Communication systems are often used for purposes for which they were not originally intended, which can place new, stringent requirements on legacy communication systems. In one example, a wireless local area network (WLAN) can be used to locate a device connected to the WLAN (e.g., determine the position of the device), when location was not originally intended for the WLAN. For instance, later versions of a protocol may support location services, while earlier versions of the protocol may not. Since precise location, such as sub-meter positioning, usually requires accurate timing estimates to determine time of flight for triangulation equations, timing requirements of devices connected to the WLAN can be more strict than originally intended for the devices.
Factors that previously could be ignored can prevent satisfying the stricter timing requirements needed for location services. For instance, in multi-carrier systems, such as WLAN's using orthogonal frequency division multiplexed (OFDM) signals, including the Institute of Electrical and Electronics Engineers (IEEE) 802.11 family of protocols (e.g., see www.standardsieee.org), timing requirements for earlier protocol versions could usually be met by positioning a fast Fourier transform (FFT) window according to a phase roll common across all subcarriers caused by a group delay independent of frequency. The frequency-independent group delay may be introduced by filters having a linear phase response. Even if the positioning of the FFT window were off by a few samples, a guard interval, such as including a cyclic prefix, prevented inter-symbol interference, so that the positioning was sufficiently good to decode data packets, meeting the original purposes intended by the system. However, for later protocol versions that support location services, positioning the FFT window incorrectly, such as off by a few samples, can introduce timing errors sufficient to prevent acceptable sub-meter location.
Furthermore, group delay introduced by filters in the analog front end of a device in practice is frequency dependent, rather than frequency independent. The frequency dependent group delay can be caused by a non-linear phase response, such as the phase response of infinite-impulse response (IIR) filters, higher-order filters (e.g., 3rd-order or higher Chebyshev analog filters), non-linear circuits such as limiters and analog-to-digital converters, combinations thereof, and the like. Traditionally, such non-linearities are ignored in deriving timing parameters, such as FFT window position, in OFDM communication systems. Errors in timing estimates resulting from the frequency-dependent group delays of non-linear phase responses, however, can introduce timing errors sufficient to prevent acceptable sub-meter location. To exacerbate this problem, the non-linearities are usually device-specific (e.g., different devices exhibit different non-linearities), making generic solutions unacceptable. Moreover, when combining separate delay values, such as from different training fields that use different subcarriers to form a single delay value to position an FFT window, the non-linear phase responses introduce different delays at different frequencies and thus can result in an unacceptable combination.