High-order Quadrature Amplitude Modulation Signals Research Articles

23.1-Gb/s 135-GHz Wireless Transmission Over 4.6-Km and Effect of Rain Attenuation

In this article, we have experimentally demonstrated a fiber-wireless-integration <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$D$</tex-math> </inline-formula> -band (110–170 GHz) transmission system. To extend the wireless transmission distance while maintaining the wireless bit rate as high as possible, we designed high-gain lens horn antenna modules consisting of a pair of dielectric plano-convex lenses and horn antennas for long-haul wireless links. In addition, we employ the Volterra nonlinear equalization (VNE) algorithm based on the multiple-input–multiple-output (MIMO) structure to precisely compensate for the in-phase/quadrature (I/Q) imbalance and nonlinear impairment of quadrature amplitude modulation (QAM) signals mainly caused by photoelectric (O-E) conversion and electric-photo (E-O) conversion. Meanwhile, one of the methods adopted in our experiment to decrease the influence of nonlinearity on high-order QAM signals is coupling the high-order modulation format with the probabilistic shaping (PS) technology. As a result of outdoor field experimental verification, the demonstration at 135 GHz carrier with a net rate of 23.1 Gb/s over 10 km optic-fiber and 4.6 km wireless transmission distance has been successfully carried out. It is, as we know, the first time that a record-breaking product of net bit rate and wireless transmission distance, i.e., 23.1 Gb/s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> 4.6 km <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$=$</tex-math> </inline-formula> 106.3 Gb/s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\cdot$</tex-math> </inline-formula> km, has been accomplished based on a fiber-wireless-integration system. Also, for the first time, we have measured the effect of rain attenuation for the 135 GHz millimeter-wave (mm-wave) wireless link and established more accurate rainfall models for the Shanghai region of China by comparing them with multiple rainfall models. This work can be used as a complement to the International Telecommunication Union-Radiocommunication sector (ITU-R) recommendations.

High Order QAM Modulation in Massive MIMO Systems With Asymmetrically Quantized 1-Bit ADCs

Deploying 1-bit analog-to-digital converters (ADCs) in massive multiple-input multiple-output (MIMO) systems is promising to reduce the energy consumption. However, serious quantization errors limit the feasibility of high order quadrature amplitude modulation (QAM). This paper focuses on the performance analysis of 1-bit ADC massive MIMO systems with high order QAM. Firstly, we theoretically analyze the relationship between the quantization error and various quantization parameters. We reveal that there exists an overlapping of constellations at high signal to noise ratio (SNR) with symmetric quantization. This is because the amplitude information in the detected signal at high SNR is lost which is multiplied by the zero quantization threshold in the symmetric quantization. To overcome this problem, asymmetric quantization should be considered. Based on the analysis of the quantization error, we propose two approaches to recover the amplitude information. One is a near unbiased detection (NUD) by scaling the traditional linear detector and optimizing the quantization threshold. The other is a sub-array detection based on non-uniform quantization (SAD-NQ) to correct the deviation of the detection result by averaging over sub-arrays. Simulation results show that the proposed approaches can significantly improve the detection performance of high order QAM signal in the 1-bit ADC massive MIMO systems.

4096-QAM OFDM THz-Over-Fiber MIMO Transmission Using Delta-Sigma Modulation

A terahertz (THz)-over-fiber multiple-input multiple-output (MIMO) transmission of 4096-ary quadrature amplitude modulation (QAM) orthogonal frequency division multiplexing (OFDM) supported by 46-GBaud quadrature phase shift keying (QPSK) signal at 320 GHz is experimentally demonstrated in this letter. By employing the polarization division multiplexing (PDM) technique and 1-bit delta-sigma modulation (DSM) quantization, we successfully implement 4.6-GHz 4096-QAM OFDM signal transmission over 20 km of standard single-mode fiber (SSMF) and a 3-m MIMO wireless link, and satisfy the soft-decision forward error correction (SD-FEC) threshold of 1.0 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> with 15% overhead, which corresponds to a net rate of 84.4 Gbps for THz-over-fiber transmission. To the best of our knowledge, fusing OFDM and PDM, this is the highest rate achievable for DSM applications in THz communication. This experimental demonstration can provide a promising solution for high-order QAM signals in a fiber-wireless seamless network in future 6G networks.

