Modified Constant Modulus Algorithm Research Articles

A Simple and Robust Equalization Algorithm for Variable Modulation Systems

This paper proposes a simple and robust variable modulation-decision-directed least mean square (VM-DDLMS) algorithm for reducing the complexity of conventional equalization algorithms and improving the stability of variable modulation (VM) systems. Compared to conventional adaptive equalization algorithms, known information was used as training sequences to reduce the bandwidth consumption caused by inserting training sequences; compared with conventional blind equalization algorithms, the parameters and decisions of the equalizer were determinate, which was conducive to a stable equalization performance. The simulation and implementation results show that the proposed algorithm has a better bit error rate (BER) performance than that of the constant modulus algorithm (CMA) and modified constant modulus algorithm (MCMA) while maintaining the same level of consumption of hardware resources. Compared to the conventional decision-directed least mean square (DDLMS) algorithm, the proposed algorithm only needs to make quadrature phase shift keying (QPSK) symbol decisions, which reduces the computational complexity. In parallel 11th-order equalization algorithms, the operating frequency of VM-DDLMS can reach up to 333.33 MHz.

Concurrent Modified Constant Modulus Algorithm and Decision Directed Scheme With Barzilai-Borwein Method.

At present, in robot technology, remote control of robot is realized by wireless communication technology, and data anti-interference in wireless channel becomes a very important part. Any wireless communication system has an inherent multi-path propagation problem, which leads to the expansion of generated symbols on a time scale, resulting in symbol overlap and Inter-symbol Interference (ISI). ISI in the signal must be removed and the signal restores to its original state at the time of transmission or becomes as close to it as possible. Blind equalization is a popular equalization method for recovering transmitted symbols of superimposed noise without any pilot signal. In this work, we propose a concurrent modified constant modulus algorithm (MCMA) and the decision-directed scheme (DDS) with the Barzilai-Borwein (BB) method for the purpose of blind equalization of wireless communications systems (WCS). The BB method, which is two-step gradient method, has been widely employed to solve multidimensional unconstrained optimization problems. Considering the similarity of equalization process and optimization process, the proposed algorithm combines existing blind equalization algorithm and Barzilai-Borwein method, and concurrently operates a MCMA equalizer and a DD equalizer. After that, it modifies the DD equalizer's step size (SS) by the BB method. Theoretical investigation was involved and it demonstrated rapid convergence and improved equalization performance of the proposed algorithm compared with the original one. Additionally, the simulation results were consistent with the proposed technique.

Convex Combination of SISO Equalization and Blind Source Separation for MIMO Blind Equalization

For Multiple-Input Multiple-Output (MIMO) system the received signal will suffer not only inter-symbol interference but also inter-antenna interference under frequency selective fading channel. This paper proposes a MIMO blind equalization algorithm consisting of the convex combination of Single-Input Single-Output (SISO) blind equalization algorithm and blind source separation (BSS). The main purpose of the SISO equalization algorithm is to convert the convolution channel into multiplicative channel, and the BSS algorithm is mainly used to separate the different sources. The SISO equalization algorithm used in the paper is the modified constant modulus algorithm (MCMA) because of its simplicity and effectiveness. The BSS algorithm is the constraint fitting probability density function algorithm (CFPA). The MIMO blind equalization algorithm is named as MCMA–CFPA. Moreover, a low complexity MCMA–CFPA and a dual mode algorithm based on soft switching are presented. Simulation results show that the proposed algorithms can simultaneously equalize and separate all transmission signals.

Logarithmic cost-based improved constant modulus type blind channel equalisation algorithm for M-QAM/M-PSK signal

In this paper, authors have proposed the blind channel equalisation algorithm based on logarithmic cost function for QAM/PSK signal which is widely used in the digital communication system. Constant modulus algorithm (CMA) and modified constant modulus algorithm (MCMA), the two widely referenced algorithms for blind equalisation of a QAM/PSK signal, exhibit very slow convergence rates and large steady-state mean square error. The proposed algorithm attains faster convergence speed and low steady state mean square error by incorporating the improved logarithmic cost-based error function in the resilient back propagation-based framework. This makes the weight adaption of equaliser simple. Simulation results show that the proposed algorithm has better convergence rate and lower steady state error in comparison to CMA and MCMA algorithms.

