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EEE-752 Emerging Wireless Networks OFDM

Large bandwidth penalty since the subcarriers can’t have perfectly rectangular pulse shapes and still be time-limited. Very high quality (expensive) low pass filters will be required to maintain the orthogonality of the subcarriers at the receiver. | EEE-752 Emerging Wireless Networks OFDM Riaz Hussain FA08-PCE-003 rhussain@comsats.edu.pk Ph.D. Student Department of Electrical Engineering COMSATS Institute of Information Technology Islamabad, Pakistan Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM OFDM FDM Division on the basis of frequency But a very special case Orthogonal Carefully selecting the frequencies that are orthogonal In FDM Divided bands must be separate In fact should have some guard band To prevent cross-talk among modulated signals To prevent adjacent channel interference (ACI) In OFDM Bands can overlap Still signals can be separated No fear of ACI Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM Orthogonality & Vector Space Two vectors are orthogonal if their inner product (dot product) is zero e.g.: A = 4 B = 3i A . B = |A| |B| Cosθ = 0 In 2- or 3-dimensionl Euclidean space, two vectors are orthogonal if their dot product is zero, i.e. they make an angle of 90° or π/2 radians. e.g.: The vectors (1, 3, 2), (3, −1, 0), (1/3, 1, −5/3) are orthogonal to each other Since (1)(3) + (3)(−1) + (2)(0) = 0, (3)(1/3) + (−1)(1) + (0)(−5/3) = 0, (1)(1/3) + (3)(1) − (2)(5/3) = 0 Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM Orthogonality in OFDM In geometry orthogonal is synonym to perpendicular, but here orthogonality has no geometric significance When you trough a ball in a projectile does its horizontal velocity change? --- assuming no friction. NO Why Not? when gravitation force is acting on it? Example: Orthogonal CDMA Codes So in OFDM orthogonality signifies that no component of one signal contributes to the other signal Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM 0000 0001 0010 0011 0100 0101 0110 0111 Orthogonal Functions In mathematics, two functions f and g are called orthogonal if their inner product is zero. ∫ f*(x) g(x) dx = 0 Here, the star is the complex conjugate. f(x) = sin(ωx); g(x) = sin (2 ωx) f(x) = sin(ωx); g(x) = sin (3 | EEE-752 Emerging Wireless Networks OFDM Riaz Hussain FA08-PCE-003 rhussain@comsats.edu.pk Ph.D. Student Department of Electrical Engineering COMSATS Institute of Information Technology Islamabad, Pakistan Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM OFDM FDM Division on the basis of frequency But a very special case Orthogonal Carefully selecting the frequencies that are orthogonal In FDM Divided bands must be separate In fact should have some guard band To prevent cross-talk among modulated signals To prevent adjacent channel interference (ACI) In OFDM Bands can overlap Still signals can be separated No fear of ACI Riaz Hussain rhussain@comsats.edu.pk EEE752-EWN: OFDM Orthogonality & Vector Space Two vectors are orthogonal if their inner product (dot product) is zero e.g.: A = 4 B = 3i A . B = |A| |B| Cosθ = 0 In 2- or 3-dimensionl Euclidean space, two vectors are orthogonal if their dot product is zero, i.e. they make an angle of 90° or π/2 radians. .