I. Introduction
Radio over fiber (RoF) links, which integrate optical and wireless transmission techniques, have been well studied for the past few decades, due to their intrinsic advantages including low insertion loss, large bandwidth, and immunity to electromagnetic interference (EMI) [1], [2]. The basic principle of a RoF link for microwave signal transmission is to convert a radio frequency (RF) or microwave signal into an optical signal and transmit it over an optical fiber to a remote location, where it is then converted back into an RF signal. Thanks to the ultrawide bandwidth and low loss of an optical fiber, a RoF link, compared with a coaxial cable link, has a much broader bandwidth and lower loss. On the other hand, a RoF link is essentially an analog system, which suffers from signal distortion due to system nonlinearities induced by various optical and electrical devices, such as lasers, modulators, and RF amplifiers. The methods to linearize a RoF link can be divided into two categories: analog linearization [3], [4], [5], [6] and digital linearization [7], [8], [9], [10]. Analog linearization can be implemented in the optical domain [3], [4] or the electrical domain [5], [6]. Compared with digital linearization, analog linearization is faster, but it cannot handle high-order nonlinearity and memory effects. Different from analog linearization, digital linearization is implemented at the baseband [7], [8], [9], [10]. In general, in a RoF link, digital linearization is implemented at the transmitter for the downlink and at the receiver for the uplink [9]. Digital predistortion (DPD) at a transmitter has been investigated intensively. In a DPD algorithm, a polynomial model is commonly used to model a nonlinear system. However, the coefficient estimation for the polynomial model tends to be numerically unstable due to the inversion of an ill-conditioned matrix. In [11], orthogonal polynomials for an input signal with uniform distribution were introduced to reduce numerical errors. However, the orthogonal polynomials proposed in [11] are not orthogonal for complex Gaussian distributed signals, such as orthogonal frequency division multiplexing (OFDM) signals widely used in current wireless communication systems. In [12], orthogonal polynomials for a complex Gaussian distributed signal were introduced, but they are limited to odd orders which can only handle in-band nonlinearity. On the other hand, due to the large bandwidth of a RoF link, it is desirable to transmit multiband signals to provide multiple services. For multiband signals transmitted over a nonlinear system, not only in-band but also interband nonlinearity is incurred. To linearize a nonlinear system transmitting multiband signals, multiband DPD techniques were proposed [13], but the approaches again suffer from numerical instability. Therefore, multivariate orthogonal polynomials were introduced to improve the numerical stability [14], [15]. Again, similar to the orthogonal polynomials proposed in [11], multivariate orthogonal polynomials can only be used for uniformly distributed signals. For multiband OFDM signals with complex Gaussian distribution, a new solution must be found.