Logarithmic cost-based improved constant modulus type blind channel equalisation algorithm for M-QAM/M-PSK signal

In this paper, authors have proposed the blind channel equalisation algorithm based on logarithmic cost function for QAM/PSK signal which is widely used in the digital communication system. Constant modulus algorithm (CMA) and modified constant modulus algorithm (MCMA), the two widely referenced algorithms for blind equalisation of a QAM/PSK signal, exhibit very slow convergence rates and large steady-state mean square error. The proposed algorithm attains faster convergence speed and low steady state mean square error by incorporating the improved logarithmic cost-based error function in the resilient back propagation-based framework. This makes the weight adaption of equaliser simple. Simulation results show that the proposed algorithm has better convergence rate and lower steady state error in comparison to CMA and MCMA algorithms.

MIMO blind equalization algorithm based on successive interference cancellation

Modified Constant Modulus Algorithm (MCMA) is widely used in the SISO blind equalization for its simplicity. For MIMO systems MCMA can only equalize one of the source signals. Through the combination of channel estimation and successive interference cancellation, source signals can be equalized in turn. However the recovery of the first source and the channel estimation are the key points, which directly affects the recovery of the subsequent sources. This paper proposes a channel estimation method with a small amount of calculation, and can accurately estimate the channel vector. Meanwhile, a new blind equalization algorithm is put forward to reliably recovery the first source signal. Simulation results verify the effectiveness of the proposed algorithm.

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.

Fast and adaptive chromatic dispersion compensation scheme for digital coherent systems utilizing two-stage estimation.

A two-stage fast and adaptive chromatic dispersion (CD) estimation algorithm is proposed and demonstrated for coherent polarization-division-multiplexed (PDM) systems. The first stage uses signal power auto-correlation function for the coarse estimation while the second stage utilizes a modified constant modulus algorithm (MCMA) to obtain much more accurate accumulated CD. Simulation results show that the proposed algorithm is sufficient for CD estimation in non-dispersion-managed optical transmission of 112-Gb/s PDM-QPSK or 224-Gb/s PDM-16QAM signals. The concept is further experimentally verified in a 40-Gb/s PDM-QPSK system. Only ~7% estimation time is required to achieve similar accuracy compared to previous MCMA algorithm.

New FSE Based on MCMA and PLL

In the digital transmission system, an efficient fractionally-spaced equalizer (FSE) for blind equalization based on modified constant modulus algorithm (MCMA) and phase locked loop (PLL) is proposed. Comparing with conventional FSE based on famous CMA, the proposed algorithm has not only lower steady-state mean square error and faster convergence rate but also the ability to recover carrier phase rotation. The efficiency of the method is proved by computer simulation.

Instantaneous Gradient Based Dual Mode Feed-Forward Neural Network Blind Equalization Algorithm

To further improve the performance of feed-forward neural network blind equalization based on Constant Modulus Algorithm (CMA) cost function, an instantaneous gradient based dual mode between Modified Constant Modulus Algorithm (MCMA) and Decision Directed (DD) algorithm was proposed. The neural network weights change quantity of the adjacent iterative process is defined as instantaneous gradient. After the network converges, the weights of neural network to achieve a stable energy state and the instantaneous gradient would be zero. Therefore dual mode algorithm can be realized by criterion which set according to the instantaneous gradient. Computer simulation results show that the dual mode feed-forward neural network blind equalization algorithm proposed in this study improves the convergence rate and convergence precision effectively, at the same time, has good restart and tracking ability under channel burst interference condition.

RCA 비용 함수를 개선한 Advanced CMA 등화기 알고리즘

In this paper, the concerned CMA (Constant Modulus Algorithm) adaptive equalizer convergence rate and residual inter-symbol interference using cost function in order to improved to the ACMA (Advanced CMA). The CMA method compensates amplitude but does not compensate phase. On the other hand, The RCA (Reduced Constellation Algorithm) method compensates both the amplitude and the phase but it has the convergence rate problem. MCMA method is a way to solve the phase problem of CMA method compensates both the amplitude and the phase after respectively calculating the real and imaginary components. But it is more than poor CMA method in the complexity of hardware and the compensation performance. The cost function can advantages by improving the CMA and a MCMA (Modified CMA) equalizer so that the amplitude and phase retrieval the equalization steady-state to reduce the error by using ISI and faster convergence rate and performance is good SER (Symbol Error Ratio) was confirmed by computer simulations.

