## 1 Introduction
In [7], the lower bound on the secrecy capacity of artificial noise wireless communication systems subject to transmit power is proposed. Ref. [8] proposes the secrecy capacity expression with imperfect channel estimation. This expression is non-convex, so the gradient descent method cannot be used for this optimization problem. Therefore, it is impossible to get the optimal solution of the secrecy capacity expression. The study in [9, 10, 11, 12] consider the effects of active eavesdropper. The active eavesdropper can interfere with pilot to reduce the secrecy capacity of the wire-tap system. This is something that hasn't been explored in previous studies. The past research on AN is summarized into two main aspects:  
1. Research on AN noise technology under different communication modes [13, 14, 15, 16, 17, 18, 19, 20, 21]; examples include the AN power allocation problem in OFDM, GSM, and other communication modes [22] and the application of AN under intelligent reflecting surface [23]. The simplified communication model is \(Y=HX+e\), where \(Y\) denotes the received signal, \(H\) denotes the channel, \(X\) denotes the transmitted signal, and \(e\) is the noise. The above researches focus on \"\(H\)\". 2. Reshaping certain features of AN. For example, Ref. [24] designs an artificial noise that has interference alignment characteristics. The research focused on \"\(X\)\" from the equation above [25, 26, 27, 28]. Still, there has been little to no research attention on redesigning the core of AN. Therefore, our research focus on creating a new kind of AN. Our research shows that our new artificial noise has a better performance compared to its traditional counterpart. In [29], the secrecy capacity optimization artificial noise (SCO\(-\)AN) is proposed. The core of AN technology is to design a noise in the null space of the channel state information space. Unlike the traditional AN, which ignores the range space of the channel state information space, SCO\(-\)AN is located in that range space. While SCO\(-\)AN may slightly impact the channel capacity of the legitimate receiver, SCO\(-\)AN significantly reduces the channel capacity of the eavesdropper. Therefore, this method still increases the difference between the legitimate channel capacity and the eavesdropping channel capacity. SCO\(-\)AN is a tool to convert the noise immunity of communication systems into secrecy capacity. As there is a limitation in the transmission power, it is critical to draw an optimization problem to maximize the secrecy capacity under that limitation. The power allocation problem becomes essential. Therefore, in this paper, we study the power allocation problem of SCO\(-\)AN. The Hessian matrix of the SCO\(-\)AN power allocation objective function is not positive definite, which means the objective function is non-convex. The maximum value of the SCO\(-\)AN power allocation function cannot be obtained by the gradient descent method. An improved sequential quadratic programming (ISQP) is proposed to solve this problem. With the effects of imperfect channel estimation considered, the objective power allocation function containing imperfect channel estimation parameters is constructed. The main contributions of this paper are summarized as follows:  
1. In reality, the secrecy capacity of a wireless communication system using SCO\(-\)AN is limited by transmission power. Considering this limitation, this paper constructs a power distribution function for SCO\(-\)AN and the information-bearing signal. 2. Since the power allocation objective function is non-convex, it is difficult to optimize the power distribution function using a power optimization scheme based on gradient descent. ISQP is then proposed to allocate power between SCO\(-\)AN and the information-bearing signal. ISQP improves the traditional iterative algorithm and reduces the computational complexity by simplifying the initial iterative matrix and improving computational efficiency. 3.