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4 Conceptual OFDM System Multipath Channel and Cyclic Prefix - PowerPoint PPT Presentation

Feb 26, 2024 •616 likes •724 views

3G Evolution Outline OFDM Signals Chapter: 4 Conceptual OFDM System Multipath Channel and Cyclic Prefix Frequency Domain Model Channel Coding OFDM Transmission OFDM Parameters Channel Estimation User

  1. 3G Evolution Outline • OFDM Signals Chapter: 4 • Conceptual OFDM System • Multipath Channel and Cyclic Prefix • Frequency Domain Model • Channel Coding OFDM Transmission • OFDM Parameters • Channel Estimation • User Multiplexing and OFDMA • OFDM and Multicast Transmission • Summary Department of Electrical and Information Technology Johan Löfgren 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 1 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 2 Outline Subcarriers in Time Domain • OFDM Signals • Conceptual OFDM System • Multipath Channel and Cyclic Prefix • Frequency Domain Model • Channel Coding • OFDM Parameters • Channel Estimation • User Multiplexing and OFDMA • A number of different, orthogonal frequencies are transmitted • OFDM and Multicast Transmission simultaniously – Requires full period for each subcarrier • Summary • The number of carriers varies – Number of carriers denoted N c 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 3 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 4

  2. OFDM Symbol in Time Domain Subcarrier Orthogonality • In the frequency domain the orthognality is seen by zeros • Combined symbol looks random – All other subcarriers are zero when one subcarrier peaks – Gives good spectral effiency 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 5 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 6 Outline Conceptual Transmitter and Receiver − 2 π • OFDM Signals j f t 2 π e 0 j f t e 0 ∫ K • Conceptual OFDM System − 2 π j f t e 1 2 π j f t e 1 ∫ K • Multipath Channel and Cyclic Prefix x ( t ) r ( t ) • Frequency Domain Model • Channel Coding − π j 2 f t − π e N c 1 j 2 f t − e N c 1 ∫ K • OFDM Parameters • Channel Estimation • The transmitter can be seen as a number of single carrier system • User Multiplexing and OFDMA added together • OFDM and Multicast Transmission • The receiver is in the same way thought of as a set of independent • Summary correlators, one for each subcarrier 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 7 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 8

  3. IFFT/FFT Implementation Outline • In an actual OFDM system, there is only one transmit path • OFDM Signals – The structure with orthogonal subcarriers enables an • Conceptual OFDM System implementation using an IFFT that translates the different • Multipath Channel and Cyclic Prefix frequencies into a combined time signal • Frequency Domain Model • The receive side is also simplified • Channel Coding – An FFT unit replaces the N c correlators – The different subcarriers still have to be detected separately • OFDM Parameters • The IFFT/FFT implemenation requiers sufficient sampling • Channel Estimation – If so, the OFDM signal can be described mathematically as • User Multiplexing and OFDMA − − − N 1 N 1 N 1 ≤ ≤ ∑ ∑ ∑ ⎧ • OFDM and Multicast Transmission c c a 0 k N π Δ π π = = = = j 2 k fnT j 2 kn / N ' j 2 kn / N = ' ⎨ k c x x ( nT ) a e s a e a e a ≤ ≤ k n s k k ⎩ N k N 0 k = = = c k 0 k 0 k 0 • Summary 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 9 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 10 Multi-path Components Cyclic Prefix • Since the paths do not arrive simultaniously the orthogonality between the different subcarriers will be destroyed. • Often there are many reflections of a signal sent between a transmitter – When integrating over a full period the non-wanted subcarriers do not and a receiver cancel – These are seen as different paths for the signal to travel • The solution is to pro-long the symbol with a so called cyclic prefix (CP) • Different paths have different delays which might pose a probelm – Copy of the final piece of each sub-carrier inserted in beginning – Restores the orthogonality 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 11 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 12

  4. Outline Frequency Domain Model • OFDM Signals • With a sufficient CP it is possible to decouple the N c different • Conceptual OFDM System subcarrieres n * H H 0 0 • Multipath Channel and Cyclic Prefix 0 – Each subcarrier is treated separately • Frequency Domain Model – Independent channel n * H H • Channel Coding 1 1 parameters and noise 1 • OFDM Parameters • The receiver can equalize the independently • Channel Estimation – One-tap equalizer • User Multiplexing and OFDMA – Maximum Likelihood Estimation (per subsymbol) • OFDM and Multicast Transmission n * H H − − N 1 N 1 − c c N 1 • Summary c 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 13 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 14 Time Frequency Grid Outline • OFDM Signals • Conceptual OFDM System • Multipath Channel and Cyclic Prefix • Frequency Domain Model • Channel Coding • OFDM Parameters • Channel Estimation • User Multiplexing and OFDMA • The different subsymbols are thus time and frequency independent • OFDM and Multicast Transmission – They can be illustrated in a time frequencey grid • Summary – Each square is an indepedent subsymbol 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 15 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 16

  5. Fading and Channel Coding Outline • OFDM Signals • Conceptual OFDM System • Multipath Channel and Cyclic Prefix • Frequency Domain Model • Channel Coding • OFDM Parameters • Channel Estimation • User Multiplexing and OFDMA • Another effect due to multi path is frequency fading • OFDM and Multicast Transmission – Some frequencies will be much weaker due to canceling wave fronts • This may lead to poor SNR at certain frequencies • Summary – Problem in OFDM since each subcarrier have different data • Calls for channel coding – Channel coding spreads the information over many subcarriers 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 17 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 18 OFDM Parameters Subcarrier Bandwidth • The subcarrier bandwidth (or spacing) is affected by – Cost of cyclic prefix • When dessigning an OFDM system a number of different • A small spacing leads to long symbol duration parameters have to be considered hence less cost of cyclic prefix – Doppler spread – Subcarrier bandwidth • A small bandwidth leads to high relative doppler spread thus sensitivity to movement – Number of subcarriers • The system designer has to trade off these contradicting demands depending on the system – Length of cyclic prefix – How mobile is the system? – What data rates are needed? – et c. 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 19 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 20

  6. Number of subcarriers Cyclic Prefix Length • When the subcarrier separation is decided the number of • The cyclic prefix should be long enough to ensure subcarriers can be calculated orthogonality of the system – If the system has a limited bandwidth this will give the maximum – Multipath spread has to be considered number of subcarriers • Longer transmission distances normally call for longer CPs • Some slack is needed to ensure low enough out-of-band transmission – However at long distances, e.g. at cell edges, other effects may limit – If instead a certain througput is needed, the number of subcarriers the performance and therefore it is possible to allow a system which can be calculated based on constellation and coding is not completely orthogonal everywhere • This will then set the total bandwidth of the system • Some systems support multiple cyclic prefix lengths to handle different environments 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 21 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 22 Outline Channel Estimation • OFDM Signals • In the receiver the channel needs to be equalized so that the transmitted information can be correctly interpreted • Conceptual OFDM System • For this to be possible, the channel must be known • Multipath Channel and Cyclic Prefix • Since the channel constantly changes due to movement of • Frequency Domain Model both the mobile unit and the surroundings, the channel • Channel Coding cannot be known once and for all • OFDM Parameters • The channel has to be re-estimated every once in a while • Channel Estimation • So called pilots are used to estimate the channel • User Multiplexing and OFDMA – These are data that are known to the receiver • OFDM and Multicast Transmission • Summary 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 23 2009-03-19 3G Evolution - HSPA and LTE for Mobile Broadband 24

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