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Analysis of Chirp Spread Spectrum System for Multiple Access International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 1 Issue 3, May - 2012 Analysis of Chirp Spread Spectrum System for Multiple Access Rajni Billa Pooja Sharma Javed Ashraf M. Tech Scholar M. Tech Scholar Asst. Professor Department of Electronics Department of Electronics Department of Electronics and Communication and Communication and Communication AFSET, Faridabad, India AFSET, Faridabad, India AFSET, Faridabad, India E-mail: E-mail: E-mail: [email protected] [email protected] [email protected] Abstract 1. Introduction This paper evaluates the performance of an efficient Through the years, the Federal Communication chirp spread spectrum multiple access technique. The Commission (FCC) managed the spectrum allocations technique is motivated by the inherent interference on a request-by-request basis; the FCC has realized that rejection capability of such spread-spectrum type it had no more spectra to allocate [5], which gave rise system, especially in circumstances where immunity to spread spectrum techniques. With the rapid against Doppler shift and fading due to multipath development in wireless communication, spread propagation are important. Linear chirp of different spectrum techniques and spread spectrum systems have chirp rates and phases spreads the modulated signal, received quite some attention. As a future that creates a pseudo-orthogonal set of spreading communication systems a spread spectrum system has codes. An efficient system for spread spectrum multiple the advantage of inherent detection protection due to access can be made by combining linear chirp their noise-like spectra, interference rejection, modulation with polar signaling, which reduces the multipath suppression, code division multiple access, multiple access interference. A simulation model has and high resolution ranging. Spread spectrum is a been outlined in MATLABTM and bit error rates over technique whereby a modulated waveform is fading channels in different Doppler environments, modulated (spread) a second time in such a way as to have been calculated when the coherence time is of the generate an expanded-bandwidth wideband signal by order of bit duration. Simulation results show that means of a code which is independent of the under proper selection of parameters; the proposed information message, and a synchronized reception technique performs approximately well in all flat with the code at the receiver is used for dispreading fading channels in terms of bit error rate. and subsequent data recovery [3]. The spread spectrum techniques are classified as direct sequence, carrier sense multiple access, chirp modulation, frequency Keywords: spread spectrum multiple access, chirp hopping, time hopping and hybrid spread spectrum spread spectrum, wireless network, MATLABTM, flat [12]. Chirp modulation or linear frequency modulation fading. was introduced by Winkler [8] in 1962. She suggested www.ijert.org 1 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 1 Issue 3, May - 2012 the use of one pair of linear chirps that have opposite conjunction with a good selection of the chirp chirp rates, for binary signalling. Chirp spread parameters. spectrum is a spread spectrum technique that uses 2. System Model wideband linear frequency modulated chirp pulses to The chirp spread spectrum for N users is shown in encode information. A chirp is a sinusoidal signal Figure 1. Let the transmitted power Pi of each user for its whose frequency increases or decreases over a certain amount of time [7]. Theoretically, chirp modulation is transmitted bit 푏푖 푡 ∈ {−1; +1 ⃒0 ≤ 푡 < 푇푏 } be same found to be superior in the partially coherent and Pi= Pt ⩝ i; where i =1, 2, … N and Tb denotes the bit frequency-selective fading cases over certain ranges of duration. On transmitter side the binary data sequence channel conditions [9]. Multi-user phased chirp spread modulates a linear chirp signal centered at some given spectrum systems was introduced by Khamy for carrier frequency fc i.e. multiple access [4]. In 1974, Cook [1] assigned pairs of 푥 푡 = 푐 푡 푏 푡 (1) linear chirps with different chirp rates to several users, 푖 푖 From the set of spreading signals each user is thus allowing multiple access within a common assigned a separate chirp signal ci(t). Spreading and up frequency band. The performance of chirp spread conversion to a carrier frequency fc is achieved by spectrum systems can still be further improved in the multiplication with one of the chirp signals. case of multiple access by means of polar signalling in 2 t Tb 2 cos 2πf t + iπ∆α + θ , 0 ≤ t < c T2 2 b ct t = 2 (2) t 1 t 1 1 Tb 2 cos 2π fct + M − i π∆α − + iπ∆α − + iπ∆α + θ , ≤ t < Tb Tb 2 Tb 2 4 2 where ∆훼 denotes the chirp rate and 휃 denotes the values of ∆훼 , the linear chirp