Multi-carrier and Multiple antennas

Transcription

1 RADIO SYSTEMS ETIN15 Lecture no: 10 Multi-carrier and Multiple antennas Ove Edfors, Department of Electrical and Information Technology 1

2 Contents Multicarrier systems History of multicarrier Modulation/demodulation Equalization Performance Multiple antenna systems Different configuratuons Diversity gains Datarates using MIMO (capacity) 2

3 Multi-carrier or OFDM orthogonal frequencydivision multiplexing 3

4 Single/multi-carrier Single Singlecarrier carrier Data Mod. fc fc f Multi-carrier Multi-carrier Mod. f1 Data f1 Using N cubcarriers increases the symbol length by N times. The ISI is reduced by the same amount (in symbols). Mod. fn fn f 4

5 History and evolution [1] 1950 s: Few subcarriers, with non-overlapping spectra f Military systems, e.g. the Kineplex-modem 5

6 History and evolution [2] 1960 s: Subcarriers with overlapping spectra f Increased subchannel density and increased data rate. 6

7 History and evolution [3] 1970 s: Digital modulation of subcarriers Analog Analogmodulation modulation New Newdigital digitalmodulation modulation Data f1 Data IDFT Mod. D/A ftx Mod. fn 7

8 History and evolution [4] 1980 s: Improved digital circuits increses interest No guard interval => Interference between both subcarriers and symbols Channel #n-1 #n #n+1 #n-1 #n time #n+1 time Guard interval => No interference between symbols Channel #n-1 #n #n+1 #n-1 #n time #n+1 time Cyclic prefix => No interference between neither subcarriers nor symbols Copy Copy #n { #n-1 Copy { { { #n-2 Copy #n+1 time 8

9 History and evolution [5] 1990 s: Commercial applications appear Increased interest for OFDM in wireless applications First applications in broadcasting (Audio/Video) One of the candidates for UMTS (Beta proposal) Applied in wireless LANs 2000 s: One of the really hot technologies 54 Mbps and beyond WLANs (based on OFDM) hit the mass market (IEEE802.11g/n) OFDM is the technology used when improving and moving beyond 3G systems (LTE long term evolution) 9

10 Transmitters and receivers An N-subcarrier transmitter x N 1, k N-point IDFT x 1, k s1, k s N 1, k 1 N-point IDFT: s m, k = N Parallel to serial s 0, k x 0, k htx CP 1 2 k symbol m sample n subcarrier L CP length Tsamp sampling period htx TX filter s t 3 L=3 N 1 n= 0 1 mn x n, k exp j2 for 0 m N 1 N 2 Adding CP: s m, k =s N m, k for L m 1 N 1 TX filtering: s t =h TX t k m= L s m, k t k N L m T samp N =8 3 10

11 Transmitters and receivers... through the channel... Channel Noise n t s t hch t r t =s t hch t n t } t T ch s t CP r t CP t CP } } L T samp CP T ch t As long as the CP is longer than the delay spread of the channel, LTsamp > Tch, it will absorb the ISI. By removing the CP in the receiver, the transmission becomes ISI free. 11

12 Transmitters and receivers N-subcarrier receiver hrx 1 RX filtering: Sampling: Removing CP: 2 r N 1, k q symbol p sample n subcarrier L CP length Tsamp sampling period hrx RX filter y N 1, k L=3 N =8 1 z k = z k T samp 2 r p,q = z q N L p for 0 p N 1 y n, q = r p, q exp j2 p=0 3 y 1, k z t =h RX t r t N 1 N-point DFT: CP r 1, k y 0, k N-point DFT r t T samp Serial to parallel r 0, k np for 0 n N 1 N 3 12

13 Transmitters and receivers Modulation spectrum [1] Transmitted OFDM symbol decomposed into different subcarriers (ideal case, 4 subcarriers shown, no CP) Power spectrum of one subcarrier transmitted at fn Hz. Sn f n t 1 S f 2 n n S n f sinc 2 f f n N T samp N T samp fn N T samp - Subcarriers - Sampling period f 1/ N T samp sin x sinc x = x 13

14 Transmitters and receivers Modulation spectrum [2] The distance between each subcarrier becomes 1/ N T samp which is the same as the 3 db bandwidth of the individual subcarriers. Using all N subcarriers (8 in this case) we get: The total modulation spectrum is a sum of the individual subcarrier spectra (assuming independent data on them). f B=N 1/ N T samp =1/T samp f B=1/ T samp 14

