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Multicarrier code division multiple access (MCCDMA) systems using complex-quadratic spreading sequences and cyclic delay diversity (CDD) facilitate frequency or time domain chip combining to mitigate different types of jamming. In this paper, multiple-input multiple-output (MIMO) channel coefficients, jamming power, and jammer state information (JSI) are jointly estimated to suppress the adverse effects of partial-band noise jamming. We derive weighted least square error (LSE) and linear minimum mean square error (MMSE) channel estimators operating under jamming and investigate the constraints on the cyclic delays. The JSI for the pilot symbols is estimated to assist estimation of the time-varying frequency selective channel coefficients by updating the noise covariance matrix. We also derive the optimum (sufficient statistics) chip combining weights for the data symbols that require the JSI; hence, the JSI for the data symbols is iteratively estimated using the decoder output. Simulation results demonstrate that the proposed iterative despreading (includes JSI estimation and chip combining), demapping, and decoding receiver with soft- JSI-assisted channel estimation and chip combining is very robust against partial-band noise jamming.