An Investigation Of The Improved Nyquist Pulses Families For OFDM Use Ligia Alexandra ONOFREI, Nicolae Dumitru ALEXANDRU “Ştefan cel Mare” University of Suceava, str. Universităţii no.13, RO-720225, Suceava, onofreial@eed.usv.ro , “Gh. Asachi” Technical University of Iaşi, , Bd. Carol I, no 11, RO-700506 Iaşi, nalex@etc.tuiasi.ro Abstract: The new families of Nyquist pulses recently proposed and studied [15, 16, 17, 18] are investigated for the OFDM use, to reduce the sensitivity of the OFDM systems to the frequency offset. The results presented in this paper are comparable or outperform the recently found pulses [2, 3, 4, 5, 8, 9] in terms of the intercarrier interference (ICI) power. I. INTRODUCTION OFDM (Orthogonal Frequency Division Multiplexing) is a multi-carrier transmission technique used in digital communications systems. This technique is built on the principle that the modulated signals are orthogonal so they do not interfere with each other. This paper is focused on the problem of reducing the ICI power in transmission over OFDM systems. OFDM is very sensitive to carrier frequency offset caused by the jitter of carrier wave and phase errors between the transmitter and receiver. Recent papers have reported and examined new families of pulses which are intersymbol interference (ISI)- free [15], [16], [17], [18]. In the sequel we present and examine the employment of new ISI-free pulses in an OFDM system. II. SYSTEM MODEL AND ICI ANALYSIS The complex envelope of one radio frequency (RF) N- subcarrier OFDM block with pulse-shaping [10] is expressed as: () () ∑ - = = 1 0 2 2 N k t f j k t f j k c e t p a e t x π π (1) where: 1 - = j , c f is the carrier frequency, k f is the subcarrier frequency of the k-th subcarrier, () t p is the time- limited pulse shaping function and k a is the data symbol transmitted on the k-th subcarrier and has mean zero and normalized average symbol energy; data symbols are uncorrelated. Frequency offset, ( ) 0 ≥ ∆ ∆ f f , and phase error θ , are introduced during transmission because of channel distortion or receiver crystal oscillator inaccuracy. The average ICI power, averaged across different sequences [8] is: ∑ - = ≠ ∆ +       - = 1 0 2 N k m k m ICI f T m k P σ (2) The average ICI power depends not only on the desired symbol location m , and the transmitted symbol sequence, but also on the pulse-shaping function at the frequencies ( ) ( ) ( ) 1 ,..., 1 , 0 , , / - = ≠ ∆ + - N k m k f T m k and the number of subcarriers. The ratio of average signal power to average ICI power is denoted SIR and expressed in equation (3). ( ) ( ) ( ) ∑ - = ≠ ∆ + - ∆ = 1 0 2 2 / / N k m k f T m k P F P SIR (3) III. A NEW FAMILY OF PULSE SHAPES The proposed new family of pulses are generated by low-pass filter with odd symmetry about the corresponding ideally band- limited cutoff frequency.[15], [16],[18]. In [15] a new family of Nyquist pulses has been proposed, which is defined as ( ) ( ) 2 1 2 1 + - = i i i i f B B f G α (4) For i - odd the pulses show odd symmetry around B and their definition can be: ( ) ( ) ( ) ( ) ( )      < + + ≤ ≤ - - ≤ = f B B f B f G B f S i α α α α 1 , 0 1 1 , 1 , 1 (5) For i - even, the flipped- technique is used and they are denoted flipped- ( ) f G [4]. In [16] the Nyquist filter characteristic is obtained from combining two types of characteristics with odd-symmetry. Here ) ( f G is the flipped-exponential characteristic proposed in [2] and ) ( f H i is the family of parabolic, cubic and quartic ramps proposed in [15]. 1-4244-0969-1/07/$25.00 ©2007 IEEE.