# Frequency division multiple access model to design and MATLAB simulation

Print View , by: **iSee** ,Total views: **31** ,Word Count: **2060** ,Date: Sun, 21 Jun 2009 Time: 11:25 AM

O INTRODUCTION

MATLkB environment (Chinese name is the matrix laboratory) is NEWMEXICO University by the United States CLEVE MOLER began developing in 1980. It was first used FORTRON languages, the **matlab** program by using THF MATH WORKS Inc. **c** language in 1984 by the MATH WORKS introduced the first commercial version. After nearly two decades of **development** and competition, and perfect, has become internationally recognized science and technology the best applications. MATLAB is a complex matrix as the basic unit of programming an advanced programming language, mainly for matrix calculation and control and information processing analysis of the field of design, it is easy to expand by users and set their own scientific and **engineering** computing, graphics and visualization , and image processing, multimedia processing in one, and provides the Windows graphical **interface** and practical design methods, allows users to design a friendly graphical interface.

MATLAB includes a control **system** analysis and design of the toolbox to be a function of control system toolbox contains almost classical control theory and modern control theory of the main contents, including the function are: modeling, model transformation, model simplification , models, model characteristics, equation solving, time-domain response, frequency response, root locus.

Used in wireless communications is a way instead of a point-to-point radio transmission, that is, net of any user to launch other users can receive the signal. Therefore, how to identify the sender object signal the key to a problem, to solve the problem of the method is based on the principle of partition orthogonal signal multiple **access** methods.

As we all know, radio signals can be expressed as time, frequency and code-based function, so the three can be used as multiple access based on the identification, Frequency Division Multiple Access is a transmission signal in accordance with the different carrier frequency division multiple access to the establishment of method. The method is the frequency of reuse of resources, technology is mature, easy and simulation **systems** and signal **power** on the advantages of no stringent requirements. Typical applications include radio, TV and so on.

1 model

Modern frequency division multiple access communication system will be a limited frequency band is divided into a number of domains, such as spacing and non-overlapping channels, the different **mobile** applications available through the different channels of communication between the process of non-interfering. The communication system model shown in Figure 1.

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2 Model

Modern communication systems transmit signals of uncertainty can be divided into consecutive periodic signal, for non-periodic signal, discrete periodic signal and discrete non-periodic signal. Due to the characteristics of time-domain signal less obvious and easy analysis of signals, and frequency-domain characteristics of signals clearly visible for the signal analysis provides an effective way, which can be compared in the frequency domain and analysis of signal transmission characteristics before and after the change.

The assumption that the system for transmission of a non-periodic signal f (x), its frequency domain representation for the Fourier transform. The signal for the Fourier Transform

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In order to effectively and reliably to FDMA communications, the need for a high-frequency carrier signal (cos (w0t)) multiplied by the original signal, that is, the signal transmission channel into a cos (wot) f (t), the signal of the Fourier Transform for

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Comparison (1), type (2), we can see that the original signal multiplied with the carrier frequency, its spectrum was linear to the frequency point is the load.

Based on the above analysis, the assumption that the system is n at the same time the signal transmission path, then the transmission signal can be expressed as

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Where: f1 (t), f2 (t), ..., fn (t) that signal, f1, f2, ..., fn that the carrier frequency, cos (2πf1t), cos (2πf2t), ..., cos (2πfnt) that high-frequency carrier wave, S (t), said multiplexing signal.

Due to the high-frequency carrier signal to the transfer to a different band of spectrum, multiplexing the signal spectrum for the superposition of the signal, therefore, only transmit the signal can be multiplexed to achieve the same channel at the same time multi-channel signal transmission, transmission after the completion of by N a suitable bandpass filter to receive N signals have been transferred, and then, through the style (4) of the various signal demodulation, and finally, through the low-pass filter and filter out the restoration of the original signal.

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Where an (t) through the band-pass filter, said after the first N signals, bn (t) the way that the first N-signal demodulator.

Based carrier frequency signal for the cosine signal uc, modulation signal for the un, the transmission signal with AM signal for bilateral (uDSB), that is,

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By type (7), we can see that the spectrum modulation signal was linear on both sides of the transfer to the carrier frequency, upper frequency of wc + Ω, below a frequency of wc Ω, bandwidth of 2Ω. Assumptions need to transfer 3-way with the bandwidth of the cosine signal, prior to the assumption that the 3 signals, respectively Acos (Ωt), Beos (Ωt), Coos (Ωt) in order to prevent transmission of the interference between spectrum, inter-carrier frequency spacing should be greater than 2Ω, the transmission flow chart shown in Figure 2.

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Through band-pass filter (bandpass) filter after the demodulation of the signal (demodulation), the original low-frequency signals are transferred to the low-frequency band, and then through the corresponding low-pass (1owpass) filtering out the restoration of the original signal, in order to achieve FDMA communication transmission .

3 Examples

Authors in the MATLAB environment, the use of FDMA communication programming model simulation. MATLAB supports the microphone, so voice can be recorded directly. MATLAB call 3 times the following procedure will be 3-way voice signal (yo, yt, yh):

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Of which: fs as sampling frequency, in Hz (Joseph times); duration time for the recording, unit s (seconds).

By calling each sample value of 2205 will be the use of sampled values of the signals Fourier transform, the signal from various sampling points in relation to the time-domain waveform shown in Figure 3, the figure, A for the voltage amplitude , unit V; compared with the sampling points of the spectrum shown in Figure 4.

We can see from the analysis: the signal l, 2,3, respectively, for the main frequency of 20 ~ 1300Hz, 20 ~ 3400Hz, 20 ~ 1200Hz, at frequencies of 1300 ~ 3040Hz, 3400 ~ 4600Hz, 1200 ~ 2782Hz. Thus, as complete as possible to restore the original signal and the prevention of inter-frequency interference, the carrier frequency signal 3 desirable 19kHz, signal 2

Desirable carrier frequency of 12Hz, the carrier frequency signal l desirable 4kHz. Through further analysis of the frequency spectrum we can see: Signal 1 and Signal 2 is the two-aliasing of the high-frequency part of the part 2 of the amplitude of the signal is twice the signal 2, in order to reduce the impact of signal 2, in the multiplexing signal before the sampling point 2 relative to the spectrum shown in Figure 5.

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Can be seen from the chart, there are the ripple signal spectrum, so the use of Chebyshev type 2 (cheby2) band-pass filter, the signal of a band-pass filter design procedure

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The same token, can be designed to signal 2 and signal band-pass filter 3. Demodulation signal using the following procedure:

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Through the low-pass filter, to restore the original signals of sampling points in relation to time-domain waveform as shown in Figure 6. We can see from Figure 6, the signal waveforms are basically the same as the original signal, but in the vicinity of t = 0 some distortion, which is due to spectrum aliasing due to aliasing of the signal part of the spectrum are high-frequency part of the restoration of signal in the vicinity of Change the fastest peak. Is the highest frequency region, in part caused by high-frequency distortion, this is because the introduction of sound recording during the speech signal frequency is higher than the noise, so if there is no noise in the environment for the conduct of sound recordings, available for the restoration of the signal without distortion.

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4 Conclusion

In this paper, frequency division multiple access communication model, the theoretical analysis, in MAT-LAB environment, the use of programming models for the simulation of communication studies, and gives the 3-way signal simulation results modem. Simulation results show that the signal in frequency division multiplexing there is also the issue of frequency interference. In this regard, the authors used appropriate methods to increase the sampling frequency, to a greater extent in theto resolve this problem. As for the total elimination of the interference between spectrum, as well as further study and improvement.

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