Αν. Καθηγητής Γεώργιος Ευθύμογλου OFDM Transmission Αν. Καθηγητής Γεώργιος Ευθύμογλου Module Title

Introduction Orthogonal Frequency Division Multiplexing (OFDM) OFDMA Transmitter based on orthogonal sub-carriers Cyclic Prefix Examples OFDMA Subcarrier assignment based on channel’s frequency response OFDM design example Physical layer description of Long Term Evolution (LTE) Module Title

OFDM systems OFDM was invented more than 50 years ago… OFDM has been adopted by several standards: Asymmetric Digital Subscriber Line (ADSL) services. − IEEE 802.11a/g. − IEEE 802.16a. − Digital Audio Broadcast (DAB). − Digital Terrestrial Television Broadcast: DVB-T in Europe and ISDB in Japan. • Because OFDM is suitable for high data-rate systems, it is being considered for the following standards: − Fourth/Fifth generation (4G/5G) wireless services. − IEEE 802.11n, IEEE 802.16, and IEEE 802.20.

OFDM vs FDM

OFDM using N orthogonal subcarriers

Carriers with duration T sec (1/6) Example: BW = Fs = 20MHz and N=128 In the 20MHz spectrum, there are 128 narrowband sub-carriers. The duration of each subcarrier is The frequency separation between them is fixed at The 128 subcarrier frequencies are

Carriers with duration T sec (1/6) Spectrum of a single subcarrier with time duration Tu

Carriers with duration T sec (1/6) Example: BW=Fs=20MHz and Δf = 156.25 KHz The duration of each subcarrier is The number of subcarriers are given by The 128 subcarrier frequencies are

Carriers with duration T sec (3/6) The N subcarrier frequencies can be written as The discrete time signal is given by Theory: Two sinusoids that occupy time T will be orthogonal iff their frequency separation Δf is a multiple of !! Result:All N subcarriers sk with duration N samples are orthogonal

Carriers of limited duration (4/6) For example, assume Fs = 16 and N=16 (T=N/Fs=1sec) The subcarrier frequencies are The spectrum of subcarrier f10 is Sinc centered around f10 Notice that sidelobes have nulls at the frequencies

Carriers of limited duration (5/7) Spectrum of 16 samples of frequency 10 Hz with sampling freq. 16Hz Matlab code for previous plot: clear Fs=16; f0=10; N=16; x1T = exp(j*2*pi*f0*[0:N-1]/Fs); % exp(j 2 π f0 t) with t = n Ts x1F = fft(x1T, N*16); % 16 x resolution in frequency domain figure (1) plot([0:N*16-1]/16, x1F) xlabel('frequency bin') ylabel('amplitude') title('spectrum of 1 subcarrier with N samples')

Carriers of limited duration (6/6) When two sinusoids occupy time T=NTs, then if their frequency separation is then the sinusoids will be orthogonal (peak of 1 carrier happens at a null frequency of the other).

Spectrum of OFDM – orthogonal carriers If we take an FFT of the OFDM signal we see that when each carrier has a peak, all others are zero. This is expected, since the spectrum of each sub-carrier of length T has a zero at multiples of 1/T (peaks of other subcarriers)

Generation of OFDM sub-carriers using IDFT (1/5) All complex sinusoids transmitted for duration N*Ts=T will be orthogonal, since they differ in frequency between them by integer multiple of (1/T). Therefore, we can use each frequency to transmit one symbol X(k) (symbol is BPSK or QPSK or 16-QAM, etc). Then we can add them in parallel for duration T (N samples) and transmit them (A) However, eq. (A) is the IDFT of vector X (symbol vector)

Generation of OFDM sub-carriers using IDFT (2/5) Example: generate the 5th (k=5) subcarrier with frequency 5*0.15625 MHz and amplitude 0.5 (BW = Fs = 20 MHz and N = 128) Input signal X(k) is sampled with Fs and goes through a serial to parallel conversion. Input vector X = [zeros(1,5), 0.5, zeros(1,128-6)]T at input of IDFT of length 128. IFFT(X,N)

