Principles of Multicarrier Modulation and OFDM a

Transcription

1 Principles of Multicarrier Modulation and OFDM a Lie-Liang Yang Communications Research Group Faculty of Physical and Applied Sciences, University of Southampton, SO17 1BJ, UK. Tel: , Fax: lly@ecs.soton.ac.uk a Main reference: A. Goldsmith, Wireless Communications, Cambridge University Press, Southampton School of ECS, Univ. of Southampton, UK. 1/ 49

2 MC Modulation and OFDM - Summary Principles of multicarrier (MC) modulation; Principles of orthogonal frequency-division multiplexing (OFDM); Inter-symbol interference (ISI) suppression; Implementation challenges. Southampton School of ECS, Univ. of Southampton, UK. 2/ 49

3 Multicarrier Modulations - Introduction In multicarrier (MC) modulation, a transmitted bitstream is divided into many different substreams, which are sent in parallel over many subchannels; The parallel subchannels are typically orthogonal under ideal propagation conditions; The data rate on each of the subcarriers is much lower than the total data rate; The bandwidth of subchannels is usually much less than the coherence bandwidth of the wireless channel, so that the subchannels experience flat fading. Thus, the ISI on each subchannel is small; MC modulation can be efficiently implemented digitally using the FFT (Fast Fourier Transform) techniques, yielding the so-called orthogonal frequencydivision multiplexing (OFDM); Southampton School of ECS, Univ. of Southampton, UK. 3/ 49

4 Multicarrier Modulations - Application Examples Digital audio and video broadcasting in Europe; Wireless local area networks (WLAN) - IEEE802.11a, g, n, ac, ad, etc.; Fixed wireless broadband services; Mobile wireless broadband communications; Multiband OFDM for ultrawideband (UWB) communications; Main modulation scheme in the 4th generation cellular mobile communications systems (uplink SC-FDMA, downlink OFDMA); A candidate for many future generations (802.11ax, 5th generation cellular) of wireless communications systems. Southampton School of ECS, Univ. of Southampton, UK. 4/ 49

5 Multicarrier Modulations - Transmitter R/N bps Symbol s 0 g(t) Mapper s 0 (t) R bps Serial-to- Parallel Converter R/N bps Symbol Mapper s 1... g(t) cos(2πf 0 t) s 1 (t) cos(2πf 1 t) + s(t) R/N bps Symbol Mapper s N 1 g(t) s N 1 (t) cos(2πf N 1 t) Figure 1: Transmitter schematic diagram in general multicarrier modulations. Southampton School of ECS, Univ. of Southampton, UK. 5/ 49

6 Multicarrier Modulations - Principles Consider a linearly modulated system with data rate R and bandwidth B; The coherence bandwidth of the channel is assumed to be B c < B, so signals transmitted over this channel experience frequency-selective fading. When employing the MC modulations: the bandwidth B is broken into N subbands, each of which has a bandwidth B N = B/N for conveying a data rate R N = R/N; Usually, it is designed to make B N << B c, so that the subchannels experience (frequency non-selective) flat fading. In the time-domain, the symbol duration T N 1/B N of the modulated signals is much larger than the delay-spread T m 1/B c of the channel, which hence yields small ISI. Southampton School of ECS, Univ. of Southampton, UK. 6/ 49

7 An example Consider a MC system with a total passband bandwidth of 1 MHz. Suppose the channel delay-spread is T m = 20 µs. How many subchannels are needed to obtain approximately flat fading in each subchannel? The channel coherence bandwidth is B c = 1/T m = 1/ = 50 KHz; To ensure flat fading on each subchannel, we take B N = B/N = 0.1 B c << B c ; Hence, N = B/(0.1 B c ) = /5000 = 200 subcarriers. Southampton School of ECS, Univ. of Southampton, UK. 7/ 49

8 Multicarrier Modulations - Transmitted Signals s(t) = N 1 i=0 s i g(t) cos (2πf i t + φ i ) (1) where s i : complex data symbol (QAM, PSK, etc.) transmitted on the ith subcarrier; φ i : phase offset of the ith subcarrier; f i = f 0 + i(b N ): central frequency of the ith subcarrier; g(t): waveform-shaping pulse, such as raised cosine pulse. Southampton School of ECS, Univ. of Southampton, UK. 8/ 49

