# Low Complexity DSP for High Speed Optical Access Networking +
## 2 Experimental Setup  
Figure 1a illustrates the experimental setup and Figure 1b depicts the detailed architecture of the nonlinear equalizer. In the transmitter, an offline PAM-4 signal is generated after a 2-tap symbol-spaced digital pre-distortion and a Nyquist shaping with a roll-off factor of 0.45. The generated signal is loaded into a 16 GHz, 80 GS/s digital-to-analog convertor (DAC) with an output swing of approximately 250 mV. Without using any driver amplifier, a 10-G tunable transmitter assembly (TTA) consisting of a tunable laser operating at 1543.3 nm and a differentially driven InP Mach-Zehnder intensity modulator (MZM) with a bandwidth of approximately 11 GHz [8] is driven by the DAC output directly. Following the MZM, a tunable optical band-pass filter (OBPF) mimicking an optical multiplexer with a 3 dB bandwidth of approximately 40 GHz is adopted and its output is amplified by a booster Erbium-doped fiber amplifier (EDFA). The OBPF has a 2 nd order super Gaussian filtering profile. A variable optical attenuator (VOA) at the output of the  
EDFA optimized the launched optical power into the fiber link, thus, always providing the lowest BER. After transmission over an SMF link of up to 30 km, a combined optical receiver consisting of a VOA, a pre-amplifier EDFA, a 40-GHz bandwidth OBPF mimicking an optical de-multiplexer with identical configuration of the transmitter OBPF, and a 10-G p-i-n photodiode- transimpedance amplifier (PIN-TIA) is utilized to detect the received optical signal. The PIN-TIA has a bandwidth of roughly 11 GHz and its input power is adjusted and optimized by a prior VOA. The detected PAM-4 signal is then converted into a digital signal by analog to digital convertor (ADC) sampling at 80 GS/s and the following DSP is conducted offline. The detailed process of offline DSPs for the receiver is also presented in Figure 1. The clock recovery obtains the optimum sampling phase and then a re-sampler downsamples the signal into 2 samples per symbol. A following blind nonlinear feedforward and decision feedback equalizer (FFE/DFE), together with a noise suppression (NS) filter, is then adopted to combat both linear and nonlinear effects from the low-bandwidth components and fiber link. After symbol-to-bit mapping, the BER prior to forward error correction (FEC) is the result of a one-on-one comparison between the transmitted and the recovered bits. The adaptive nonlinear equalizer (NLE) is the core of the receiver DSP, which is indicated in Figure 1b. The proposed reconfigurable NLE has the capability to combat both linear and nonlinear distortions as well as to suppress the signal noise. The DSP is operated in a completely blind manner with zero overhead. As indicated in Figure 1b, the nonlinear equalizer consists of both a Volterra FFE, a DFE and an NS filter to recover the symbols. The cost function adopted for the optimization of the coefficients is the least mean square (LMS), which is expressed as:  
\[ \begin{array}{ll}\tilde{y}^{\prime}[k]=&\sum_{i=0,-1}^{M-1,N}\left(a_{ij}[k- i]-b_{j}\tilde{y}^{\prime}[k-j]\right)\\ &+\sum_{i=0,j=i}^{M-1}a_{ij}y[k-i]y[k-j]-\sum_{i=1,j=i+1}^{N}b_{ij}\tilde{y}^{ \prime}[k-i]\tilde{y}^{\prime}[k-j]\\ &-\sum_{h=1}^{H}p_{h}(y^{\prime}[k-h]-g^{\prime}[k-h])\end{array}  \tag{1}\]  
where \(M\), \(N\), and \(H\) are the FFE, DFE and NS filter orders, and \(y\) and \(y^{\prime}\) represent the FFE input and output, respectively. \(\tilde{y}^{\prime}\) is obtained from a hard decision of \(y^{\prime}\). Only linear and the 2 nd-order Volterra kernels are considered to maintain a low level of complexity. \(a_{i}(b_{j})\) and \(a_{ij}(b_{j})\) are the linear and nonlinear FFE (DFE) tap coefficients, respectively. \(p_{h}\) is the NS filter tap coefficient. The idea of the NS filter is to predict the noise of the current FFE output sample based on the past \(H\) noise samples and the predicted noise is then subtracted from the signal sample.