Generation of OFDM sub-carriers using IDFT (3/5) Implementation of eq. (A) using IFFT Channel Serial To Parallel IFFT Parallel To Cyclic Prefix Symbol Source (BPSK, QPSK, 16-QAM, 64-QAM)

Generation of OFDM sub-carriers using IDFT (4/5) OFDM transmission based on matrix multiplication: Each column of NxN matrix is a subcarrier. Transmit signal:

Generation of OFDM sub-carriers using IDFT (5/5) OFDM transmission based on N x N Fourier matrix (F = WNH ) where H is Hermitian transpose. Transmit signal: Received signal:

OFDM Transmitter/Receiver (1/3) Therefore, instead of transmitting X(k) k=0,1,…,N-1 symbols serially, each one with time Ts (for total time NTs=T), in OFDM, we transmit for time T all of them in parallel (signal given by eq. A) The OFDM transmitter-receiver in block diagram is given below

OFDM Transmitter/Receiver (2/3) Το IDFT δίνει το OFDM symbol που αποτελείται από τη σειρά μήκους Ν, όπου OFDM σύμβολο ονομάζουμε την έξοδο του IFFT: δηλαδή όλα τα Ν δείγματα αποτελούν 1 OFDM symbol. Στο δέκτη, παίρνοντας το DFT του λαμβανομένου σήματος ανακτούμε τα αρχικά σύμβολα της ψηφιακής διαμόρφωσης Χ.

OFDM Transmitter/Receiver (3/3) Tx – Rx for OFDM transmission over a multipath fading channel.

OFDM transmitter with encoder and interleaver Block diagram of 802.11a/g transceiver architecture The sequence of interleaved bits is mapped into a sequence of modulation symbols, e.g., 16-QAM. Therefore, 4 consecutive coded bits at the encoder output will be separated and each coded bit will combine with 3 other bits and will be sent with a different symbol, that is, it will be sent with a different subcarrier.

Coded OFDM Problem solution

Frequency selective channel Multipath propagation results in frequency selective fading. OFDM solution to maintain subcarrier orthogonality is Cyclic Prefix

Wireless Multipath Channel Έστω η είσοδος στο κανάλι είναι η ακολουθία εκπομπής με μήκος Ν και ένα διακριτού χρόνου κανάλι με κρουστική απόκριση με μήκος L+1 = τmax/Τs, όπου τmax είναι το maximum channel delay spread και Ts (=1/Fs) είναι το sampling time των δειγμάτων του σήματος εκπομπής x(n).

Cyclic Prefix (1/5) Το cyclic prefix του ορίζεται ως δηλαδή αποτελείται από τις τελευταίες M τιμές του . Για κάθε ακολουθία εκπομπής μήκους Ν, αυτά τα M δείγματα μπαίνουν στην αρχή της ακολουθίας εκπομπής. Αυτό δημιουργεί μία νέα ακολουθία μήκους Ν+M: x[N-M] x[N-M+1] … x[N-1] x[0] x[1] x[2] ... x[N-M-1] x[N-M] x[N-M+1]… x[N-1]

Cyclic Prefix (2/5) OFDM symbol with cyclic prefix Total OFDM symbol time is Tu + Tg

Cyclic Prefix (3/5) Έστω ότι το είναι είσοδος στο κανάλι πολλαπλών διακριτών διαδρομών (ισοδύναμο με ένα FIR φίλτρο). Η έξοδος θα είναι: όπου η τρίτη ισότητα ισχύει για M>L επειδή για

