Inverse QR Decomposition (IQRD) Blind Equalizer for QAM Coherent Optical Systems Amr Ragheb 1,3 , Mobien Shoaib 3 , Saleh Alshebeili 1,2,3 , and Habib Fathallah 1,2 1 Electrical Engineering Dept. 2 KACST-Technology Innovation Center in Radio Frequency and Photonics (RFTONICS) 3 Prince Sultan Advanced Technologies Research Institute (PSATRI) King Saud University Abstract—Advanced digital signal processing techniques have a vital role in the development of emerging and next generation ultrahigh speed optical networks. These techniques highly contribute to the improvement of system spectral efficiency. Blind equalizers have recently been used to compensate for linear fiber impairments. In this paper we apply the inverse QR decomposition (IQRD), algorithm for blind equalization in 14Gbaud-16QAM coherent receiver. IQRD is widely used in wireless communications and known for its inherent stability in finite precision environment. We compare its performance with the standard Constant Modulus Algorithm (CMA) and Recursive Least Squares (RLS) algorithm in terms of convergence rate (CR) and bit error rate (BER). Our simulation results show that IQRD algorithm achieves similar CR and BER performance as those of standard RLS algorithm. However, in finite precision environment, which is more appropriate for practical implementation, and results in lower system power consumption (human friendly or Green solution), IQRD completely outperforms the RLS technique. A substantial reduction in BER of two orders of magnitude at 14 bit resolution is achieved for the optical system under consideration. Index terms— Coherent detection, Finite impulse response (FIR) filters, Recursive least squares (RLS), inverse QR decomposition (IQRD). I. INTRODUCTION During the last 20 years the world traffic has increased 10,000 times at a rate of 0.2dB per year. The exponential scaling in data rates will cause the world traffic to reach thousands and thousands of Exabyte by the end of 2020. Emerging optical transmission systems are coherent involving multilevel modulation, such as M-ary quadrature amplitude modulation (MQAM), polarization division multiplexing (PDM) and robust digital signal processing (DSP) techniques. This considered as one of the pioneer solutions to increase the spectral efficiency and to achieve the tremendous increase in data rates of the optical communication system. Numerous modulation formats have recently been introduced in the literature in order to enhance the system performance. For example, IEEE P802.3ba standard has recently adopted QPSK with polarization multiplexing (PolMux) for 100 Gbps traffic. Using two polarizations and M = 4 symbols (i.e. 2bits/symbol/pol.), only 25GHz bandwidth is needed to carry 100Gbps rate. In next generation systems, per wavelength data rate is expected to achieve 400 Gbps and 1Tbps [1]. Research community is still investigating different possible modulation schemes for these targeted data rates [2]. Unfortunately, the performance of ultrahigh speed systems suffers due to challenges faced at either the optical transmitter and receiver or the fiber channel. In this work, we focus the study on the behavior of the optical coherent receiver under the effect of fiber channel impairments. There are two categories of linear impairments in the fiber channel. The first is independent of polarization mainly including chromatic dispersion (CD). This causes system Inter-Symbol Interference (ISI) [3]. The second is polarization dependent which originates from optical polarization mode dispersion (PMD) and polarization dependent loss (PDL). This category causes pulse broadening, rotation of the principle state of polarization (PSPs) in the fiber, and polarization dependent optical power fluctuations Different solutions have been proposed in the literature to combat the linear fiber impairments. Digital finite impulse response (FIR) filters have been used to diminish the effect of CD. 3.7 taps per 1000ps/nm have been used to compensate CD at 10.7Gbaud QPSK transmission [4]. However, the residual effect of CD still remains noticeable. Fractionally spaced equalizer (FSE) [5] with MIMO structure was proposed to not only compensate for the residual CD but also for the PMD. The well-known types of adaptive equalizers used in optical coherent receivers include the constant modulus algorithm (CMA), direct-detection least mean squares (DD-LMS) algorithm [4], and the recursive least squares (RLS) algorithm[6]. These equalizers update their weights blindly, without training sequence, which in turn increases the system spectral efficiency. Fig. 1 shows the block diagram of the compensation system, where the input signal x in is first compensated from the CD effect using FIR filter. Then, the compensated signal x p is passed through the blind equalizer in order to remove the residual CD distortion and get the estimated signal x out . Fig. 1 Impairments compensation diagram