FBMC/OQAM transceivers for 5G mobile communication systems François Rottenberg
Modulation Wikipedia definition: Process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that typically contains information to be transmitted. Someone I know definition: Convert bits of information into an electromagnetic wave 0,1,1,0,1 Digital modulations here Modulation 2
Evolution of telecommunication standards 2010 2030 2020 2040 4G modulation format might not be the best to address 5G challenges 2
Outline Some basics Single-carrier systems Classical multicarrier systems FBMC-OQAM systems Principle Pros and cons My research 4
Outline vulgarized Some basics La télécom pour les nuls Single-carrier systems How are old systems working? Classical multicarrier systems "4G-like systems" FBMC-OQAM systems The systems I study Principle How do they work? Pros and cons Why are they the best? My research What am I doing? 5
Outline Some basics Single-carrier systems Classical multicarrier systems FBMC-OQAM systems Principle Pros and cons My research 6
Outline Some basics Single-carrier systems How are old systems working? Classical multicarrier systems FBMC-OQAM systems Principle Pros and cons My research 7
Modulation Someone I know definition: Convert bits of information into an electromagnetic wave Digital modulations here 0,1,1,0,1 Modulation 8
Bits to symbols mapping 0,1,1,0,1 Bits to symbols mapping d[n] 1/T s T s is called the sampling period Symbols d n might be complex, contain one or more bits of information 9
Bits to symbols mapping d n might be complex, contain one or more bits of information I I 1 + j +1 + j 2 2 1 +1 R R 1 bit of information Incoming bits Symbol d[n] 0-1 1 +1 +1 j 1 j 2 2 00 01 2 bits of information 1 j 2 1 + j 2 10 11 +1 j 2 +1 + j 2 10
Bits to symbols mapping d n might be complex, contain one or more bits of information, depending on link quality I I R R 2 bits of information 4 bits of information 11
Digital to analog conversion (DAC) γ s (f) d[n] u(t) s(t) f 1/T s 1 2T s 1 2T s s t = n d n δ t nt s u(t) System bandwidth B = d n u(t nt s ) n 12
Wait s(t) complex?! s(t) is called the baseband equivalent of the transmitted signal γ s (f) Real passband transmitted signal s pb (t) is obtained by modulation around carrier frequency f c B f f f c B f c B 13
How in practice? Analog mixer/oscillator/modulator e jω ct d[n] u(t) s(t) R 1/T s s pb (t) s pb t = R s t e jω ct = R s t cos ω c t I s t sin(ω c t) 14
What about the receiver? e jω ct d[n] u(t) s(t) R 1/T s s pb (t) r [n] 1/T s ε τ TO ADC low-pass u(t) r(t) e jω ct Δft CFO r pb (t) If p t = δ(t) and several conditions, we will have r n = d[n]. In practice, not really equality p(t) n(t) Additive noise 15
Noise and impairments 1 + j 2 d[n] I +1 + j 2 r[n] R 1 j 2 +1 j 2 16
Equivalent transmission chain d[n] DAC u(t) s(t) e jω ct R 1/T s s pb (t) e jω ct p(t) r [n] 1/T s u(t) r(t) r pb (t) ADC h[n] 17
All discrete baseband equivalent model, why? d[n] Abstraction model Easy to simulate 1/T s h[n] r[n] How it is done in practice Easy to understand, more tractable Very accurate 18
What are the disadvantages of single-carrier systems? d[n] h[n] R ω = H ω D(ω) r[n] h eq [n] d [n] 1/T s D ω = H eq ω H ω D(ω) h n H(ω) n In practice, multipath channel, intersymbol interference, R ω = H ω D(ω) Need for channel «equalization», might require long filters H ω H eq ω 1 D ω D ω h h eq n δ[n] f 19
Outline Some basics Single-carrier systems Classical multicarrier systems "4G-like" FBMC-OQAM systems Principle Pros and cons My research 20
0,1,1,0,1 Multicarrier systems Subcarrier index Symbol mapping d[n] 1/T s S/P d 0,l 1/T d 1,l 1/T g 0,l[n] g 1,l [n] Multicarrier symbol index 1/T s 1/T s s[n] 1/T s T = 2MT s T is the multicarrier symbol period Baseband equivalent of the transmitted signal s n = d 2M 1,l 1/T 2M 1 m=0 + l= g 2M 1,l [n] 1/T s g m,l n = g n l2m e j2π 2M mn d m,l g m,l [n] 21
