Fast frequency allocation in WDM systems with unequally spaced channels

A new method for allocating the unequally space channels (USCs) in WDM systems to minimise the crosstalk caused by four-wave mixing is presented. The proposed method has the advantages of easy computer implementation, fast generation of USC sets, and flexible change of system parameters. The results show that a larger-size set can be easily constructed from the smaller-size set to facilitate engineering applications. The optimal/suboptimal USC sets are also obtained.     

A generalized suboptimum unequally spaced channel allocationtechnique. II. In coherent WDM systems

For pt.I see ibid., vol.46, no.8, p.1027-37 (1998). Four-wave mixing (FWM) in dispersion-shifted optical fiber is a major problem associated with low optical input power levels in optical wavelength-division multiplexed (WDM) systems. To reduce the crosstalk caused by FWM, a generalized suboptimum unequally spaced channel allocation (S-BISCA) technique has been proposed. While the S-USCA technique reduces the PWM power substantially, it also reduces the minimum channel spacing compared to conventional equal channel spacing (ECS) systems when the same number of carrier channels are accommodated in a fixed optical bandwidth. This results in more interchannel interference (ICI) when employing the S-USCA scheme. The power penalty of the ECS and the S-USCA systems caused by crosstalk and frequency drift are investigated and compared in this paper. The superior system performance region, where S-USCA systems out perform ECS systems, is also quantified. For 20-channel systems using an amplitude-shift keying (ASK) heterodyne detection scheme, for instance, results show that the S-USCA technique pays less power penalty up to bit rates of 5.5, 7.5, and 9.5 Gb/s, when all channels have identical states of polarization and the launched input power per channel P_in, equals to -6, -3, and 0 dBm, respectively     

Analysis of repeated unequally spaced channels for FDM lightwavesystems

In long-haul optical frequency-division-multiplexing (FDM) systems, transmission characteristics are degraded by four-wave mixing (FWM). To overcome this problem, repeated unequally spaced (RUS) channels have been recently proposed as a new frequency allocation. In this paper, frequency distribution and intensity of generated FWM lights, and a total bandwidth of signal lights of RUS channels are compared with those of already known equally spaced (ES) and unequally spaced (US) channels. It is found that intensities of generated FWM lights of RUS are less than those of ES when the number of channels and a total bandwidth of signals are common in both channels. It is also revealed that RUS has a narrower total bandwidth than US when the number of channels and the minimum channel spacing are common in both channels. Since RUS simultaneously satisfies a low FWM light intensity and a narrow signal bandwidth, it is considered that RUS is suitable for FDM lightwave transmission systems     

A generalized suboptimum unequally spaced channel allocationtechnique. I. In IM/DD WDM systems

Four-wave mixing (FWM) is the most serious fiber nonlinearity associated with low-input optical power levels in long-haul multichannel optical systems employing dispersion-shifted fiber. To reduce the crosstalk due to FWM, a generalized suboptimum unequally spaced channel allocation (S-USCA) technique is proposed and investigated. Even though the developed technique is useful in combating FWM crosstalk in wavelength division multiplexing (WDM) lightwave systems with up to 12 channels, its main virtue is in designing multichannel WDM lightwave systems with more than 12 channels. Comparisons of power penalty due to FWM between equal channel spacing (ECS) systems and the S-USCA systems are presented. It is shown that for an intensity modulation/direct detection (IM/DD) transmission system operating in an optical bandwidth of 16 nm with 0 dBm (1 mW) peak optical input power per channel, while a conventional ECS WDM system with 0.84-nm channel spacing cannot even achieve a bit-error rate (BER)=10^-9, the suboptimum technique developed in this paper, for the same minimum channel spacing, can achieve a BER=10^-9 with an FWM crosstalk power of less than 1 dB at the worst channel in a 20-channel WDM system     

Reduction of four-wave mixing crosstalk in WDM systems usingunequally spaced channels

Crosstalk due to four-wave mixing (FWM) is the dominant nonlinear effect in long-haul multichannel optical communication systems employing dispersion-shifted fiber. A technique to design the channel frequency allocation in order to minimize the crosstalk due to FWM is presented. It is shown that suitable unequal channel separations can be found for which no four-wave mixing product term is superimposed on any of the transmitted channels. This is obtained at the expense of some expansion of the system bandwidth. Simulations are presented to show the effectiveness of this technique in a 10-channel, 10-Gb/s per channel, system     

Dynamic programming applied to unequally spaced arrays

The application of the optimization technique known as dynamic programming to the design of "thinned" arrays with unequally-spaced elements is described. Dynamic programming is a systematic procedure for efficiently utilizing the capabilities of modern high-speed digital computing machines to find solutions to problems not computationally feasible by conventional means. In this paper it is applied to the design of linear arrays of 25 elements spaced within a 50 wavelength aperture. The results obtained compare favorably with similar results found by other design techniques. The effect on the sidelobes of varying the angular region of optimization and the spacing-quantization is also explored.     

