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Ofdm(tutorial)
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Ofdma

  1. 1. Orthogonal Frequency Division Multiple-Access Dr.Ayman Elezabi Yasser Monier 900062323
  2. 2. Orthogonal Multiplexing Principle and structure of OFDM symbols in practical standards  An OFDM signal consists of orthogonal subcarriers modulated by parallel data streams. Each baseband subcarrier is of the form  , (1)  where is the frequency of the th subcarrier. One baseband OFDM symbol (without a cyclic prefix) multiplexes modulated subcarriers:  (2)  where is the th complex data symbol (typically taken from a PSK or QAM symbol constellation) and is the length of the OFDM symbol. The subcarrier frequencies are equally spaced  (3)
  3. 3. Orthogonal Multiplexing Principle and structure of OFDM symbols in practical standards  The OFDM symbol (2) could typically be received using a bank of matched filters. However, an alternative demodulation is used in practice. T-spaced sampling of the in-phase and quadrature components of the OFDM symbol yields (ignoring channel impairments such as additive noise or dispersion)  , (4)
  4. 4. Effect of Carrier Frequency Offset and Sampling Time offset  At the front-end of the receiver OFDM signals are subject to synchronization errors due to oscillator impairments and sample clock differences. The demodulation of the received radio signal to baseband, possibly via an intermediate frequency, involves oscillators whose frequencies may not be perfectly aligned with the transmitter frequencies. This results in a carrier frequency offset. Figure 6 illustrates the front end of an OFDM receiver where these errors can occur. Also, demodulation (in particular the radio frequency demodulation) usually introduces phase noise acting as an unwanted phase modulation of the carrier wave. Carrier frequency offset and phase noise degrade the performance of an OFDM system.
  5. 5. Effect of Carrier Frequency Offset and Sampling Time offset  When the baseband signal is sampled at the A/D, the sample clock frequency at the receiver may not be the same as that at the transmitter. Not only may this sample clock offset cause errors, it may also cause the duration of an OFDM symbol at the receiver to be different from that at the transmitter. If the symbol clock is derived from the sample clock this generates variations in the symbol clock. Since the receiver needs to determine when the OFDM symbol begins for proper demodulation with the FFT, a symbol synchronization algorithm at the receiver is usually necessary. Symbol synchronization also compensates for delay changes in the channel.
  6. 6. Channel Estimation Algorithms  System Architecture
  7. 7. System Architecture
  8. 8. System Architecture (cont’d) 1. Input to time domain 2. Guard Interval 3. Channel 4. Guard Removal 5. Output to frequency domain 6. Output 7. Channel Estimation xn  IDFTXk n  0,1,2,...,N 1          x N n n N N       , , 1,..., 1 x n g g x n n N    , 0,1,..., 1 f y x n hn wn f f    yn  y n n  0,1,..., N 1 f Yk  DFTynk  0,1,2,...,N 1 Channel ICI AWGN           Y k  X k H k  I k  W k k N  0,1,..., 1       Y k  k  0,1,..., N 1 H k X k e e Estimated Channel
  9. 9. Pilot for Channel Estimation Time Carriers Time Carriers  Comb Type:  Part of the sub-carriers are always reserved as pilot for each symbol  Block Type:  All sub-carriers is used as pilot in a specific period
  10. 10. Block-type Channel Estimation  LS: Least Square Estimation   h X y where X diag x x x                     1 0 0 1 1 1 y . . . , ,..., N N LS y y
  11. 11. Comb-type Estimation     X k  X mL  l xp m l , 0          data l L inf . , 1,..., 1 Np pilot signals uniformly inserted in X(k) L=Number of Carriers/Np xp(m) is the mth pilot carrier value {Hp(k) k=0,1,…,Np} , channel at pilot sub-carriers Xp input at the kth pilot sub-carrier Yp output at the kth pilot sub-carrier LS Estimate       Y k p p k N   0,1,..., 1 p X k p H k LMS Estimate Yp(k) Xp(k) LMS + - e(k)
  12. 12. Interpolation for Comb-type  Linear Interpolation H k H mL l e e  Second Order Interpolation     l H k  H mL  l            l L H m L H m H m p p p e e   0 1                        c  c    c H p m c H p m c H p m                    l N c where / 1 0 1 1 1 , 2 1 1 1 1 , 0 , 2 1 1   
  13. 13. OFDMA, the multi user communication system.  The main motivation for adaptive subcarrier allocation in OFDMA systems is to exploit multiuser diversity. Although OFDMA systems have a number of subcarriers, we will focus temporarily on the allocation for a single subcarrier amongst multiple users for illustrative purposes.
  14. 14. principles that enable high performance in OFDMA: multiuser diversity and adaptive modulation. Multiuser diversity describes the gains available by selecting a user of subset of users that have “good” conditions. Adaptive modulation is the means by which good channels can be exploited to achieve higher data rates. OFDMA, the multi user communication system. Multiuser Diversity main motivation for adaptive subcarrier allocation in OFDMA systems is to exploit multiuser diversity. Although OFDMA systems have a number of subcarriers, we will focus temporarily on the allocation for a  Consider a K-user system, where the subcarrier of interest subcarrier amongst multiple users for illustrative purposes. experiences i.i.d. Rayleigh fading, that is, each user’s channel gain is independent of the others, and is denoted by hk. The probability density function (pdf) of user k’s channel gain p(hk) is given by Consider a K -user system, where the subcarrier of interest experiences i.i.d. Rayleigh fading, that is, user’s channel gain is independent of the others, and is denoted by hk . The probability density function user k’s channel gain p(hk ) is given by p(hk) = ( 2hke− h2 k if hk ≥ 0 0 if hk < 0. (6.1) suppose the base station only transmit to the user with the highest channel gain, denoted as hmax = h1, h2, · · · , hK } . It is easy to verify that the pdf of hmax is p(hmax) = 2K hmax ⇣ 1 − e− h2 m ax ⌘K− 1 e− h2 m ax . (6.2) 8
  15. 15. channel gain p(hk ) is given by ( 2hke− h2 k if hk ≥ 0 OFDMA, the multi user communication system. p(hk) = 0 if hk < 0.  Now suppose the base station only transmit to the user with base station only transmit to the user with the highest channel gain, hK the highest channel gain, denoted as hmax = max{h1,h2,··· ,hK}. It is easy to verify that the pdf of hmax is } . It is easy to verify that the pdf of hmax is p(hmax) = 2K hmax ⇣ 1 − e− h2 m ax ⌘K− 1 e− h2 m ax . 8
  16. 16. THANKS

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