Cyclic Prefix (4/5) Επομένως με την προσθήκη του cyclic prefix στην αρχή του καναλιού, η γραμμική συνέλιξη y[n] που δίνει την έξοδο για γίνεται κυκλική συνέλιξη. Παίρνοντας επομένως στο δέκτη το DFT του y[n] (χωρίς θόρυβο) έχουμε: και επομένως, αν γνωρίζουμε το DFT{h}, τα σύμβολα εκπομπής μπορούν να βρεθούν στο δέκτη με μία απλή διαίρεση:

Cyclic Prefix (5/5) Άρα, γνωρίζοντας τα Υ, Η, το Χ βρίσκεται με απλή διαίρεση

Ισοδύναμο Μοντέλο στη Συχνότητα (1/2)

Ισοδύναμο Μοντέλο στη Συχνότητα (2/2) Η ανάκτηση γίνεται στο πεδίο της συχνότητας (στο δέκτη μετά από τον FFT). Η ανάκτηση γίνεται με απλή αντιστροφή διαύλου (Zero Forcing linear receiver)

ZF and MMSE OFDM receiver Zero Forcing MMSE where is the k-th element of the DFT of the channel impulse response is the variance of the noise.

ZF and MMSE OFDM receiver in Matlab switch equalizer case 'ZF' EstimatedSignalInFrequencyDomain= ReceivedSignalInFrequencyDomain./ChannelInFrequencyDomain; case 'MMSE' ReceivedSignalInFrequencyDomain./ (ChannelInFrequencyDomain+(sum(abs(FadedSignal).^2)/10^(SNR/10))/length(FadedSignal)); end

OFDM transceiver in Matlab clear; N = 16; % Number of subcarriers. M = 4; % Length of Cyclic Prefix a = randsrc(1, N); % Generate BPSK symbols. data = ifft(a); % OFDM transmitter % insert cyclic prefix tx=[data(N-M+1):data(N), data]; h=[(randn(1,1)+i*randn(1,1)), (randn(1,1)+i*randn(1,1)), ... (randn(1,1)+i*randn(1,1))]/sqrt(2); % random channel with 3 paths % channel impulse response with length < M=4 rx = conv(h, tx); % linear convolution with channel impulse response

OFDM transceiver in Matlab for i=1:N rx_data(i) = rx(i+M); % cyclic prefix removed end f = fft(rx_data, N); % DFT at receiver side h_dft = fft(h, N); % DFT of channel response f_rx = f./h_dft; % Data recovery with Channel estimation % (Frequency equalization) errors = sum(a -real(f_rx)) %Compare rx with tx data symbols

Cyclic Prefix deletes ISI Παρατηρήστε ότι η , , έχει μήκος Ν+Μ, όμως τα πρώτα Μ δείγματα , δεν χρειάζονται για να ανακτήσουμε το , . Αυτό είναι ιδιαίτερα βολικό γιατί τα πρώτα L από τα Μ δείγματα θα έχουν Inter-Symbol Interference (ISI) από τα τελευταία δείγματα του προηγούμενου μπλοκ (λόγω των καθυστερημένων διαδρομών διάδοσης στο κανάλι). Prefix Data Block Prefix Data Block Prefix … ISI ISI ISI M N

Effect of CP length on SER Multipath channel h=[h(1),0, h(2),h(3),0, h(4)] with power delay profile (PDP) p=[0.35, 0, 0.25,0.25, 0, 0.15] Time delay spread of channel: length(h)*Ts = 6*Ts (Ts=1/Fs) Error Floor is observed only when M < L, due to Inter-Carrier Interference (ICI) (which increases as the signal power (SNR) increases).

Effect of wireless channel Intersymbol interference in single carrier systems due to multipath propagation with channel delay spread τΜΑΧ >> symbol time Ts ( symbols overlap!!!)