9 Amplitude 0 T Time Figure 2: Illustration of multicarrier modulated signals. Southampton School of ECS, Univ. of Southampton, UK. 9/ 49

10 Multicarrier Modulations - Receiver f 0 s 0 (t) + n 0 (t) Demodulator R/N bps cos(2πf 0 t) s(t) + n(t) f 1 s 1 (t) + n 1 (t) Demodulator R/N bps Parallel- to-serial Converter R bps... cos(2πf 1 t) f N 1 s N 1 (t) + n N 1 (t) Demodulator R/N bps cos(2πf N 1 t) Figure 3: Receiver schematic diagram in general multicarrier modulations. Southampton School of ECS, Univ. of Southampton, UK. 10/ 49

11 Overlapping MC f 0 f 1 f 2 f 3 f 4 f 5 f 6 f 7 The set of orthogonal subcarrier frequencies, f 0, f 1,..., f N 1 satisfy: 1 TN 0.5, if i = j cos(2πf i t + φ i ) cos(2πf j t + φ j )dt = T N 0 0, else (2) The total system bandwidth required is: B = N + 1 T N N/T N (3) Southampton School of ECS, Univ. of Southampton, UK. 11/ 49

12 Overlapping MC - Detection Without considering fading and noise, the received MC signal can be expressed as r(t) = N 1 i=0 s i g(t) cos (2πf i t + φ i ) (4) Assuming that the detector knows {φ i }, then, s j can be detected as ŝ j = = = TN 0 TN 0 N 1 i=0 =C r(t)g(t) cos (2πf j t + φ j ) dt ( N 1 i=0 s i TN N 1 i=0 where C is a constant. 0 s i g(t) cos (2πf i t + φ i ) ) g(t) cos (2πf j t + φ j ) dt g 2 (t) cos (2πf i t + φ i ) cos (2πf j t + φ j ) dt s i δ(i j) = C s j, j = 0, 1,..., N 1 (5) Southampton School of ECS, Univ. of Southampton, UK. 12/ 49

13 Fading Mitigation Techniques in MC Modulation Coding with interleaving over time and frequency to exploit the frequency diversity provided by the subchannels experiencing different fading; Frequency-domain equalization: When the received SNR is α 2 i P i, the receiver processes it as α 2 i P i /ˆα 2 i P i to reduce the fading; Precoding: If the transmitter knows that the channel fading gain is α i, it transmits the signals using power P i /ˆα 2 i, so that the received power is P i ; Adaptive loading: Mitigating the channel fading by adaptively varying the data rate and power assigned to each subchannel according to its fading gain. Southampton School of ECS, Univ. of Southampton, UK. 13/ 49

14 Implementation of MC Modulation Using DFT/IDFT Let x[n], 0 n N 1, denote a discrete time sequence. The N-point discrete Fourier transform (DFT) of {x[n]} is defined as X[i] =DFT{x[n]} 1 N 1 N n=0 x[n] exp ( j2πni ), 0 i N 1 (6) N Correspondingly, given {X[i]}, the sequence {x[n]} can be recovered by the inverse DFT (IDFT) defined as x[n] =IDFT{X[i]} 1 N 1 N i=0 X[i] exp ( ) j2πni, 0 n N 1 (7) N Southampton School of ECS, Univ. of Southampton, UK. 14/ 49

15 Implementation of MC Modulation Using DFT/IDFT When an input data stream {x[n]} is sent through a linear time-invariant discrete-time channel having the channel impulse response (CIR) {h[n]}, the output {y[n]} is given by the discrete-time convolution of the input and the CIR, expressed as y[n] = h[n] x[n] = x[n] h[n] = k h(k)x[n k] (8) Circular Convolution: when {x[n]} is a N-length periodic sequence, then the N-point circular convolution of {x[n]} and {h[n]} is defined as y[n] = h[n] x[n] = x[n] h[n] = k h(k)x[n k] N (9) which has the property DFT{y[n] = h[n] x[n]} = X[i]H[i], i = 0, 1,..., N 1 (10) Southampton School of ECS, Univ. of Southampton, UK. 15/ 49