15 Transmitters and receivers Modulation spectrum [3] 2048 subcarriers 0 Power spectral density [db] Power spectral density [db] 64 subcarriers ν Normalized frequency ν Normalized frequency Normalized freq.: =T samp f = f / B 15

16 Transmitters and receivers Simplified model Simplified Simplifiedmodel modelunder underideal idealconditions conditions (no (nofading fadingand andsufficient sufficientcp) CP) H 0, k n 0, k x 0, k y 0, k Total filter in the signal path: h tot t =h TX t h ch t hrx t H tot f =H TX f H ch f H RX f H N 1, k n N 1, k x N 1, k y N 1, k Given that subcarrier n is transmitted at frequency fn the attenuations become: H n,k =H tot f n 16

17 Transmitters and receivers Focus on one subchannel Before BeforeIDFT IDFTininTX TX After AfterDFT DFTininRX RX xn, k Subchannel k H n,k yn, k nn, k xn, k yn, k Amplitude scaling: H n, k Rotation: (16QAM) Noise: H n,k nn, k Simple equalization of each subchannel: Back-rotate and scale 17

18 Coded OFDM (CODFM) Uncoded performance H n,k xn, k nn, k yn, k PROBLEM: Only one fading tap per subchannel => NO DIVERSITY => POOR PERFORMANCE The diversity is in there... but additional techniques are needed to exploit it! SOLUTION: Spreading the information (data) across several subcarriers or OFDM symbols This can be done using interleaving and coding => Coded OFDM (CODFM) 18

19 One OFDM symbol Channel attenuation Channel attenuations are correlated in the time/frequency grid. If we spread each bit of information over several well separated points in the OFDM time/frequency grid, the same bit is is received over several one tap fading channels. N subcarriers Frequency Coded OFDM (CODFM) Channel correlation Combining these in the receiver, we obtain diversity. Time 19

20 Coded OFDM (CODFM) Coding and interleaving New blocks Interleaving Parallel to serial Coding N-point IDFT (Corresponding ones at RX) CP htx Interleaving can be performed: The code spreads the information across several code symbols. The interleaver reorders the code symbols so that neighbouring code symbols are well separated in frequency and/or time during transmission. - across subcarriers in an OFDM symbol (small delay) - in time over several OFDM symbols (longer delay) - or in a combination of the above. 20

21 Coded OFDM (CODFM) Diversity The better the coding and interleaving scheme, the larger the obtained diversity order. Bit error rate (4QAM) 0 10 Rayleigh fading No diversity = uncoded OFDM 10 db x db Rayleigh fading Kth order diversity (Coded OFDM) K x No fading Eb/N0 [db] 21

22 Multiple antenna systems or MIMO multiple input/multiple output 22

23 System model [2] A simple model: Superposition of received waves [Movement -> fading] h No diversity (SISO): x y = hx + n TX RX Fading -> Poor performance 23

24 System model [3] An improvement: Antenna diversity 1 2 TX diversity (MISO): 1 y 1 = [ h1,1 h1,2 ] [] x1 n1 x2 RX diversity (SIMO): [ ][ ] [] y1 h n = 1,1 x 1 1 y2 h2,1 n TX&RX diversity (MIMO): 2 [ ][ ][ ] [ ] y1 h h x n = 1,1 1,2 1 1 y2 h2,1 h2,2 x 2 n2 24

25 Lobe-forming at transmitter The lobe forming coefficients can steer the direction in which the signal is transmitted. a1 s t a2 am T 25

26 Several input signals One set of lobe forming coefficients for each input signal s1 t s1 t s2 t s2 t s3 t s3 t 26

27 Several output signals Lobe forming on the receiver side can give several output signals. r1 ( t ) r2 ( t ) r3 ( t ) 27

28 Multiple antennas at both ends With N antennas on each side we can form N different lobes and hence create N parallel channels! TX RX Note that the three channels are separated spatially and can therefore use the same bandwidth! We have trippled the channel capacity. 28

29 A general (narrow-band) model The general case with MT TX antennas and MR RX antennas: [ ][ h1,1 h1,2 y1 h2,2 y= y 2 = h 2,1 ym hm, 1 hm,2 R R R h1, M h2, M hm, M T T R T ][ ] [ ] x1 n1 x 2 n2 =Hx n xm nm T R Some fundamental questions: - How do we model the channel matrix H? - How do we model the noise (interference) n? We will see that these have a large impact on what we can obtain. 29