New Variable Step-Size Blind Equalization Based on Modified Constant Modulus Algorithm

This paper presents a new blind equalization algorithm based on MCMA to attain fast convergence speed and low steady-state error. The channel equalization without resorting to training sequence is called blind equalization. The CMA (Constant Modulus Algorithm) and MCMA (Modified Constant Modulus Algorithm) are two widely referenced algorithms for blind equalization of a QAM system. These algorithms exhibit very slow convergence rates and large steady-state mean square error when compared to algorithms employed in conventional equalization schemes. To obtain better results, we used varying step-size in MCMA, based on estimate of error at the output of equalizer. Simulation results show that the proposed algorithm has a better convergence rates and lower steady state error in comparison to CMA and MCMA algorithms.

변형된 CMA의 수렴상수 갱신 방법의 성능 비교

변형된 CMA는 CMA에 비해 고차 신호점을 등화 시 보다 적은 수의, 균등한 간격을 갖는 모듈러스를 이용함으로써 정상상태 성능 개선과 고차 신호점으로의 확장이 용이하다. 본 논문에서는 변형된 CMA에 가변 수렴상수를 적용하여 정상상태 성능을 더욱 개선하여 다른 경판정 알고리즘으로의 전환 없이도 충분히 만족스러운 성능을 달성할 수 있음을 보인다. 새로운 두 가지 수렴상수 가변 방법을 제안하고, 이를 적용한 변형된 CMA의 성능 개선을 모의실험을 통해 CMA와 고정 수렴상수의 변형된 CMA에 대해 확인하였다. Compared to the constant modulus algorithm (CMA), the modified CMA (MCMA) is easy not only to improve the steady-state performance but also to be expanded to higher-order constellations by using fewer moduli with evenly spaced. In this paper, it is shown that the MCMA is sufficient to achieve satisfactory steady-state performance by applying a variable step-size to the MCMA without switching to an hard decision-directed algorithm. Two new methods varying the step-size are proposed, and the performance improvement of the MCMA with the new methods of variable step-size is presented as compared to the CMA and the fixed step-size MCMA through computer simulations.

Performance Improvement of MCMA Equalizer with Parallel Structure

In digital communication system that the Modified Constant Modulus Algorithm (MCMA) reduced the use of the adaptive equalization algorithm to combat the Inter-symbol Interference (ISI). MCMA is relatively brief operation. The major point of MCMA that it only achieves moderate convergence rate and steady state mean square error (MSE). In this paper suggest, MCMA equalization improve the performance with parallel structure. It combines Modified Constant Modulus Algorithm(MCMA) and Modified Decision Directed(MDD) algorithm. By exploiting the inherent structural relationship between the 4-QAM signal's coordinates and 16-QAM signal's coordinates, another style of cost function for Modified Constant Modulus Algorithm(MCMA) is defined and If it happen to offset of received signals and MCMA is poor performance in order to overcome this because the paper combines apply for MCMA and MDD(Modified Decision Direct) algorithm. By computer simulation, we confirmed that the proposed PMCMA-MDD algorithm has the fater convergence rate and steady mean square error than the conventional MCMA.

A Supervised Constant Modulus Algorithm for Blind Equalization

Blind equalization is a technique for adaptive equalization of a communication channel without the aid of the usual training sequence. Although the Constant Modulus Algorithm (CMA) is one of the most popular adaptive blind equalization algorithms, it suffers from slow convergence rate. A novel enhanced blind equalization technique based on a supervised CMA (S-CMA) is proposed in this paper. The technique is employed to initialize the coefficients of a linear transversal equalizer (LTE) filter in order to provide a fast startup for blind training. It also presents a computational study and simulation results of this newly proposed algorithm compared to other CMA techniques such as conventional CMA, Normalized CMA (N-CMA) and Modified CMA (M-CMA). The simulation results have demonstrated that the proposed algorithm has considerably better performance than others.