Design of unequally spaced arrays for performance improvement

Classical antenna array synthesis techniques such as Fourier, Dolph-Chebyshev and Taylor synthesis efficiently obtain array current distributions for equally spaced arrays that generate a desired far-field radiation pattern function or keep important parameters like beamwidth and sidelobe level within prescribed performance bounds. However, the concept of optimization of the field pattern (e.g., by decreasing sidelobes or beamwidth) of an given equally spaced array realization by altering its element spacings still represents a challenging problem having considerable practical advantages. These include reduction in size, weight, and number of elements of the array. This paper describes a new approach to synthesis of unequally spaced arrays utilizing a simple inversion algorithm to obtain the element spacings from prescribed far-zone electric field and current distribution, or current distributions from prescribed far-zone electric field and element spacings     

Synthesis of unequally spaced arrays by simulated annealing

Simulated annealing is applied to the synthesis of arrays in order to reduce the peaks of side lobes by acting on the elements' positions and weight coefficients. In the case considered, the number of array elements and the spatial aperture of an unequally spaced array are a priori fixed. Thanks to the high flexibility of simulated annealing, the results obtained for a 25-element array over an aperture of 50λ improve those reported in the literature     

Synthesis of unequally spaced arrays using dynamic programming

The application of dynamic programming to the synthesis of unequally spaced symmetrical antenna arrays is further investigated. The design criterion is to obtain a combination of elements, in a quantized aperture which has the lowest value of the peak sidelobe level over a specified angular interval. A 25- element array in an aperture length of50lambdais synthesized, and it is shown that the designs obtained are considerably superior to those obtained by other investigators using different techniques.     

玫瑰扫描亚成像系统中非均匀采样参数的确定

在实时图像处理系统中，图像的分辨率和系统的计算量之间总存在矛盾。高分辨率意味着大数据量和较大的计算量，但较低的分辨率又会影响图像处理的质量。为了解决图像数据量和分辨率之间的矛盾。根据玫瑰扫描视场中心区域扫描频率高，扫描迹线密；边缘区域扫描频率低；扫描迹线疏的特点，提出了在玫瑰扫描红外亚成像系统中应用高斯型非均匀采样函数进行非均匀采样的新方法。讨论了图像数据量和分辨率与非均匀采样参数之间的关系，在此基础上给出了确定非均匀采样参数的方法。     

Densely spaced WDM coherent optical star network

An optical WDM star network consisting of three lasers transmitting at about 234 000 GHz, spaced by 300 MHz, has been used to demonstrate dense packing of WDM signals. The three optical signals, FSK-modulated at 45Mbit/s, are multiplexed by a 4 × 4 star coupler and demultiplexed by a balanced heterodyned receiver. Receiver sensitivity is -61dBm for a BER of 10?9, or 113 photons/bit, which is 4.5dB from the shot noise limit and represents the best sensitivity yet reported for FSK modulation. The results indicate that 100 000 users in a 10km radius could be interconnected with such a system.     

Transport performance in optical path cross-connect systememploying unequally spaced channel allocation

The transmission performance of an optical path cross-connect (OPXC) system employing unequally spaced channel allocation is evaluated. Four-wave mixing (FWM) light is generated at a different wavelength from all other signal lights when unequally spaced channel allocation is employed in the OPXC system. This evaluation shows that FWM light degrades the transmission performance because the received FWM light power is added to the signal and closes the eye aperture of the signal. The FWM light is rejected by the employed demultiplexer when the full-width at the half maximum (FWHM) of the demultiplexer is reduced. The FWHM of the demultiplexer should be designed in order to minimize the transmission performance degradation caused by the FWM crosstalk. The FWHM of the arrayed-waveguide-grating (AWG) demultiplexer that is developed for the OPXC system is 0.6 nm, and a 400 km transmission with optical path cross-connections is successfully completed in a 4×4 OPXC system test-bed employing unequal channel spacing with a 10 GHz frequency slot, i.e., the minimum frequency separation between signal light and FWM light. Further reduction in the FWM crosstalk is required for the OPXC system in order to support longer distances between nodes. The distance of 120 km ×5 requires that the frequency slot is increased to 30 GHz and the FWHM of the AWG demultiplexer is 0.3 nm     

A simple model for mutual coupling effects on patterns of unequally spaced arrays

The effects of mutual coupling on the patterns of unequally spaced arrays are not generally negligible. A simple method for approximating the effect of coupling for the purpose of checking the sensitivity of an array design is presented and justified. Attempts to include the approximation in a synthesis technique have not been successful.     

