set of channel parameters in processing the input signal. The circuit can further approximate a second set of channel parameters of a second adaptation algorithm for use by the circuit as the set of channel parameters in processing the input signal based on the first set of channel parameters and a relationship between a third set of channel parameters generated using the first adaptation algorithm and a fourth set of channel parameters generated using the second adaptation algorithm. In addition, the circuit can perform the processing of the input signal using the second set of channel parameters as the set of channel parameters.

A method is provided of receiving user data from multiple transmitters, the user data from each transmitter having been encoded as a Low Density Lattice codeword, and the multiple Low Density Lattice codewords having been transmitted so as to be received as a combined signal at a receiver, the method of receiving comprising the steps of: (i) receiving the signal, (ii) calculating coefficients of linear combinations of the codewords from the multiple transmitters, (iii) calculating a scaling factor to be applied to the signal based on the coefficients, (iv) applying the scaling factor to the signal to provide a linear combination of the codewords, (v) decoding the linear combination of the codewords based on channel state information to obtain an optimal independent linear combination of user data, (vi) repeating steps (ii), (iii) (iv) and (v) to obtain at least as many optimal independent linear combinations as the number of transmitters, and recovering the user data from the optimal independent linear combinations.

An apparatus may include a circuit configured to receive a first phase control value of a phase control value signal, generate a first phase interpolator control signal value of a phase interpolator control signal and generate a first digital interpolator control signal value of a digital interpolator control signal. The apparatus may further be configured to phase interpolate a clock signal based on the first phase interpolator control signal value to produce a phase shifted clock signal and digitally interpolate a digital sample based on the first digital interpolator signal value to produce a phase shifted digital sample having an effective phase based on the first phase control value, the digital sample generated using the phase shifted clock signal as a sample clock.

Systems and methods are disclosed for head delay calibration and tracking multi-sensor magnetic recording (MSMR) systems. In certain embodiments, an apparatus may comprise a first reader and a second reader configured to simultaneously read from a single track of a data storage medium, the first reader offset from the second reader so that the first reader and the second reader detect a same signal pattern offset in time. The apparatus may further comprise a circuit configured to determine a relative offset between the first reader and the second reader, including setting a fixed delay for a first signal from the first reader, setting a second delay for a second signal from the second reader, and adjusting the second delay to align the second signal to the first signal using a timing loop, with the first signal used as a reference signal.

Systems and methods are disclosed for full utilization of a data path's dynamic range. In certain embodiments, an apparatus may comprise a circuit including a first filter to digitally filter and output a first signal, a second filter to digitally filter and output a second signal, a summing node, and a first adaptation circuit. The summing node combine the first signal and the second signal to generate a combined signal at a summing node output. The first adaptation circuit may be configured to receive the combined signal, and filter the first signal and the second signal to set a dynamic amplitude range of the combined signal at the summing node output by modifying a first coefficient of the first filter and a second coefficient of the second filter based on the combined signal.

An apparatus may include a circuit configured to receive first and second samples of an underlying data from respective first and second sample periods and which correspond to respective first and second sensors, a phase control value may have first and second values during respective first and second sample periods. The phase control value may be a control value for a sample clock signal. The circuit may also determine a difference in the phase control value between the first value and the second value. The circuit may then digitally interpolate the first and second samples to produce a phase shifted first and second samples where the digital interpolation of at least one of the first and second samples mat be at least in part based on the difference in the phase control value to compensate for a phase misalignment between the first sample and the second sample.

A reception-side apparatus includes: M receive antennas; and a processor configured to execute a first process of acquiring a first signal received from a first transmission-side apparatus from among signals simultaneously received from the N transmission-side apparatuses by receive diversity processing, and acquiring first data by demodulating and decoding the first signal. In the case of N>M, the processor acquires, for each of all patterns of a combination of a first signal, second signals from M1 transmission-side apparatuses which are to be cancelled by receive diversity processing and third signals from NM transmission-side apparatuses which are not to be cancelled by the receive diversity processing, a power ratio of power of the first signal relative to total power of the second and third signals based on a predetermined weight and a channel estimate of each signal, and selects a combination with the largest power ratio from among all the patterns.

Systems and methods are disclosed for full utilization of a data path's dynamic range. In certain embodiments, an apparatus may comprise a circuit including a first filter to digitally filter and output a first signal, a second filter to digitally filter and output a second signal, a summing node, and a first adaptation circuit. The summing node combine the first signal and the second signal to generate a combined signal at a summing node output. The first adaptation circuit may be configured to receive the combined signal, and filter the first signal and the second signal to set a dynamic amplitude range of the combined signal at the summing node output by modifying a first coefficient of the first filter and a second coefficient of the second filter based on the combined signal.