30 What started the interest in MIMO? J.H. Winters. On the Capacity of Radio Communication Systems with Diversity in Rayleigh Fading Environment. IEEE JSAC, vol. SAC-5, no. 5, June Model Findings Equal number of RX and TX Linear processing at receiver: antennas, MT = MR = M. Up to M /2 channels, each with the same data rate as a single H Independent Rayleigh channel. fading. [i.i.d. complex Gaussian variables]. Non-linear processing at receiver: n I.i.d complex Gaussian variables. Up to M channels, each with the same data rate as a single channel. 30

31 Capacity No fading & AWGN [1] Singular value decomposition of the (fixed) channel H: H y=hx n=q 1 Q 2 x n where Q1 (MRxMR) and Q2 (MTxMT) are unitary matrices and (MRxMT) is a matrix containing the singular values on its diagonal. Multiply by Q H 1 from left: Q 1H y= Q 2H x Q1H n y x Only rotations of y, x and n. y = x n n All-zero, exept diagonal. 31

32 Capacity No fading & AWGN [2] What have we obtained? Parallel independent channels: [ 1 y = r 0 ] 1 n 1 x 1 x n y 1 r x r Number of non-zero singular values r = rank(h). Shannon s standard case : n r y r (+ channels with k =0) 32

33 Capacity No fading & AWGN [3] Shannon: The total capacity of parallel independent channels is the sum of their individual capacities. C k =log 2 1 SNR k C = C k = log 2 1 SNR k k k Equal power distribution (channel not known at TX): Constant dep. on e.g. TX power and noise. r C = C k = log 2 1 =log 2 1 k k k 2 k 2 k =1 33

34 Capacity No fading & AWGN [4] A neat trick: det I M HH =det Q 1 Q1 Q 1 Q 2 Q 2 Q1 H H H H H R IM H R HH =det Q1 I M Q 2H Q 2 H Q 1H R =det I M H =det [ R r = 1 2k 1 1 ] r k =1 34

35 Capacity No fading & AWGN [5] CONCLUSION: r C =log 2 1 2k =log 2 det I M HH H [bit/sec/hz] R k =1 Normalization: r - SNR at each receiver branch C =log 2 det I M HH H MT R This leads to the fact that we can increase data rate by increasing the number of antennas, without using more transmit power. This relation is also derived in e.g G.J. Foschini and M.J. Gans. On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas. Wireless Personal Communications, no 6, pp ,

36 Massive MIMO Massive MIMO implies that we let the number of base station antennas (M) grow very large in the hundreds! Base station Down-link: Base station Up-link: Channel reciprocity assumed 36

37 Two typical precoders Maximum-ratio transmission (MRT) Hermitian transpose of channel Base station Zero-forcing (ZF) Pseudoinverse of channel 37

38 Why do we care about Massive MIMO? Massive MIMO with 100 BS antennas Several orders of magnitude more energy efficient! Much higher spectral efficiency! [Plot from Larsson, E. ; Edfors, O. ; Tufvesson, F. ; Marzetta, T., Massive MIMO for next generation wireless systems, IEEE Communications Magazine, Vol. 52, Issue 2, 2014] 38

39 What happens if we use many antennas in the hundreds? The Lund University Massive MIMO (LuMaMi) testbed 100-antenna base station 50 synchronized software-radio units (USRPs), each with two antennas and Kintex 7 FPGA processing. 10 single-antenna terminals Each pair of terminal antennas served by a USRP. All multiplexed in the same timefrequency resource LTE-like physical layer OFDM 1200 subcarriers, 20 MHz BW Full flexibility Architecture, antenna array, and baseband processing can be configured 39

40 Video time... Understanding massive MIMO in roughly two minutes 40

41 Summary Multi-carrier technology (OFDM) reduces the effect of intersymbol interference (as compared to single carrier). Only simple equalization is required in an OFDM receiver. Modulation/demodulation can be done using Fast Fourier Transforms (FFTs). Multiple antenna systems increase our ability to obtain diversity gains. With MIMO systems we can increase the datarate by using more antennas, without increasing transmit power or bandwidth. Massive MIMO can give very large gains. 41