16 Implementation of MC Modulation: Cyclic Prefix Cyclic Prefix Original Length N Sequence x[n µ], x[n µ + 1],..., x[n 1] x[0], x[1],..., x[n µ 1] x[n µ], x[n µ + 1],..., x[n 1] Append Last µ Symbols to Beginning Figure 4: Cyclic prefix of length µ. The original N-length data block is x[n] : x[0],..., x[n 1]; The µ-length cyclic prefix block is x[n µ],..., x[n 1], which is constituted by the last µ symbols of the data block {x[n]}; The actually transmitted data block is length N + µ, which is x[n] : x[n µ],..., x[n 1], x[0], x[1],..., x[n 1] Southampton School of ECS, Univ. of Southampton, UK. 16/ 49

17 Implementation of MC Modulation: Cyclic Prefix Then, when { x[n]} is input to a discrete-time channel having the CIR h[n] : h[0],..., h[l], the channel outputs are Therefore, y[n] = x[n] h[n] = L h[k] x[n k] = k=0 L h[k]x[n k] N k=0 =x[n] h[n], n = 0, 1,..., N 1 (11) Y [i] = DFT{y[n] = x[n] h[n]} = X[i]H[i], i = 0, 1,..., N 1 (12) When {Y [i]} and {H[i]} are given, the transmitted sequence can be recovered as { x[n] = IDFT X[i] = Y [i] } { } DFT{y[n]} = IDFT, n = 0, 1,..., N 1 (13) H[i] DFT{h[n]} Southampton School of ECS, Univ. of Southampton, UK. 17/ 49

18 OFDM Using Cyclic Prefixing - An Example Consider an OFDM system with total bandwidth B = 1 MHz and using N = 128 subcarriers, 16QAM modulation, and length µ = 8 of cyclic prefix. Then The subchannel bandwidth is B N = B/128 = khz; The symbol duration on each subchannel is T N = 1/B N = 128 µs; The total transmission time of each OFDM block is T = T N + 8/B = 136 µs; The overhead due to the cyclic prefix is 8/128 = 6.25%; The total data rate is 128 log /(T = ) = 3.76 Mbps. Southampton School of ECS, Univ. of Southampton, UK. 18/ 49

19 OFDM - System Structure Transmitter processing X N IDFT x N P/S CP Signal shaping g(t) Channel Receiver processing Y N DFT y N S/P CP removing Matchedfiltering g ( t) Figure 5: Schematic block diagram of the transmitter/receiver for OFDM systems using IDFT/DFT assisted multicarrier modulation/demodulation and cyclicprefixing (CP). Southampton School of ECS, Univ. of Southampton, UK. 19/ 49

20 OFDM - Transmitter X[0] x[0] R bps QAM Modulation X Serial-to- Parallel Converter X[1] IFFT x[1] Add Cyclic Prefix, and Parallelto-Serial Converter D/A x(t) s(t) X[N 1] x[n 1] cos(2πf 0 t) Figure 6: Transmitter of OFDM with IFFT/FFT implementation. Southampton School of ECS, Univ. of Southampton, UK. 20/ 49

21 OFDM - Receiver Y [0] y[0] R bps QAM Demod Y Remove Prefix, and Serial-to- Parallel Converter Parallelto-Serial Converter Y [1] FFT y[1] y[n] LPF and A/D r(t) Y [N 1] y[n 1] cos(2πf 0 t) Figure 7: Receiver of OFDM with IFFT/FFT implementation. Southampton School of ECS, Univ. of Southampton, UK. 21/ 49

22 OFDM - Transmitted Signal Let the N data symbols (thought as in the frequency-domain) to be transmitted on the N subcarriers within a DFT period is given by m=0 X = [X 0, X 1,..., X N 1 ] T (14) After the IDFT on X, it generates N time-domain coefficients expressed as x n = 1 N 1 ( X m exp j 2πmn ), n = 0, 1,..., N 1 (15) N N Let F be a fast Fourier transform (FFT) matrix given by the next slide. Then, we can express x = [x 0, x 1,..., x N 1 ] T as x = F H X (16) Southampton School of ECS, Univ. of Southampton, UK. 22/ 49

23 FFT/IFFT Matrices FFT matrix: F = 1 N W N WN 2 W N 1 N W N 1 N W 2(N 1) N W (N 1)2 N (17) where W N = e j2π/n ; IFFT matrix is given by F H ; Main Properties: F H F = FF H = I N. Southampton School of ECS, Univ. of Southampton, UK. 23/ 49