Symbol times in one OFDM symbol OFDM increases the modulation symbol time duration by N times !!! Ts=TOFDM=N*T where T=1/BW, frequencies that differ by Δf = 1/TOFDM and N=BW/Δf

OFDM example Using single carrier with data rate of 10 Mbps with QPSK modulation (2 bits per symbol, BW=5MHz) gives a symbol rate Rs = 5 Msymbols/sec or symbol time Ts = 1/(5M sym/sec) = 0.2 μseconds. With a bandwidth of 5 MHz, if we have an OFDM system with 1000 carriers, the OFDM symbol time is TOFDM= 1/Δf = 1/(5MHz/1000) = 200 μseconds. At the speed of light, an object in an urban environment (typically 1 Km away) generates a delay of 6.6 μsec. This reflected signal would be completely out of sync with the direct signal and will affect 6.6/0.2 = 33 symbols with single carrier. However, for OFDM, the delay of 6.6 μseconds is only 1/30th of the OFDM symbol duration TOFDM =200 μseconds.

CALCULATING THE NUMBER OF SUBCARRIERS BASED ON MULTIPATH DELAY SPREAD Περιορισμοί στο Φασματικό Πεδίο Το μοντέλο καναλιού Vehicular Β ITU-R, παρουσιάζει τιμές καθυστέρησης έως 20 μsec, για κινητά περιβάλλοντα. Ο σχεδιασμός της απόστασης Δf των υπο-φερόντων απαιτεί flat fading για κάθε υπο-φέρον ακόμα και για τις χειρότερες τιμές καθυστέρησης των 20 μsec. Το coherence bandwidth, δηλαδή το εύρος ζώνης που παρουσιάζει την ίδια διάλειψη, υπολογίζεται να είναι περίπου 10KHz: Περιορισμοί στο Χρονικό πεδίο Η μέγιστη ταχύτητα για την υποστήριξη κινητικότητας είναι 125Km/hr. Η μέγιστη μετατόπιση Doppler στα 3.5GHz είναι: Χρησιμοποιώντας ένα εύρος ζώνης υπoφέροντος ίσο με 10KHz, η ισχύς Διακαναλικής Παρεμβολής (InterCarrier Interference) που αντιστοιχεί στην παραπάνω μετατόπιση Doppler φαίνεται ότι περιορίζεται στο -27dB.

Estimating data rates in OFDM For an OFDM system with 192 subcarriers and Δf = 156.25 KHz, the useful symbol duration is Assume a CP with duration TCP = (¼)TOFDM = 0.8 μsec. The number of coded bits carried by an OFDM symbol are 192 *k where k = bits/modulation symbol.

Estimating data rates in OFDM The information bit rate achieved depends on the modulation and channel coding rate used in each subcarrier and is given by Numerical example using QPSK and R=1/2

Estimating data rates in OFDM CAPACITY ANALYSIS OFDM BW efficiency (b/s/Hz) 0,69 Modln+coding efficiency (b/s/Hz) 0,50 1,00 1,50 2,00 3,00 4,00 4,50 Overall PHY layer efficiency, (b/s/Hz) 0,35 1,04 1,38 2,07 2,76 3,11 User Data Rate, Mbps 1,21 2,42 3,63 4,84 7,26 9,68 10,89 (BW=3.5 MHz) OFDM Bandwidth efficiency' N_fft = Number of OFDM tones 256 N_data = Number of data tone 192 n = Sampling factor 8/7=1,152 Guard band efficiency (192*8/7) /256=0,864 Cyclic prefix guard time factor (Tg/Tb) 0,250 Guard time efficiency 1/(1+0,250)=0,8 OFDM Bandwidth efficiency factor (downlink) 0,864*0,8=0,691 OFDM Bandwidth efficiency factor (uplink) 0,691

Received OFDM symbol and channel Παίρνοντας επομένως στο δέκτη το DFT του y[n] (χωρίς θόρυβο) έχουμε: Επομένως, τo k σύμβολo εκπομπής εμφανίζεται στην k έξοδο του DFT πολλαπλασιασμένο με την απόκριση του πολυδιαδρομικού καναλιού στην συχνότητα

