Systems and methods for frequency domain realization of non-integer fractionally spaced time domain equalization
View Patent ↗Various systems and methods are described for performing fractionally spaced time domain equalization (TEQ). One embodiment is a method implemented in a communication system for training a fractionally spaced time domain equalizer (TEQ). The method comprises performing an initialization phase, averaging a received signal in the system to reduce effects of noise in a channel, determining a channel estimate, and aligning an ideal reference signal with the received signal. The method further comprises updating a target response filter according to a non-integer multiple of a base sampling rate, determining an adaptation error based on useful information both inside and outside a Nyquist band of the TEQ, and updating the TEQ according to the adaptation error.
1. A method for training a time domain equalizer (TEQ) in the frequency domain, comprising:
setting a sampling rate of the TEQ according to a base sampling rate multiplied by an oversampling factor F 0 , wherein the oversampling factor F 0 is a non-integer value greater than 1 and less than 2; and
determining a difference between a desired frequency domain signal and an actual frequency domain signal,
wherein the actual frequency domain signal is determined according to a received frequency domain signal convolved with a frequency response of the TEQ, where both the received frequency domain signal and the frequency response of the TEQ are constructed from time domain signals sampled at a rate equal to F 0 times the base sampling rate.
2. The method of claim 1 , wherein F 0 is defined according to a first integer L and a second integer M such that F 0 is defined according to L/M.
3. The method of claim 2 , wherein L=3 and M=2.
4. The method of claim 1 , wherein the desired frequency domain signal is determined according a transmit frequency domain signal convolved with a target frequency response.
5. The method of claim 4 , wherein the target frequency response is determined according to a time domain signal constrained to a specific number of non-zero samples at the base sampling rate.
6. A method implemented in a communication system for training a fractionally spaced time domain equalizer (TEQ), comprising:
performing an initialization phase;
averaging a received signal in the system to reduce effects of noise in a channel;
determining a channel estimate;
aligning an ideal reference signal with the received signal;
updating a target response filter according to a non-integer multiple of a base sampling rate;
determining an adaptation error based on useful information both inside and outside a Nyquist band of the TEQ; and
updating the TEQ according to the adaptation error.
7. The method of claim 6 , wherein the target response filter and the TEQ are limited to corresponding windows, each window having a fixed numbers of non-zero samples.
8. The method of claim 7 , wherein the corresponding windows have different fixed numbers of non-zero samples.
9. The method of claim 6 , wherein the received signal comprises a substantially periodic signal.
10. The method of claim 9 , wherein the communication system comprises a digital subscriber line (xDSL) system, and wherein the periodic signal comprises REVERB symbols.
11. The method of claim 6 , wherein the target response filter is limited to a predetermined number of non-zero samples at the base sampling rate.
12. The method of claim 6 , further comprising setting a sampling rate of the TEQ according to a base sampling rate and an oversampling factor F 0 , wherein the oversampling factor F 0 is greater than 1.
13. The method of claim 12 , wherein the oversampling factor F 0 is 3/2.
14. The method of claim 6 , wherein the steps of updating a target response filter, determining an adaptation error, and updating the TEQ are performed according to a least mean squares (LMS) algorithm.
15. The method of claim 14 , wherein performing an initialization phase comprises:
setting an initial step size associated with the LMS algorithm; and setting a maximum iterations.
16. The method of claim 6 , wherein the steps of updating a target response filter, determining an adaptation error, and updating the TEQ are performed a number of iterations less than or equal to the maximum iterations.
17. The method of claim 6 , wherein the non-integer multiple of a base sampling rate is 3/2.
18. A system for training a fractionally spaced time domain equalizer (TEQ), comprising:
logic for setting a sampling rate of the TEQ according to a base sampling rate and an oversampling factor F 0 , wherein the oversampling factor F 0 is between a value of 1 and 2;
logic for determining a convergence rate and maximum number of iterations for a least mean square (LMS) process for adjusting the TEQ; logic for averaging a received signal in the system to reduce effects of noise in a channel;
logic for determining a channel estimate;
logic for aligning an ideal reference signal with the received signal;
logic for updating a target response filter according to a non-integer multiple of the base sampling rate;
logic for determining an adaptation error based on useful information both inside and outside a Nyquist band of the TEQ; and
logic for updating the TEQ according to the adaptation error.
19. The system of claim 18 , wherein the oversampling factor F 0 is 3/2.
20. The system of claim 18 , wherein logic for aligning an ideal reference signal with the received signal comprises logic for performing a circular shift in the time domain on the averaged received signal based on a delay.
21. The system of claim 20 , wherein the delay is determined based on a peak location in the channel estimate in the time domain.
22. The system of claim 20 , wherein the delay is determined based on energy in a window of the channel estimate.