24 OFDM - Transmitted Signal After adding the cyclic-prefix (CP) of length µ, x is modified to x of length N + µ; The normalized transmitted base-band OFDM signal is formed as where s(t) = N 1 n= µ =A x n ψ Tψ (t nt ψ ) N 1 m=0 A: Constant related to the transmit power; X m exp(j2πf m t), µt ψ t < T N (18) ψ Tψ (t): time-domain waveform construction function, such as the sinc( )-function; T ψ : chip-duration and T ψ 1/B. Southampton School of ECS, Univ. of Southampton, UK. 24/ 49

25 OFDM - Representation of Received Signals When the OFDM signal of (18) is transmitted over a frequencyselective fading channel with the CIR h n, 0 n L as well as Gaussian noise, the discrete-time received observation samples in correspondence to x 0, x 1,..., x N 1 are obtained from sampling the received signal, which can be expressed as y n = x n h n + v n = L k=0 h k x n k + v n, n = 0, 1,..., N 1 (19) Let y = [y 0, y 1,, y N 1 ] T. Then, it can be shown that y can be expressed as y = H x + v (20) Here, it is very important to represent the matrix H. Southampton School of ECS, Univ. of Southampton, UK. 25/ 49

26 OFDM - Representation of Received Signals (Linear Convalution) x L x 1 x 0 x 1 x 2 x 3 x 4 hl h 1 h hl h 1 h hl h 1 h hl h 1 h hl h 1 h v 0 v 1 v 2 v 3 v 4 = = = = = y 0 y 1 y 2 y 3 y 4 Southampton School of ECS, Univ. of Southampton, UK. 26/ 49

27 OFDM - Representation of Received Signals (Another Way) x L x 1 x 0 x 1 x 2 x 3 x 4 h 0 h 0 x 0 h 0 x 1 h 0 x 2 h 0 x 3 h 0 x 4 h 1 h 1 x 1 h 1 x 0 h 1 x 1 h 1 x 2 h 1 x h L h L x L h L x L+1 h L x L+2 h L x L+3 h L x L+4 +v 0 +v 1 +v 2 +v 3 +v 4 = = = = = y 0 y 1 y 2 y 3 y 4 Southampton School of ECS, Univ. of Southampton, UK. 27/ 49

28 OFDM - Representation of Received Signals From the previous slide, we can see that y 0 h L x L + h L 1 x L h 0 x 0 + v 0 y 1 h L x L+1 + h L 1 x L h 1 x 0 + h 0 x 1 + v 1.. = y ṇ. h L x n L + h L 1 x n L h 1 x n 1 + h 0 x n + v n. y N 1 h L x N L 1 + h L 1 x N L + + h 1 x N 2 + h 0 x N 1 + v N 1 (21) Southampton School of ECS, Univ. of Southampton, UK. 28/ 49

29 OFDM - Representation of Received Signals When expressed in matrix form, (21) is y 0 y 1. y N 1 } {{ } y h L h L 1 h h L h L 1 h = h L h L 1 h 0 }{{} H + v 0 v 1. v N 1 } {{ } v Southampton School of ECS, Univ. of Southampton, UK. 29/ 49 x L. x 1 x 0. x N 1 } {{ } x (22)

30 OFDM - Representation of Received Signals Therefore, we have H = h L h L 1 h h L h L 1 h (23) h L h L 1 h 0 Southampton School of ECS, Univ. of Southampton, UK. 30/ 49

31 OFDM - Representation of Received Signals In (22), if CP is used and set as x i = x N i, i = 1,..., L, then, (22) can be represented as y 0 y 1. y N 1 } {{ } y h h 2 h 1. h 1 h h L h L h L 1 h = h h L 1 h 0 0 x 0 x 1.. x N 1 } {{ } x + v 0 v 1.. v N 1 } {{ } v } {{ h L h 1 h 0 } H (24) Southampton School of ECS, Univ. of Southampton, UK. 31/ 49

32 OFDM - Representation of Received Signals H = h h 2 h 1. h 1 h h L h L h L 1 h h h L 1 h h L h 1 h 0 (25) Southampton School of ECS, Univ. of Southampton, UK. 32/ 49

33 An Example Let we assume x = [x 0, x 1, x 2, x 3 ] T and L = 2. Then, we have h 2 h 1 h h 2 h 1 h H = 0 0 h 2 h 1 h 0 0, H = h 0 0 h 2 h 1 h 1 h 0 0 h 2 h 2 h 1 h 0 0 (26) h 2 h 1 h 0 0 h 2 h 1 h 0 Southampton School of ECS, Univ. of Southampton, UK. 33/ 49