Nonlinear Blind Equalizers: NCMA and NMCMA

This paper proposes two nonlinear blind equalizers: the nonlinear constant modulus algorithm (NCMA) and the nonlinear modified constant modulus algorithm (NCMA) by applying a nonlinear transfer function (NTF) into constant modulus algorithm (CMA) and modified constant modulus algorithm (MCMA), respectively. The effect of the NTF on CMA and MCMA is theoretically analyzed, which implies that the NTF can make their decision regions much sharper so that the proposed two nonlinear blind equalizers are more robust against the convergency error compared to their linear counterparts. The embedded single layer in NCMA and NMCMA simultaneously guarantees a comparably speedy convergency. On 16-quadrature amplitude modulation (QAM) symbols, computer simulations show that NCMA achieves an 8dB lower convergency mean square error (MSE) than CMA, and NMCMA achieves a 15dB lower convergency MSE than MCMA.

Efficient fast blind equalization with two‐stage single/multilevel modulus and DD algorithm for 64/256/1024qam wired cable communications

In this paper, an efficient blind equalization with two‐stage single/multilevel modulus and decision directed (DD) least mean square (LMS)‐like algorithm is proposed for high‐order QAM (64/256/1024QAM) cable modem systems. In wire‐lined cable systems, it seems that the cable channel may display a nearly invariant multi‐path effect over a considerable time, and then the blind equalizer can have the capability to recover the received high‐order QAM symbols on wired cables. The proposed blind equalization algorithm applies a two‐stage convergence scheme, which results from the multi‐modulus algorithm (MMA), sometimes called the modified constant modulus algorithm (MCMA), and the DD LMS‐like method. In the first equalization stage, the joint MMA and DD LMS‐like methods are applied for the purpose of fast convergence. When the convergence process reaches an acceptably steady condition, the convergence detector changes the process into the second stage. In the second equalization stage, the enhanced DD LMS‐like method with the generalized multi‐modulus is applied to reduce the mean square error (MSE) of equalizations further. For high‐order QAM cable systems, the proposed method performs faster than the previous well‐known blind methods do. Simultaneously, the proposed algorithm also provides less MSE and lower symbol error rate (SER) than the other blind methods do at the same signal‐to‐noise ratio (SNR).

Blind equalization algorithm based on MCMA and DSE-CMA

A new blind equalization algorithm based on the modified constant modulus algorithm (MCMA) and dithered signed-error constant modulus algorithm (DSE-CMA) is proposed. This dithered signed-error MCMA (DSE-MCMA) can not only reduce the computational complexity, but also recover the phase rotation in the complex channel. Simulation results have verified the analysis and indicated the good property of DSE-MCMA.

A Hybrid Adaptive Blind Equalization Algorithm for QAM Signals in Wireless Communications

A hybrid adaptive channel equalization technique for quadrature amplitude modulation (QAM) signals is proposed. The proposed algorithm, which is referred to as the modified constant modulus algorithm (MCMA), minimizes an error cost function that includes both amplitude and phase of the equalizer output. In addition to the amplitude-dependent term that is provided by the conventional constant modulus algorithm (CMA), the cost function includes an additive signal constellation matched error (CME) term. This term can be designed to satisfy a set of desirable properties. The MCMA is compared with the CMA for blind equalization. The performance is measured for wireless channels using both transient and steady-state behavior of the mean square error (MSE). It is shown that MCMA is superior and more robust in low signal-to-noise ratio (SNR) environments. Simulation results demonstrate that using MCMA improves adaptive channel equalization by increasing the convergence rate and decreasing the steady-state mean square error.

Modified constant modulus algorithm for digital signal processing adaptive antennas with microwave analog beamforming

This paper proposes a novel algorithm, called modified constant modulus algorithm (M-CMA), which is able to give adaptability to microwave beamforming phased array antennas. Since microwave analog beamformers basically require much fewer RF devices than digital beamformers, microwave analog beamformers based on M-CMA, that is, adaptive microwave beamformers, can be cheaply fabricated. Therefore, they are very suitable for mobile communication systems where both miniaturization and low cost are required for the mobile terminals. M-CMA obtains a gradient vector by a combination of analytical calculation and perturbation of the microwave beamforming control voltage. Though M-CMA is implemented with a digital signal processor, M-CMA controls the microwave analog beamformer by utilizing the gradient vector. The microwave analog beamformer based on M-CMA is analyzed to have the following characteristics: (1) the beamformer can point its main beam to the desired direction in additive white Gaussian noise (AWGN) channels; (2) although the beamformer may possibly fail in ill solutions in cochannel interference (CCI) channels, M-CMA can converge to the optimum solution when the desired direction is roughly a priori known.