**5. References**


Fink L.M*.* (1984). *Signals, hindrances, errors*, Radio and communication, 1984.

22 Applications of Digital Signal Processing

The use of complex number mathematics greatly enhances the power of DSP, offering techniques which cannot be implemented with real number mathematics alone. In comparison with *real* DSP, *complex* DSP is more abstract and theoretical, but also more powerful and comprehensive. Complex transformations and techniques, such as complex modulation, filtering, mixing, z-transform, speech analysis and synthesis, adaptive complex processing, complex Fourier transforms etc., are the essence of theoretical DSP. *Complex*  Fourier transforms appear to be difficult when practical problems are to be solved but they

*Complex* DSP techniques are required for many wireless high-speed telecommunication standards. In telecommunications, the complex representation of signals is very common,

Adaptive complex filtering is examined in this chapter, since it is one of the most frequentlyused real-time processing techniques. Adaptive complex selective structures are investigated, in order to demonstrate the high efficiency of adaptive complex digital signal

The *complex* DSP filtering method, based on the developed ACFB, is applied to suppress narrowband interference signals in MIMO telecommunication systems and is then compared to other suppression methods. The study shows that different narrowband interference mitigation methods perform differently, depending on the parameters of the telecommunication system investigated, but the *complex* DSP adaptive filtering technique

Advances in diverse areas of human endeavour, of which modern telecommunications is

It is indeed fair to say that complex digital signal processing techniques still contribute more to the expansion of theoretical knowledge rather than to the solution of existing practical

This work was supported by the Bulgarian National Science Fund – Grant No. DzǼ-02- 135/2008 "Research on Cross Layer Optimization of Telecommunication Resource

Baccareli, E.; Baggi, M. & Tagilione, L. (2002). A novel approach to in-band interference

Crystal, T. & Ehrman, L. (1968). The design and applications of digital filters with complex

Douglas, S. (1999). Adaptive filtering, in *Digital signal processing handbook*, D. Williams & V.

Madisetti, Eds., Boca Raton: CRC Press LLC, pp. 451-619, 1999. Fink L.M*.* (1984). *Signals, hindrances, errors*, Radio and communication, 1984.

mitigation in ultra wide band radio systems. *IEEE Conf. on Ultra Wide Band Systems* 

coefficients, *IEEE Trans. on Audio and Electroacoustics*, vol. 16, Issue: 3, pp. 315-

offers considerable benefits, including comparatively low computational complexity.

overcome the limitations of *real* Fourier transforms in a mathematically elegant way.

hence complex processing techniques are often necessary.

only one, will continue to inspire the progress of *complex* DSP.

*and Technologies*, pp. 297-301, 7 Aug. 2002.

problems - but watch this space!

320, Sept. 1968.

**4. Acknowledgment** 

Allocation".

**5. References** 

**3. Conclusions** 

processing.


Rameez Asif, Chien-Yu Lin and Bernhard Schmauss

**Digital Backward Propagation:** 

**and Non-Linear Impairments** 

*Cauerstr. 9, (91058) Erlangen*

*Germany*

**2**

*Chair of Microwave Engineering and High Frequency Technology (LHFT), Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander University of Erlangen-Nuremberg (FAU),*

**A Technique to Compensate Fiber Dispersion** 

Recent numerical and experimental studies have shown that coherent optical QPSK (CO-QPSK) is the promising candidate for next-generation 100Gbit/s Ethernet (100 GbE) (Fludger et al., 2008). Coherent detection is considered efficient along with digital signal processing (DSP) to compensate many linear effects in fiber propagation i.e. chromatic dispersion (CD) and polarization-mode dispersion (PMD) and also offers low required optical signal-to-noise ratio (OSNR). Despite of fiber dispersion and non-linearities which are the major limiting factors, as illustrated in Fig. 1, optical transmission systems are employing higher order modulation formats in order to increase the spectral efficiency and thus fulfil the ever increasing demand of capacity requirements (Mitra et al., 2001). As a result of which compensation of dispersion and non-linearities (NL), i.e. self-phase modulation (SPM), cross-phase modulation (XPM) and four-wave mixing (FWM), is a point of high interest these

Various methods of compensating fiber transmission impairments have been proposed in recent era by implementing all-optical signal processing. It is demonstrated that the fiber dispersion can be compensated by using the mid-link spectral inversion method (MLSI) (Feiste et al., 1998; Jansen et al., 2005). MLSI method is based on the principle of optical phase conjugation (OPC). In a system based on MLSI, no in-line dispersion compensation is needed. Instead in the middle of the link, an optical phase conjugator inverts the frequency spectrum and phase of the distorted signals caused by chromatic dispersion. As the signals propagate to the end of the link, the accumulated spectral phase distortions are reverted back to the value at the beginning of the link if perfect symmetry of the link is assured. In (Marazzi et al., 2009), this technique is demonstrated for real-time implementation in 100Gbit/s POLMUX-DQPSK

Another all-optical method to compensate fiber transmission impairments is proposed in (Cvecek et al., 2008; Sponsel et al., 2008) by using the non-linear amplifying loop mirror (NALM). In this technique the incoming signal is split asymmetrically at the fiber coupler

**1. Introduction**

days.

transmission.