34 OFDM - Signal Detection In (24), H is a circulant channel matrix, which can be decomposed into H = F H ΛF, where Λ = diag{h 0, H 1,, H N 1 } is a (N N) diagonal matrix, and H n is in fact the fading gain of the nth subcarrier. Using x = F H X of (16), we can re-write (24) as y = HF H X + v = F H Λ FF }{{ H } X + v = F H ΛX + v (27) =I N Carrying out the FFT on y gives Therefore, for n = 0, 1,..., N 1, based on which {X n } can be detected. Explicitly, there is no ISI. Y = Fy = FF }{{ H } ΛX + Fv = ΛX + v (28) =I N Y n = H n X n + v n (29) Southampton School of ECS, Univ. of Southampton, UK. 34/ 49

35 OFDM - Peak-to-Average Power Ratio The peak-to-average power ratio (PAPR) is an important attribute of a communication system; A low PAPR allows the transmit power amplifier to operate efficiently, whereas a high PAPR forces the transmit power amplifier to have a large backoff in order to ensure linear amplification of the signal; A high PAPR requires high resolution for the receiver A/D converter, since the dynamic range of the signal is much larger for high-papr signals. High-resolution A/D conversion places a complexity and power burden on the receiver front end. Southampton School of ECS, Univ. of Southampton, UK. 35/ 49

36 Amplitude 0 T Time Figure 8: Illustration of multicarrier modulated signals. Southampton School of ECS, Univ. of Southampton, UK. 36/ 49

37 OFDM - Peak-to-Average Power Ratio The PAPR of a continuous-time signal is given by P AP R max t{ x(t) 2 } E t [ x(t) 2 ] (30) The PAPR of a discrete-time signal is given by P AP R max n{ x[n] 2 } E n [ x[n] 2 ] (31) Southampton School of ECS, Univ. of Southampton, UK. 37/ 49

38 OFDM - Peak-to-Average Power Ratio In OFDM, the transmitted signal is given by x[n] = 1 N 1 N i=0 ( ) j2πni X[i] exp, 0 n N 1 (32) N Given E [ X[i] 2] = 1, the average power of x[n] is given by E n [ x[n] 2 ] = 1 N N 1 i=0 E [ X[i] 2] = 1 (33) The maximum value occurs when all X[i] s add coherently, yields N max n { x[n] 2 } = max X[i] N = N 2 = N (34) N Therefore, in OFDM systems using N subcarriers, P AP R = N, which linearly increases with the number of subcarriers. i=0 Southampton School of ECS, Univ. of Southampton, UK. 38/ 49

39 OFDM - Techniques for PAPR Mitigation Clipping: clip the parts of the signals that are outside the allowed region; Coding: PAPR reduction can be achieved using coding at the transmitter to reduce the occurrence probability of the same phase of the N signals; Peak cancellation with a complementary signal; Southampton School of ECS, Univ. of Southampton, UK. 39/ 49

40 OFDM - Frequency and Time Offset f 0 f 1 f 2 f 3 f 4 f 5 f 6 f 7 Figure 9: Spectrum of the OFDM signal, where the subcarrier signals are orthogonal to each other. Southampton School of ECS, Univ. of Southampton, UK. 40/ 49

41 OFDM - Frequency and Time Offset OFDM modulation encodes the data symbol {X i } onto orthogonal subcarriers, where orthogonality is assumed by the subcarrier separation f = 1/T N ; In practice, the frequency separation of subcarriers is imperfect and so f is not exactly equal to 1/T N ; This is generally caused by mismatched oscillators, Doppler frequency shifts, or timing synchronization, etc.; Consequently, frequency offset generates inter-carrier interference (ICI). Southampton School of ECS, Univ. of Southampton, UK. 41/ 49

42 OFDM - Frequency and Time Offset Let us assume that the signal transmitted on subcarrier i is x i (t) = e j2πit/t N (35) where the data symbol and the main carrier frequency are suppressed; An ideal signal transmitted on subcarrier (i + m) would by x i+m (t). However, due to the frequency offset of δ/t N, this signal becomes x i+m+δ (t) = e j2π(i+m+δ)t/t N (36) Then, the interference imposed by subcarrier (i + m) on subcarrier i is TN I m = x i (t)x i+m+δ(t)dt = T ( ) N 1 e j2π(δ+m) = T ( ) N 1 e j2πδ j2π(δ + m) j2π(δ + m) 0 (37) Explicitly, when δ = 0, I m = 0. Southampton School of ECS, Univ. of Southampton, UK. 42/ 49