Synthesis of uniform amplitude unequally spaced antenna arrays using the differential evolution algorithm

A computationally efficient global optimization method, the differential evolution algorithm (DEA), is proposed for the synthesis of uniform amplitude arrays of two classes, i.e., unequally spaced arrays with equal phases and unequal phases. Phase-only synthesis and the synthesis of uniformly exited unequally spaced arrays (position only synthesis) are compared and it is seen that, by using the unequal spacing, the number of array elements can be significantly reduced for attaining reduced sidelobe levels. From the DEA-based synthesis of unequally spaced arrays with uniform amplitudes and unequal phases, it is found that a tradeoff exists between the size of the unequally spaced arrays and the range of phases for the same radiation characteristics. The proposed synthesis technique using uniform amplitudes, unequal spacing, and unequal phases (position-phase synthesis) not only decreases the size of the array for the same sidelobe level compared to both the phase-only synthesis and position-only synthesis but also retains their advantages.     

Sufficient conditions for the existence of optimum beam patterns for unequally spaced linear arrays with an example

Dolph's method for determining the optimum element currents for half-wavelength equispaced discrete linear arrays is generalized to symmetric discrete linear arrays. The theorem proved gives sufficient conditions for the existence of optimum beam patterns for arrays with elements symmetrically positioned about the array center, but with fixed unequal spacings between the elements. The conditions are such that the Remes exchange algorithm for minimax approximation of functions can be employed to compute the optimum element currents corresponding to an optimum beam pattern directly from the given spacings of the elements. Half-wavelength spaced linear arrays satisfy the conditions of the theorem; therefore, it provides a new method of calculating the well-known Dolph-Chebyshev element currents. An example with unequal spacings is included to show the utility of the method even when the hypotheses of the theorem may not be met.     

Capacity of MIMO systems with closely spaced antennas

Wide-band radio channel measurements at 5.2 GHz with four transmit and four receive antennas at variable element spacing are reported, aiming to evaluate the potential of compact antenna arrays at mobile terminals. We show that, for an element spacing d<0.5/spl middot//spl lambda/ (down to 0.2/spl middot//spl lambda/), the link capacity is not smaller than that for much larger d. This is explained by the observation that mutual coupling changes the radiation patterns of closely spaced antenna elements, individually. Compact multi-antenna terminals may thus become practical.     

Generalized analytical technique for the synthesis of unequally spaced arrays with linear, planar, cylindrical or spherical geometry

An effective method for optimizing the performance of a fixed current distribution, uniformly spaced antenna array has been to adjust its element positions to provide performance improvement. In comparison with the default uniform structure, this approach yields performance improvements such as smaller sidelobe levels or beamwidth values. Additionally, it provides practical advantages such as reductions in size, weight and number of antenna elements. The objective of this paper is to describe a unified mathematical approach to nonlinear optimization of multidimensional array geometries. The approach utilizes a class of limiting properties of sinusoidal, Bessel or Legendre functions that are dictated by the array geometry addressed. The efficacy of the method is demonstrated by its generalized application to synthesis of rectangular, cylindrical and spherical arrays. The unified mathematical approach presented below is a synthesis technique founded on the mathematical transformation of the desired field pattern, followed by the application of limiting forms of the transformation, and resulting in the development of a closed form expression for the element positions. The method offers the following advantages over previous techniques such as direct nonlinear optimization or genetic algorithms. First, it is not an iterative, searching algorithm, and provides element spacing values directly in a single run of the algorithm, thereby saving valuable CPU time and memory storage. Second, It permits the array designer to place practical constraints on the array geometry, (e.g., the minimum/maximum spacing between adjacent elements)     

WDM EDFA gain characterization with a reduced set of saturating channels

The advent of EDFA-based dense WDM places demanding optical source requirements for EDFA characterization. An iterative method is proposed here, based on a homogeneous amplifier model, to calculate the required signal conditions for WDM testing with a reduced set of saturating channels and a broad-band noise probe. EDFA gain measurements demonstrating this reduced-source technique agree to within 0.2 dB to those obtained with a four-channel WDM system operating near 1.55 /spl mu/m.