References 59 for n = 1, . . . , N AR and k = -K AR , . . . , K AR . These "TF Yule­Walker equations" constitute a system ~ of N AR (2K AR + 1) linear equations in the N AR (2K AR + 1) TFAR parameter matrices A[ n, k]. For a correlation-underspread channel (see Section 1.5.2), the phase factor e j2 n ( k - k)/N in (1.89) can be approximated by 1. With this approximation, the TF Yule­Walker equations exhibit a two-level block-Toeplitz structure and can hence be solved efficiently by means of a vector version of the Wax- Kailath algorithm (Wax & Kailath, 1983) (see Jachan & Matz, 2005; Jachan et al., 2009 for algorithmic details). ~ For a practical estimator of the TFAR parameter matrices A[ n, k], the expected matrix ambigu- ¯ ity function A[ n, k] is replaced by a sample estimate that is obtained by dropping the expectation in ^ ~ ^ (1.88) and substituting an estimate h[n] for h[n]. The resulting TFAR parameter estimates A[ n, k] can finally be used to compute an estimate of the LSF, based on an LSF expression that is similar in spirit to (1.86) (Jachan & Matz, 2005; Jachan et al., 2009). 1.8 CONCLUSION In this chapter, we provided a survey of many of the concepts and tools that have been developed during the past six decades for characterizing, modeling, and measuring time-frequency dispersive channels.