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Secrecy transmission is investigated for a cooperative jamming scheme, where a multi-antenna jam-mer generates artificial noise (AN) to confuse eavesdroppers. Two kinds of eavesdroppers are considered: passive eavesdroppers who only overhear the legitimate information, and active eavesdroppers who not only overhear the legitimate information but also jam the legitimate signal. Existing works only treat the passive and active eavesdroppers separately. Different from the existing works, we investigate the achievable secrecy rate in presence of both active and passive eavesdroppers. For the considered system model, we assume that the instantaneous channel state information (CSI) of the active eavesdroppers is available at the jammer, while only partial CSI of the passive eavesdroppers is available at the jammer. A new zero-forcing beamforming scheme is proposed in the presence of both active and passive eavesdroppers. For both the perfect and imperfect CSI cases, the total transmission power allocation between the information and AN signals is optimized to maximize the achievable secrecy rate. Numerical results show that imperfect CSI between the jammer and the legitimate receiver will do more harm to the achievable secrecy rate than imperfect CSI between the jammer and the active eavesdropper.