43 OFDM - Frequency and Time Offset It can be shown that the total ICI power on subcarrier i is given by ICI i = m i I m 2 C 0 (T N δ) 2 (38) where C 0 is a certain constant. Observations As T N increases, the subcarriers become narrower and hence more closely spaced, which then results in more ICI; As predicted, the ICI increases as the frequency offset δ increases; The ICI is not directly related to N, but larger N results in larger T N and, hence, more ICI. Southampton School of ECS, Univ. of Southampton, UK. 43/ 49

44 OFDM - Frequency and Time Offset The effects from timing offset are generally less than those from the frequency offset, as long as a full N-sample OFDM symbol is used at the receiver without interference from the previous or subsequent OFDM symbols; It can be shown that the ICI power on subcarrier i due to a receiver timing offset τ can be approximated as 2(τ/T N ) 2 ; Since usually τ << T N, the effect from timing offset is typically negligible. Southampton School of ECS, Univ. of Southampton, UK. 44/ 49

45 IEEE Wireless LAN Standard There are many IEEE (a,g,n,ac,ad) using OFDM; IEEE802.11a: Bandwidth= 300 MHz, operated in the 5 GHz unlicensed band; IEEE802.11g: Virtually identical to the IEEE802.11a, but operated in the 2.4 GHz unlicensed band. Main Parameters: 300 MHz bandwidth is divided into 20 MHz channels that can be assigned to different users; N = 64, µ = 16 samples; Convolutional code with possible rate: r = 1/2, 2/3 or 3/4; Adaptive modulation based on the modulation schemes: BPSK, QPSK, 16-QAM and 64-QAM. Southampton School of ECS, Univ. of Southampton, UK. 45/ 49

46 OFDM - Summary No interference exists among the transmitted symbols; It is a transmission scheme achieving the highest spectral-efficiency; No diversity gain is achievable in frequency-selective fading channels; Sensitive to the frequency offset and timing jitter; The transmitted OFDM signals have a high dynamic range, resulting in the high PAPR; The high PAPR requires that the OFDM transmitter has a high linear range for signal amplification. Otherwise, the OFDM signals conflict non-linear distortion, which results in out-of-band emissions and co-channel interference, causing significant degradation of the system s performance; The high PAPR has more harmful effect on the uplink communications than on the downlink communications, due to the power limit of mobile terminals; When OFDM is used for uplink communications, the high PAPR may generate severe inter-cell interference in cellular communications. Southampton School of ECS, Univ. of Southampton, UK. 46/ 49

47 Single-Carrier Frequency-Division Multiple-Access In order to take the advantages of multicarrier communications whereas circumventing simultaneously the high PAPR problem, the single-carrier frequency-division multiple-access (SC-FDMA) scheme has been proposed for supporting high-speed uplink communications; In principle, the SC-FDMA can be viewed as a DFT-spread multicarrier CDMA scheme, where time-domain data symbols are transformed to frequency-domain by a DFT before carrying out the multicarrier modulation; SC-FDMA is also capable of achieving certain diversity gain, when communicating over frequency-selective fading channels. Southampton School of ECS, Univ. of Southampton, UK. 47/ 49

48 SC-FDMA - Transmitter T-domain F-domain T-domain {X k0,..., X k(n 1) } { X k0,..., X k(u 1) } { x k0,..., x k(u 1) } s(t) {x k0,..., x k(n 1) } DFT (FFT) Subcarrier mapping IDFT (IFFT) Add CP Low-pass filter Figure 10: Transmitter schematic for the kth user supported by the SC-FDMA uplink. Southampton School of ECS, Univ. of Southampton, UK. 48/ 49

49 SC-FDMA - Receiver T-domain {Y k0,..., Y k(n 1) } F-domain {Ỹ0,..., Ỹ(U 1)} {ỹ 0,..., ỹ (U 1) } T-domain r(t) {ˆx k0,..., ˆx k(n 1) } IDFT (IFFT) Subcarrier F-domain DFT Remove Matcheddemapping processing (FFT) CP filter Figure 11: Receiver schematic for the kth user supported by the SC-FDMA uplink. Southampton School of ECS, Univ. of Southampton, UK. 49/ 49