Adaptive blind equalization for multi‐level QAM signals in impulsive noise environment

A maximum correntropy criterion-blind clustering multi-modulus algorithm (MCC-BCMMA) is proposed to equalize multi-level quadrature amplitude modulation (QAM) channels in impulsive noise environment. The novel cost function is based on the maximum correntropy criterion (MCC), theoretical analysis shows that this criterion is useful when the noise is impulsive. Moreover, this cost function is decomposed into in-phase term and orthogonal term to eliminate the phase ambiguity, treats high-order QAM signal to classical QAM4 signal to reduce the error, and calculates the weight coefficients by a simple way. Simulation results show that the newly proposed algorithm MCC-BCMMA can be used to equalize multi-level QAM signals in both Gaussian and impulsive noise environments, and it shows better equalization performance under impulsive noise. The relationship between the kernel size of MCC, the convergence speed and accuracy is also analysed.

Optimized blind equalization for probabilistically shaped high-order QAM signals

Probabilistically shaped (PS) high-order quadrature amplitude modulation (QAM) signals are attractive to coherent optical communication due to increased spectral efficiency. However, standard digital signal processing algorithms are not optimal to demodulate PS high-order QAM signals. Therefore, a compromise equalization is indispensable to compensate the residual distortion. Meanwhile, the performance of conventional blind equalization highly depends on the accurate amplitude radius and distribution of the signals. The PS high-order QAM signals make the issue worsen because of indistinct amplitude distributions. In this work, we proposed an optimized blind equalization by utilizing a peak-density K-means clustering algorithm to accurately track the amplitude radius and distribution. We experimentally demonstrated the proposed method in a PS 256-QAM coherent optical transmission system and achieved approximately 1 dB optical signal-to-noise ratio improvement at the bit error rate of 1×10-3.

QAM–OFDM transmission in underwater wireless optical communication system with limited resolution DAC

Underwater wireless optical communication (UWOC) can realize high speed, low delay and flexible information transmission. We experimentally demonstrate a 3-m UWOC system using blue laser diode and avalanche photodiode with quadrature amplitude modulation (QAM) and orthogonal frequency division multiplexing (OFDM) transmission. We achieve net bit rates of 6.23 Gb/s at a bit error rate (BER) of 1.55 × 10−3, by using 128-QAM OFDM signals. High-order QAM signals require higher bit resolution of digital-to-analog converter (DAC). Therefore, the effect of quantization noise on transmission performance is further investigated. In order to meet the requirement that the BER is lower than 3.8 × 10−3, the bit resolution of DAC is required to be at least 5, 6 and 7 bit for 32-QAM, 64-QAM and 128-QAM signals, respectively.

Convolutional-Neural-Network-Based Detection Algorithm for Uplink Multiuser Massive MIMO Systems

In the coming 6th generation (6G) and beyond in wireless communication, an increasing number of ultrascale intelligent factors, including mobile robot users and smart cars, will result in interference exploitation. The management of this exploitation will be a great challenge for detection algorithms in uplink massive multiple-input and multiple-output (MIMO) systems, especially for high-order quadrature amplitude modulation (QAM) signals. Artificial intelligence technology employing machine learning is one of the key approaches among the 6G technical solutions. In this paper, a convolutional-neural-network-based likelihood ascent search (CNNLAS) detection algorithm is proposed on the basis of a graphical detection model for uplink multiuser massive MIMO systems. Compared with other algorithms, the proposed CNNLAS detection algorithm has a stronger robustness against the channel estimation errors, and requires lower average received signal-to-noise ratios to obtain better bit error rate performance and to achieve the theoretical spectral efficiency with a lower polynomial average per symbol computational complexity, both for the graphical low-order and high-order QAM signals in uplink multiuser massive MIMO systems.