PDF of H(k), k=0,1,…,N-1 Παρατηρήστε ότι η απόκριση συχνότητας της κρουστικής απόκρισης ενός πολυδιαδρομικού καναλιού είναι όπου L είναι το μήκος της κρουστικής απόκρισης τmax είναι η μέγιστη καθυστέρηση καναλιού (maximum delay spread) H δειγματοληψία της Η(ω) για ω=2πk/N, (ισοδυναμεί στα υποφέροντα fk=kFs/N) , είναι ο DFTN{h(n)}, δηλαδή

Multipath channel in the frequency domain Show that the multipath channel results in selective fading clear; Fs = 10*10^6; % sampling frequency AND signal bandwidth L=3; % multipath fading N=64; % total number of carriers – FFT length p = [0.5, 0.3, 0.2]; % declare power delay profile h(1) = sqrt(p(1))*(randn(1,1)+i*randn(1,1))/sqrt(2); h(2) = sqrt(p(2))*(randn(1,1)+i*randn(1,1))/sqrt(2); h(3) = sqrt(p(3))*(randn(1,1)+i*randn(1,1))/sqrt(2);

Multipath channel in the frequency domain h = [h(1), 0, h(2), 0, h(3)]; % consider the multipath delay profile H = fft(h, N); % frequency response of last channel response b = abs(H); % magnitude of frequency response plot(b, ‘-o’) xlabel('subcarrier index') ylabel('frequency response')

Multipath channel in the frequency domain Παρατηρήστε ότι η απόκριση συχνότητας της κρουστικής απόκρισης με δειγματοληψία στις ψηφιακές γωνιακές συχνότητες ω = 2πk/N, , (ισοδύναμα αναλογικές συχνότητες f= kFs/N, ) είναι ο DFTN{h(n)}, δηλαδή έχει διαφορετικά πλάτη στα διάφορα k (υποφέροντα)  selective frequency fading !!! Αυτό το συμπέρασμα χρησιμοποιείται για την ανάθεση υποφερόντων σε διαφορετικούς χρήστες στο σύστημα πολλαπλής πρόσβασης χρηστών OFDM Access (OFDMA).

Multipath channel in the frequency domain Κάθε χρήστης θα έχει μία απόκριση καναλιού, όπως φαίνεται στο παρακάτω σχήμα: subchannel frequency magnitude carrier channel

Resource (frequency bins) allocation Ο Σταθμός Βάσης γνωρίζει την απόκριση συχνότητας του καναλιού κάθε χρήστη και προσπαθεί να δώσει υποφέροντα k {0,1,…, N-1} σε κάθε χρήστη στα οποία το πλάτος έχει υψηλές τιμές. User 1 User K frequency magnitude Base Station - has knowledge of each user’s channel state information thru ideal feedback from the users User 2 . . .

OFDM vs OFDMA Subchannelization is the method that differentiates OFDMA with OFDM. The available subcarriers within the total bandwidth can be divided into several groups of subcarriers called subchannels. Subchannels can be assigned to the users on a logical procedure based on user demands and channel conditions.

Subchannels in OFDM systems Subchannelization in Fixed WiMAX is done in the uplink direction only (subscriber station to base station). In the downlink direction, all the subcarriers (i.e., 192) are assigned to the base station. In the uplink direction, 16 subchannels are defined, of which any number (1, 2, 4, 8, or 16) can be assigned to a subscriber station. Only one subscriber station can transmit on a particular subchannel at one time. As there are 192 data subcarriers, one subchannel consists of 192/16 =12 subcarriers. This implies that a subscriber station can transmit at bit rates that are 1/16 the bit rates of one OFDM symbol.

