Timing misalignment estimation

• US 20020176354A1
• Filed: 03/08/2001
• Published: 11/28/2002
• Est. Priority Date: 03/08/2001
• Status: Active Grant

• Current Assignee: Google LLC (Alphabet Inc.)
• Original Assignee: Proxim Wireless Corporation
• Inventors: Chiodini, Alain
• Granted Patent: US 6,950,483 B2
• Time in Patent Office: Days
• US Class Current: 370/208
• CPC Class Codes: H04L 27/2662 Symbol synchronisation
• CPC Class Codes: H04L 27/2675 Pilot or known symbols

Abstract

Orthogonal frequency division multiplexing (OFDM) receiver embodiments of the invention provide timing misalignment estimation by calculating the intra-baud timing differential. The preferred method exploits the spectral structure of the short-preamble in that a time delay in the time-domain is manifest as a phase rotation in the frequency-domain. The timing misalignment is determined by special processing the spectral peaks of the modified short-preamble. An alternative embodiment linearly combines the two long-preamble symbols to construct a single “best estimate” long-preamble symbol. A normalized dot product of the “best estimate” long-preamble symbol and the ideal on-baud symbol is computed to obtain the magnitude of the timing misalignment. A dot product between the “best estimate” long-preamble symbol and the time derivative of the ideal on-baud sampled sequence is computed to obtain the sign of the timing misalignment.

Claims

1. A method for timing misalignment determination in a radio receiver, comprising the steps of:

estimating and correcting a frequency offset and establishing a time reference wherein the boundary between the short- and long-preamble is sufficient;

constructing a real signal from a complex time-domain signal associated with said short preamble;

extracting an n-sample sequence from a portion of said short preamble to obtain a plurality of equidistant equal amplitude frequency peaks; and

determining a timing offset estimate by inspecting the relative phases of said plurality of equidistant equal amplitude frequency peaks;

wherein, data encoded in said received radio signal may thereafter be demodulated.

2. The method of claim 1, wherein:

the step of constructing includes in-phase and quadrature-phase sampling of said received radio signal to obtain a real part and an imaginary part;

wherein real and imaginary parts are similar to one another except for a fixed time-skew between them.

3. The method of claim 2, wherein:

the step of constructing includes a simple addition of said real and imaginary parts to obtain said real signal.

4. The method of claim 1, wherein:

the step of determining is such that phase of a set of three frequency peaks Φ

₁, Φ

₂ and Φ

₃ is assumed to vary with timing misalignment between Δ

(t) and δ

(t), and an intra-baud timing offset τ

can be derived from Φ

₁, Φ

₂ and Φ

₃ wherein, a received signal can be represented by,

Ψ

(t)=Φ

₁(t)+2Φ

₂(t)+Φ

₃(t)

$\begin{array}{c}\mathrm{\Psi <br><br>}<br><br>\left(t\right)=\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\Phi <br><br>}}_1<br><br>\left(t\right)+2<br><br>{\mathrm{\Phi <br><br>}}_2<br><br>\left(t\right)+{\mathrm{\Phi <br><br>}}_3<br><br>\left(t\right)\\ =\text{\hspace{1em}<br><br>}<br><br>\frac{\mathrm{\pi <br><br>}}{4}<br><br>\left(1+\frac{t}{T_s}\right)+2<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{\mathrm{\pi <br><br>}}{4}<br><br>\left(1+2<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{t}{T_s}\right)+\frac{3<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\pi <br><br>}}{4}<br><br>\left(-1+\frac{t}{T_s}\right)\\ =\text{\hspace{1em}<br><br>}<br><br>2<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{t}{T_s}\end{array}$

and, Ψ

=(X₈P₁)(X₁₆P₂)²(X₂₄P₃), where X_k and P_n respectively designate 64-point fast Fourier transform frequency components and the phase correcting coefficients needed compensate for phase offset errors cause by a misalignment between Δ

(t) and δ

(t), and the timing misalignment τ

is expressed as a fraction of T_s, and is

$\mathrm{\tau <br><br>}=\frac{\mathrm{\Psi <br><br>}}{\mathrm{\pi <br><br>}}.$

5. The method of claim 1, wherein:

the step of determining computes a 64-point fast Fourier transform rather than a three-point discrete Fourier transform.

6. A method for timing misalignment determination in a radio receiver, comprising the steps of:

determining a boundary between a short preamble and a long preamble in a received radio signal;

linearly combining samples of two long sequences from said long preamble to obtain an idealized sequence of samples that best approaches under a certain criterion an ideal sequence of samples;

computing a normalized dot product of said idealized sequence of samples and an ideal on-baud sampled sequence to obtain a magnitude estimate of any timing misalignment; and

computing a dot product of said idealized sequence of samples and the time derivative of the ideal on-baud sampled sequence mentioned above to obtain a sign of any timing misalignment;

wherein, data encoded in said received radio signal may thereafter be corrected for timing misalignment and then demodulated.

7. The method of claim 6, wherein the steps of linearly combining and computing can use cost function can be used, and mathematically described by,

8. The method of claim 7, wherein the steps of linearly combining and computing assume that {right arrow over (N)}₁^H{right arrow over (N)}₂={right arrow over (N)}₁^H{right arrow over (X)}₂={right arrow over (N)}₂^H{right arrow over (X)}₁={right arrow over (N)}₁^H{right arrow over (R)}={right arrow over (N)}₂^H{right arrow over (R)}=0, although such is not exactly true in reality, and thereby reduces computer processing required;

and continuing with,

9. The method of claim 8, wherein the steps of linearly combining and computing produce an Γ

(ν

) that is real and much greater than |R_on(0)|², and the result is

10. The method of claim 9, wherein the steps of linearly combining and computing find {right arrow over (Z)}, and determine the absolute value and sign of the timing misalignment by computing dot products, as in,