SVR Based Blind Signal Recovery for Convolutive MIMO Systems With High-Order QAM Signals

This paper addresses the blind signal recovery for convolutive multiple-input multiple-output systems with high-order quadrature amplitude modulation (QAM) signals. First, a family of batch blind recovery algorithms is proposed. Concretely, they introduce the error function of multimodulus algorithm and the cross-correlation among different equalizer output vectors into the penalty term of the support vector regression (SVR) framework to recover all sources simultaneously. Then, the corresponding dual-mode blind recovery schemes are constructed to further decrease the interference. The new blind formulation through iterative re-weighted least square achieves low complexity optimization. The SVR framework, in essence, determines that the proposals perform better than the conventional methods in terms of data block size, total interference, and symbol error rate. Moreover, the excellent initialization provided by the first mode and the accurate error expression in the second mode ensure that the SVR-based dual-mode schemes work well with the high-order QAM signals. Finally, the efficiency of the proposals over the classical approaches is evaluated by simulations.

Semidefinite further relaxation on likelihood ascent search detection algorithm for high‐order modulation in massive MIMO system

Recent studies have shown that existing detection algorithms are not suitable for high-order quadrature amplitude modulation (QAM) in massive MIMO system. In this paper, with an equivalent objective function by QR decomposition and further relaxation on the constrains, the authors develop an improved semidefinite further relaxation detector (SFRD), which is proved to be convex and has solutions within polynomial complexity time. Using the detection result from the proposed SFRD as the initial vector, they propose a novel semidefinite further relaxation on the likelihood ascent search (SFRLAS) detection algorithm. It has been shown through their studies that the proposed SFRLAS scheme can effectively approach the optimum bit error rate from the maximum-likelihood detection algorithm for systems with high-order QAM and large-scale antennas, however, with a lower computational complexity. The spectral efficiency converges to the theoretical value at a much lower required average received signal-to-noise ratio. It is an effective method for high-order QAM signal detection in massive MIMO system.

Low-Complexity Hybrid Adaptive Blind Equalization Algorithm for High-Order QAM Signals

It is well known that the constant modulus algorithm (CMA) presents a large steady-state mean-square error (MSE) for high-order quadrature amplitude modulation (QAM) signals. In this paper, we propose a low-complexity hybrid adaptive blind equalization algorithm, which augments the CMA error function with a novel constellation matched error (CME) term. The most attractive advantage of the proposed algorithm is that it is computationally simpler than concurrent CMA and soft decision-directed (SDD) scheme (CMA+SDD), and modified CMA (MCMA), while the approximation of steady-state MSE of the proposed algorithm is same with CMA+SDD, and lower than MCMA. Extensive simulations demonstrate the performance of the proposed algorithm.

Pump-phase-noise-free optical wavelength data exchange between QAM signals with 50-GHz channel-spacing using coherent DFB pump.

An important challenge for implementing optical signal processing functions such as wavelength conversion or wavelength data exchange (WDE) is to avoid the introduction of linear and nonlinear phase noise in the subsystem. This is particularly important for phase noise sensitive, high-order quadrature-amplitude modulation (QAM) signals. In this paper, we propose and experimentally demonstrate an optical data exchange scheme through cascaded 2nd-order nonlinearities in periodically-poled lithium niobate (PPLN) waveguides using coherent pumping. The proposed coherent pumping scheme enables noise from the coherent pumps to be cancelled out in the swapped data after WDE, even with broad linewidth distributed feedback (DFB) pump lasers. Hence, this scheme allows phase noise tolerant processing functions, enabling the low-cost implementation of WDE for high-order QAM signals. We experimentally demonstrate WDEs between 10-Gbaud 4QAM (4QAM) signal and 12.5-Gbaud 4QAM (16QAM) signal with 3.5-MHz linewidth DFB pump lasers and 50-GHz channel spacing. Error-free operation is observed for the swapped QAM signals with coherent DFB pumping whilst use of free-running DFB pumps leads to visible error floors and unrecoverable phase errors. The phase noise cancellation in the coherent pump scheme is further confirmed by study of the recovered carrier phase of the converted signals. In addition to pump phase noise, the influence of crosstalk caused by the finite extinction ratio in WDE is also experimentally investigated for the swapped QAM signals.

