# Low-Complexity Online Calibration for Large-Scale Multi-Beam Antennas  
[PERSON]  
1 School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China 11 School of Cyberspace Science and Technology, Beijing Institute of Technology, Beijing  
interrupted. FDMA systems employ another adjacent frequency to modulate the calibration signal so that the normal communication is ensured. This means that amplitude and phase characteristics are achieved for the adjacent frequency channel instead of the frequency to be calibrated. CDMA calibration schemes adopt spread spectrum technology to achieve parallel calibration [13; 14]. Each array element is simultaneously injected with a unique pseudo-random code spread spectrum signal. After passing channels with amplitude and phase errors, the calibration receiver uses the same pseudo-random code for correlation reception processing. Amplitude and phase errors are reflected on the peak value of the correlation peak. These CDMA calibration systems can measure the amplitude and phase characteristics of all channels in parallel, and the spread spectrum gain improves the calibration accuracy in white noise environment. The first German synthetic aperture radar satellite TerraSAR-X with 384 array modules was launched in 2007 [15]. The simultaneous characterization of all modules was realized based on orthogonal Walsh codes. However, the correlation operation of orthogonal Walsh codes involves a large amount of operations and the complexity of parallel signal processing is unbearable.  
A novel online calibration method for large-scale antennas is proposed in this paper. A set of spread spectrum signals for calibration is injected along with the normal traffic flow. The power of calibration signal is low enough to ensure the communication performance and the calibration process can be performed simultaneously without disturbing the normal traffic flow. Utilizing the particularity of the inverse matrix of the m-sequence, a decorrelation interference cancellation algorithm is implemented with low-complexity. Moreover, the calibration accuracy can benefit from the gain brought by spread spectrum. The calibration accuracy of the proposed method can break through the limitation of orthogonal codes in [14]. Meanwhile, the system complexity can be reduced by novel design of code-division calibration waveform.  
This paper is organized as follows. Section 2 provides the system model of online calibration and analyzes the impact of normal communication traffic on amplitude and phase mismatches. Section 3 proposes a low-complexity online calibration method and derives the calibration accuracy of the proposed method. Numerical simulation results are shown in Section 4 and implementation results are provided in Section 5. Conclusions are drawn in Section 6.  
Notations: The notation \(a_{i}\) denotes the \(i\)-th entry of the vector \(\mathbf{a}\). Notations \(\mathrm{E}[\cdot]\), \(\mathrm{V}[\cdot]\), and \((\cdot)^{\mathrm{T}}\) stand for expectation, variance, and conjugate Hermitian transpose operation, respectively. \(\mathbf{I}_{K}\) represents the \(K\times K\) identity matrix. Notations \(|\cdot|\) and \(\mathrm{arg}(\cdot)\) denote the norm and phase of a vector, respectively. Notation \(X\sim\mathcal{N}(a,b)\) characterizes a random variable of Gaussian distribution with expectation \(a\) and variance \(b\). Notations \(\chi^{2}(n)\) and \(\chi^{2}(n,\lambda)\) denote chi-square distribution and non-central chi-square distribution with degree of freedom \(n\) and non-central parameter \(\lambda\).