Resource (frequency bins) allocation Ο τρόπος με τον οποίο κάθε χρήστης επιτυγχάνει να στείλει τα σύμβολα του σε συγκεκριμένα υποφέροντα (από τα Ν υποφέροντα σε ένα εύρος φάσματος 0 – Fs (Hz)), είναι να εισάγει τα σύμβολα εκπομπής μόνο στις εισόδους του IDFT που αντιστοιχούν στα υποφέροντα εκπομπής και 0 αλλού. Π.χ. για να στείλει δεδομένα στα πρώτα 8 υποφέροντα (από Ν=64), 8 σύμβολα εκπομπής θα εισέλθουν στις εισόδους 0-7 ενός IDFT με μήκος (αριθμό εισόδων) Ν=64. Με αυτό τον τρόπο, κάθε χρήστης εκπέμπει σε διαφορετικά υποφέροντα. Στο Δέκτη, χρησιμοποιείται ένας DFT με μήκος Ν, ενώ κάθε χρήστης λαμβάνει ΜΟΝΟ τα σύμβολα που του αντιστοιχούν, δηλαδή στο προηγούμενο παράδειγμα, θα “πάρει” μόνο τα πρώτα 8 σύμβολα (από τα Ν=64) της εξόδου του DFT. Ένας δεύτερος χρήστης μπορεί να λάβει τα επόμενα 8, κ.ο.κ.

Example of OFDMA with 2 users Tx 1 Tx 2 IFFT(X,N) First N/2 symbols belong to #1 Next N/2 symbols belong to #2 FFT(Y,N) IFFT(X,N)

Εφαρμογή Θέλουμε να σχεδιάσουμε ένα OFDM σύστημα με fc=2.5GHz, BW < 20MHz που να μεταφέρει δεδομένα με ρυθμό Rb = 10.24Mbps και με ρυθμό κωδικοποίησης (FEC) ρ = 1/2. H μέγιστη ταχύτητα του δέκτη είναι vmax = 216km/h και ο δίαυλος έχει τmax = 8μsec. Θέλουμε επίσης για τη χρήσιμη διάρκεια του OFDM συμβόλου να ισχύει 5τmax ≤ Tsym ≤ 0.03Tcoh όπου Coherence time Τcoh του καναλιού είναι η χρονική διάρκεια στην οποία το κανάλι παραμένει σταθερό.

Εφαρμογή

Εφαρμογή Χωρίς OFDM, 82 διαδοχικά σύμβολα QPSK επηρεάζονται από ISI

Frequency selective channel Multipath propagation results in frequency selective fading. OFDM solution to maintain subcarrier orthogonality is Cyclic Prefix

OFDM transmission Consider a time-discrete (sampled) OFDM signal where it is assumed that the sampling rate fs is a multiple of the subcarrier spacing Δf fs = 1/Ts = N • Δf As Nc • Δf can be seen as the nominal bandwidth of the OFDM signal, this implies that N should exceed Nc with a sufficient margin. N/Nc, is the over-sampling of the time-discrete OFDM signal.

OFDM transmission parameters As an example, for 3GPP LTE the number of subcarriers Nc is approximately 600 in the case of a 10 MHz spectrum allocation. The IFFT size can then, for example, be selected as N = 1024. This corresponds to a sampling rate fs = N • Δf = 15.36 MHz, where Δf = 15 kHz is the LTE subcarrier spacing. OFDM transmission parameters The subcarrier spacing Δf. The number of subcarriers Nc, which, together with the subcarrier spacing, determines the overall transmission bandwidth of the OFDM signal. The cyclic-prefix length TCP. Together with the subcarrier spacing Δf = 1/Tu, the cyclic-prefix length determines the overall OFDM symbol time T = TCP + Tu or, equivalently, the OFDM symbol rate.

OFDM demodulation Recover the modulation symbols

Coded OFDM Problem solution

Frequency Interleaving Channel coding implies that each bit of information to be transmitted is spread over several, often very many, code bits. If these coded bits are then, via modulation symbols, mapped to a set of OFDM subcarriers that are well distributed over the overall transmission bandwidth of the OFDM signal each information bit will experience frequency diversity in the case of transmission over frequency selective channel Distributing the code bits in the frequency domain, is referred to as frequency interleaving.