Pump-linewidth-tolerant optical wavelength conversion for high-order QAM signals using coherent pumps

Optical wavelength conversion (OWC) is expected to be a desirable function in future optical transparent networks. Since high-order quadrature amplitude modulation (QAM) is more sensitive to the phase noise, in the OWC of high-order QAM signals, it is crucial to suppress the extra noise introduced in the OWC subsystem, especially for the scenario with multiple cascaded OWCs. Here, we propose and experimentally demonstrate a pump-linewidth-tolerant OWC scheme suitable for high-order QAM signals using coherent two-tone pumps. Using 3.5-MHz-linewidth distributed feedback (DFB) lasers as pump sources, our scheme enables wavelength conversion of both 16QAM and 64QAM signals with negligible power penalty, in a periodically-poled Lithium Niobate (PPLN) waveguide based OWC. We also demonstrate the performance of pump phase noise cancellation, showing that such coherent two-tone pump schemes can eliminate the need for ultra-narrow linewidth pump lasers and enable practical implementation of low-cost OWC in future dynamic optical networks.

First demonstration of high-order QAM signal amplification in PPLN-based phase sensitive amplifier

We demonstrate the phase sensitive amplification of a high-order quadrature amplitude modulation (QAM) signal using non-degenerate parametric amplification in a periodically poled lithium niobate (PPLN) waveguide. The interaction between the pump, signal, and phase-conjugated idler enables us to amplify arbitrary phase components of the signal. The 16QAM signals are amplified without distortion because of the high gain linearity of the PPLN-based phase sensitive amplifier (PSA). Both the phase and amplitude noise reduction capabilities of the PSA are ensured. Phase noise cancellation is achieved by using the interaction with the phase-conjugated idler. A degraded signal-to-noise ratio (SNR) is restored by using the gain difference between a phase-correlated signal-idler pair and uncorrelated excess noise. The applicability of the simultaneous amplification of multi-carrier signals and the amplification of two independent polarization signals are also confirmed with a view to realizing ultra-high spectrally efficient signal amplification.

Design and analysis of a reduced phase error digital carrier recovery architecture for high-order quadrature amplitude modulation signals

With increasing order of quadrature amplitude modulation (QAM), the bandwidth efficiency is improved in digital communication. However, in practice, the modulation order is limited, since conventional digital carrier recovery (CR) algorithms give rise to unacceptable phase error. The authors present an efficient software-aided technique for phase error reduction in CR for high-order QAM, based on the simple and well-known fourth power CR loop. Analytical and simulation results indicate that the new technique has several attractive features such as approximate of invariance of phase error improvement over modulation order and low hardware complexity for modulation orders as high as 256-QAM. Experimental results for 64 and 256-QAM illustrate phase error variance of less than −110 dBc/Hz at the frequency offset of 10 kHz, that is, 30 dB reduction of phase error variance or 3 dB increase in system processing gain compared to the conventional fourth power CR loop. This allows a significant improvement of bandwidth efficiency by increasing the modulation order, at the cost of slight complexity overhead.

Joint blind equalization, carrier recovery and timing recovery for high-order QAM signal constellations

Two existing blind equalization tap update recursions for 64-point and greater QAM (quadrature amplitude modulation) signal constellations are studied, along with existing and novel carrier and timing recovery techniques. It is determined that the superior tap update recursion is the one known as the constant modulus algorithm. Carrier recovery requires a modified second-order decision-directed digital phase-locked loop. An all-digital implementation of band-edge timing recovery is used. With 14.4 kb/s outbound transmission using CCITT V.33 trellis-coded 128-QAM signals having 12.5% excess bandwidth, a prototype blind retrain procedure is developed to demonstrate the feasibility of the techniques for high-speed multipoint modems. A WE DSP32-based real-time digital signal processor was employed to test the retrain over a set of severely impaired channels. For each channel in the set, the retrain succeeded at least 90% of the time. >