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This paper studies the problem of blind adaptive identification, which focuses on how to obtain the consistent estimation of channel characteristics when only the output signal of each transmission channel is available. To solve this problem, traditional algorithms usually construct a single-input-multiple-output system resorting to the technique of antenna array or time oversampling. However, they simply suppose that the noise of each channel is known a priori or balanced, which cannot always be satisfied in practice. Therefore, considering the practical situation where the noise of each transmission channel is both unknown and unbalanced, a bias-compensated recursive least-squares algorithm is proposed, which can estimate the unbalanced noises in real time and obtain the consistent estimation of channel characteristics. Simulation results illustrate the good performance of the proposed algorithm under different signal-to-noise-ratio conditions. KEYWORDS bias compensation, blind adaptive identification, recursive least squares, SIMO system INTRODUCTIONSystem identification is the technique of estimating system characteristics based on measured input-output data, which has been widely applied to the fields of signal processing, digital communications, industrial control, and so on. 1 However, in many practical cases such as acoustic dereverberation, wireless communications, and time delay estimation, the input is always unavailable. 2 Therefore, it is necessary to develop a blind method that can achieve system identification without the information of input data. The "blind" refers to the feature that the input signal is unavailable, and what we can obtain is only the output signal of transmission channels. 3 Sato 4 first proposed the concept of blind channel identification. Subsequently, many blind identification algorithms have been proposed, which have played an important role in many fields, particularly in the field of communications. 5-7 Blind identification is a technique that can estimate the characteristics of transmission channels only based on the output signal, and it can be regarded as the first step of blind equalization whose objective is to recover the input signal by only using the information of the output signal. 8 Earlier studies on blind channel identification mainly focus on the higher-order statistics (HOS) of the output signal since the second-order statistics (SOS) of the outputs do not contain sufficient information for blind identification when the communication channels are nonminimum-phase systems. 9 However, the methods based on HOS are sensitive to the amount of computation. If the number of data samples is large, the huge amount of computation will be time consuming. Therefore, the HOS-based algorithms cannot track the change of transmission channels in time. 3,8 On the other hand, when the number of available measurements is small, the HOS cannot achieve accurate computation. Meanwhile, the cost Int J Adapt Control Signal Process. 2018;32:301-315.wileyonlinelibrary.com/journal/acs

The problem of finite impulse response (FIR) filtering in errors-in-variables (EIV) system is studied. Due to the input noise, traditional recursive least-squares (RLS) algorithms are biased in EIV system. Most existing bias-compensated approaches are proposed in the case that both the input-output noises are white Gaussian random processes. However, taking account of the situation where the output is corrupted by coloured noise, there are rare existing algorithms work well. Two biascompensated RLS algorithms with acceptable computational complexity are proposed, which can obtain unbiased real-time filtering in non-stationary system when the input noise is white while the output noise is coloured. Under the assumption that the input signal is a coloured process, linear prediction technique is used to estimate the sample of the input signal. Exploiting the statistical properties of the cross-correlation function between the least-squares error and the forward/backward prediction error, the input noise variance can be estimated and the bias can be compensated. Simulation results illustrate the good performance of the proposed algorithms.