(Color online) Auto-ambiguity function (AAF) of the 7 bit m-sequence. (a) The image plot of the AAF; (b) the Doppler profile; (c) the delay profile.
(Color online) Delay-Doppler spread function estimations. (a) Image plot of estimate of channel I using the cross-ambiguity function (CAF); (b) contour plot of estimate of channel I using the FPGM; (c) image plot of estimate of channel II using the CAF; (d) contour plot of estimate of channel II using the FPGM.
Mesh plots of the delay-Doppler spread function estimations. (a) The CAF method; (b) the proposed FPGM with ɛ = 5; (c) FPGM with ɛ = 20; (d) FPGM with ɛ = 50.
The convergence rates of the FPGM and the Daubechies’ method.
Scatter plots of the outputs of the linear MMSE equalizer at SNR = 12 dB using different channel estimates. (a) True channel information; (b) FPGM; (c) OMP; (d) MP.
Symbol error rates (SER) versus SNR of the linear MMSE equalizer using the true channel state information and three different channel estimation schemes.
Acoustic ray paths of an underwater multipath channel.
(Color online) True impulse response of the underwater multipath channel obtained by the geometric structure of the transmitter and receiver. (a) The 2-D time-varying response h(τ, t) in the time interval t [0,2] s; (b) the channel response at t = 2 s. The paths are labeled as D (direct arrival), B (bottom scattered arrival), S (surface scattered arrival), BS (bottom then surface), SB (surface then bottom), BSB (bottom-surface-bottom), SBS, BSBS, SBSB, and BSBSB.
(Color online) Delay-Doppler spread function estimates of the doubly spread underwater channel. (a) Conventional CAF method; (b) the proposed FPGM with ɛ = 5; (c) FPGM with ɛ = 10; (d) the OMP algorithm.
(Color online) Delay-Doppler spread function estimates of Kauai experimen tal data by the CAF and FPGM with different signal length.
Complex-valued projected gradient method.
Time delays (ms) and Doppler shifts (Hz) of channel I and II.
Multipath time delays, Doppler shifts, and amplitudes of the simulated channel.
Running times (in seconds) of the proposed FPGM and CVX.
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