ITC/USA 2011 Conference Proceedings / The Forty-Seventh Annual International Telemetering Conference and Technical Exhibition / October 24-27, 2011 / Bally's Las Vegas, Las Vegas, Nevada / OFDM has become the preferred modulation format for a wide range of wireless networks including 802.11g, 802.16e (WiMAX) and 4G LTE. For multipath channels which are time-invariant during an OFDM symbol duration, near-optimal demodulation is achieved using the FFT followed by scalar equalization. However, demodulating OFDM on the doubly-spread channel remains a challenging problem, as time-variations within a symbol generate intercarrier interference. Furthermore, demodulation and channel estimation must be effectively combined with decoding of the LDPC code in the 4G-type system considered here. This paper presents a new Turbo Equalization (TEQ) decoder, detector and channel estimator for OFDM on the doubly-spread channel based on nonlinear programming. We combine the Penalty Gradient Projection TEQ with a MMSE-type channel estimator (PGP-TEQ) that is shown to yield a convergent algorithm. Simulation results are presented comparing conventional MMSE TEQ using the Sum Product Algorithm (MMSE-SPA-TEQ) with the new PGP-TEQ for doubly-spread channels.