would be too densely phase of the spreading signals. The chirp rate spaced in the joint time frequency domain. Thus parameter ∆훼 and the phase parameter 휃 have to be pseudo-orthogonal codes can’t be obtained and system selected carefully, as they heavily impact the overall may suffer from multiple access interference. system performance. In particular, the cross-correlation Chirp modulation uses the concept of OFDM, between two spreading chirps Ci(t) and Cj(t)can be where all N user channels are parallel-sloped slices of approximated by bandwidth in joint time-frequency domain. In this way it 1 푇 can be easily compared with TDMA and FDMA, in 휌푖푗 = 퐶푖(푡) 퐶푗 (푡) (3) 푇 0 which channels are parallel slices orthogonal to time and frequency axis. Which can be further reduced to Demodulation and detection can then be realized by sin (2휋 푖−푗 ) 1 푓표푟 푎푙푙 푖푛푡푒푟푔푒푟 푖 = 푗, an array of correlation receivers. Each receiver 휌 = (4) 푖푗 2휋(푖−푗 ) 0 푓표푟 푎푙푙 푖푛푡푒푔푒푟 푖 ≠ 푗 multiplies the received signal with its coherent, locally The chirp rate parameter is given by generated replica of spreading signal of unit energy and integrates this product over one symbol interval to 2퐵푇퐵 ∆훼 = (5) 푁 obtain the decision variable. 1 푇푠 For ∆훼 ≥ 1, this will usually yield a 푢푖 = 퐶푖 푡 푥 푡 푑푡 (6) 퐸푠 0 pseudo-orthogonal set of spreading codes. For smaller www.ijert.org 2 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 1 Issue 3, May - 2012 where Es is the energy ,Ts is symbol duration and x(t) is 3. Fading Channels transmitted signal. Finally a threshold detector estimates The mobile channel places fundamental the data symbol sent, simply by detecting the sign of the limitations on the performance of wireless decision variable ui. communication systems. Figure 1. Chirp spread spectrum system. Multi-path is a condition where the transmitted small-scale fading phenomenon. The Rayleigh radio signal is reflected by physical features/structures, distribution is commonly used to describe the statistical creating multiple signal paths between the base station time varying nature of the received envelope of a flat and the user terminal. These multipath signals can fading signal, or the envelope of an individual interfere with the desired signal and make it harder for multipath component. In the Rayleigh flat fading receiver to detect the original signal that was channel model, it is assumed that the channel induces transmitted. When the waves of multi-path signals are amplitude, which varies in time according to the out of phase, reduction in signal strength can occur. Rayleigh distribution. One such type of reduction is called a fade; the In micro-cellular environments, there usually phenomenon is known as "Rayleigh fading" or "fast exists a dominant line of sight (LOS) path in addition fading." The Rayleigh, Ricean and Nakagami are the to numerous diffused multipath components between most commonly used statistical models to represent www.ijert.org 3 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 1 Issue 3, May - 2012 the transmitter and receiver [14]. In such a case, the If the set of all possible bit variations is given by other faded signal components are superimposed on 퐵푖 = 푏푗 (푡) ∈ −1; +1 푗 = 1,2, … , 푁; 푗 ≠ 푖 , where the dominant component and the resultant signal independent user bit sequences with equally likely 0s amplitude follows Rician distribution with the ratio and 1s are assumed. It is easily seen that the bit error between the LOS and diffused components denoted by probability of user i for a fixed bit variation Bi is the Rice factor K. Rice fading is caused by 푁 퐵퐸푅 퐵푖 ; 훾푏 = 푄 2훾푏 1 − 푗 =1,푗 ≠푖 푏푗 푡 휌푖푗 (10) Doppler-shifted echoes with a Gaussian distribution, This expression allows us to apply the moment but in addition there is always a direct path from the Tx generating function technique for average error antenna to the Rx antenna. A received signal envelop probability derived in Section 6.4.3 [6]. In our case, we model, which allows for different degrees of fading find α =1 and severity for the desired as well as for interfering signal 푁 2 envelopes, and which is widely used to model many 푔 = 푔푖 퐵푖 = 1 − 푗 =1,푗 ≠푖 푏푗 푡 휌푖푗 (11) mobile radio environments, is the Nakagami-m The parameter g depends on the other user’s data distribution. The Nakagami-m distribution is a bits and the cross-correlation coefficients. Hence, it versatile statistical model, because it can model fading captures the effects of multiple access interference. amplitudes that experience either less or severe fading Smaller the g is, more the multiple access interference than that of Rayleigh variants. It sometimes fits present and higher the probability of bit error. Note that experimental data much better than a Rayleigh or this derivation for g is not strictly correct since it implies Rician distribution [11], [15].
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