OFDMAccess Downlink: in each OFDM symbol interval, different subsets of the overall set of available subcarriers are used for transmission to different terminals. Uplink: in each OFDM symbol interval, different subsets of the overall set of subcarriers are used for data transmission from different terminals

DFT-Spread OFDM A block of M modulation symbols from some modulation alphabet, for example QPSK or 16QAM, is first applied to a size-M DFT. The output of the DFT is then applied to consecutive inputs (subcarriers) of an OFDM modulator where, in practice, the OFDM modulator will be implemented as a size-N inverse DFT (IDFT) with N > M and where the unused inputs of the IDFT are set to zero.

DFTS-OFDM Receiver Recover the modulation symbols

User Multiplexing with DFTS-OFDM Transmit spectrum

LTE Radio Access In the time domain, different time intervals within LTE are expressed as multiples of a basic time unit Ts = 1/30720000. The radio frame has a length of 10 ms (Tframe = 307200 ・ Ts). Each frame is divided into ten equally sized subframes of 1 ms in length (Tsubframe = 30720 ・ Ts). Scheduling is done on a subframe basis for both the downlink and uplink. Each subframe consists of two equally sized slots of 0.5 ms in length (Tslot = 15360 ・ Ts). Each slot in turn consists of a number of OFDM symbols which can be either seven (normal cyclic prefix) or six (extended cyclic prefix)

LTE Radio Access Frame structure for LTE in FDD mode (Frame Structure Type 1).

LTE Radio Access The useful symbol time is Tu = 2048 × Ts ≈ 66.7 μs. For the normal mode, the first symbol has a cyclic prefix of length TCP = 160 × Ts ≈ 5.2 μs. The remaining six symbols have a cyclic prefix of length TCP = 144 × Ts ≈ 4.7 μs. The reason for different CP length of the first symbol is to make the overall slot length in terms of time units divisible by 15360. For the extended mode, the cyclic prefix is TCP-e = 512 × Ts ≈ 16.7 μs. The CP is longer than the typical channel delay spread of a few microseconds. The normal cyclic prefix is used in urban cells and high data rate applications while the extended cyclic prefix is used in special cases like multi-cell broadcast and in very large cells (e.g. rural areas, low data rate applications).

LTE Radio Access In the frequency domain, the number of sub-carriers N ranges from 128 to 2048, depending on channel bandwidth. N= 512 and 1024 correspond to 5 and 10 MHz, respectively, being most commonly used in practice. The sub-carrier spacing is Df = 1/Tu = 15 kHz. The sampling rate is fs = Df ・ N = 15000 N. This results in a sampling rate that’s multiple or sub-multiple of the WCDMA chip rate of 3.84 Mcps: LTE parameters have been chosen such that FFT lengths and sampling rates are easily obtained for all operation modes while at the same time ensuring the easy implementation of dual-mode devices with a common clock reference.

LTE Radio Access In a macrocell, the coherence bandwidth (depends on Doppler spread which depends on user velocity) of the signal is in the order of 1 MHz. Within the LTE carrier bandwidth of up to 20 MHz there are some sub-carriers that are faded and other are not faded. Transmission is done using those frequencies that are not faded. The transmission can be scheduled by Resource Blocks (RB) 1 RB = 12 consecutive sub-carriers, or 180 kHz, for the duration of one slot (0.5 ms), that is for (7 OFDM symbols, or 6 for 72 for extended CP) A Resource Element (RE) is the smallest defined unit which consists of one OFDM sub-carrier during one OFDM symbol interval. Each Resource Block consists of 12 ・ 7 = 84 Resource Elements in case of normal cyclic prefix (72 for extended CP).

LTE Radio Access Definition of Resource Blocks and Resource Elements.

Physical layer parameters for LTE in FDD mode