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Quantum dot semiconductor optical amplifiers (QD-SOA) characteristics are analyzed by rate equations governing carrier dynamics in ground, excited, and upper continuum states and wetting layer. In this paper, using transfer matrix method, we analyze the picosecond pulse propagation in QD-SOA, considering cross gain modulation and gain saturation nonlinear effects. The effects of various parameters, including bias current and inhomogeneous broadening on pulse propagation, are researched. It is shown that for bias current densities beyond 8 kA/cm2, distortion-free pulse amplification can be achieved for input powers up to 80 mW. Lower inhomogeneous broadening leads to higher gain at central frequencies. In addition, our simulation procedure is capable of including co and counter multiwavelength signals. The simulation algorithm can handle various schemes of signal propagation in QD-SOA in reasonable simulation time, a fact that is extremely precious, especially in multiwavelength counter propagation, considering the numerous and lengthy equations that must be considered. In counter propagation, output shapes of signals are shown to be completely different from those of copropagation. The underlying reason for the differences is thoroughly researched.