Time-frequency lattice f s n = 2M 1 m=0 + l= d m,l g m,l [n] g m,l n = g n l2m e j2π 2M mn 1 T d 1,0 d 0,0 d 1,1 d 0,1 T 1 = 1 1 ΔtΔf Lattice density: symbol per second per Hertz T T Exactly the same throughput rate as SC system 1 T s 1 Ts = 1 t 22
Single-carrier baseband and multicarrier spectrum comparison SC γ s (f) 1 2T S 1 2T S f MC γ s (f) 1 T subcarrier spacing 1 2T S = M T 1 T 1 T 1 2T S = M T f 23
Channel s[n] 1/T s h[n] r [n] r n = s h [n] R ω = S ω H(ω) 24
Receiver 0,1,1,0,1 Symbol demapping d[n] 1/T s P / S d 0,l0 d 1,l0 x 0,l0 x 1,l0 1/T 1/T g 0,l [n] g 1,l [n] r[n] 1/T s d 2M 1,l0 x 2M 1,l0 g 2M 1,l [n] 1/T Demodulated symbol at subcarrier m 0 and multicarrier symbol l 0 : x m0,l 0 =< r n, g m0,l 0 [n] > n r n g m0,l 0 n 25
Orthogonality conditions Assume ideal condition, h n = δ[n] and r n = s[n] d m0,l 0 =< s n, g m0,l 0 n > 2M 1 = + m=0 l= d m,l < g m,l n, g m0,l 0 n > = d m0,l 0 if «complex» orthogonality of the pulses is fullfilled, i.e., < g m,l n, g m0,l 0 n >= δ m m0,l l 0 for m 0, m = 0,.., 2M 1 and l, l 0 (between symbols and subcarriers). Generalized Nyquist constraint. 26
Generalized Nyquist constraint < g m,l n, g m0,l 0 n >= δ m m0,l l 0 f d m,l < g m,l n, g m0,l 0 n > d m0,l 0 1 T T t Where is the gain of multicarrier systems?! 27
Practical channel conditions h n H(ω) H(ω m0 ) n ω m0 S(ω m0 ) ω Channel approximated as flat at the subcarrier level x m0,l 0 =< r n, g m0,l 0 n > H(ω m0 )d m0,l 0 and d m0,l 0 is simply recovered by d m0,l 0 = H 1 ω m0 x m0,l 0 d m0,l 0 Very simple channel equalization 28
Receiver d 0,l0 H 1 ω 0 x 0,l0 1/T g 0,l [n] 0,1,1,0,1 Symbol demapping d[n] 1/T s P / S d 1,l0 H 1 ω 1 x 1,l0 1/T g 1,l [n] r[n] 1/T s d 2M 1,l0 x 2M 1,l0 H 1 ω m 1/T g 2M 1,l [n] Demodulated symbol at subcarrier m 0 and multicarrier symbol l 0 : x m0,l 0 =< r n, g m0,l 0 [n] > n r n g m0,l 0 n 29
Multicarrier systems vs singlecarrier systems? Easy channel equalization Frequency division multiplexing Resource allocation Robust to timing offset Sensitivity to carrier frequency offset and channel variation in time High peak-to-average power ratio Used in most wireless communication standards! Wi-Fi, DSL, LTE, DVB 30
Disadvantages of classical multicarrier systems based on complex orthogonality Suppose g(t) is a square-integrable function on the real line and consider the Gabor system g m,l t = g t lδt e j2πmδft where m, l Z. If ΔtΔf = 1, the Balian-Low theorem states that, if {g m,l t, m, l Z} is an orthonormal basis for the Hilbert space L 2 (R), then either + t 2 g t 2 + dt = or ω 2 G ω 2 dω = where G(ω) is the Fourier transform of g(t). 31
Limitations of classical multicarrier systems based on complex orthogonality? In other words, if ΔtΔf = 1 (1 symbol per s per Hz, full spectral efficiency, high data rate) and < g m,l, g m0,l 0 > = δ m m0,l l 0 for all m, l (complex orthogonality), the Balian-Low theorem tells us that the prototype filter/atom g t cannot be well localized in time and frequency. Bad for spectral efficiency, robustness, synchronization 32
Wi-Fi, DSL, LTE, WiMAX, DVB OFDM leakage g t G ω = sinc ωt - T 2 T 2 t Spectral leakage + t 2 g t 2 dt ξ + ω 2 G ω 2 dω = Δt = T, Δf = 1 T and complex orthogonality (easy to show) < g m,l, g m0,l 0 > = g m,l (t)g m0,l 0 (t)dt = δ m m0,l l 0 t 33
Spectral leakage leads to interference U1 Overlapping Frequency U1 U2 U2 Synchronisation required to keep orthogonality 34
Time-frequency lattice of CP-OFDM f 2M 1 + s n = d m,l g m,l [n] m=0 l= Wi-Fi, DSL, LTE, WiMAX, DVB 1 T T + T CP t T 10 ~ T 4 Undersampled lattice, loss in throughput rate 1 T + T CP 1 T = T T + T CP < 1 35
Outline Some basics Single-carrier systems Classical multicarrier systems FBMC-OQAM systems Principle Pros and cons My research 36
Outline Some basics Single-carrier systems Classical multicarrier systems FBMC-OQAM systems Principle How does it work? Pros and cons My research 37
FBMC-OQAM principle We want: Good time-frequency localization Full spectral efficiency But how? Balian-Low Use staggered lattices to circumvent the Balian-Low theorem Idea used by FBMC-OQAM modulations [Chang, 66], [Saltzberg, 67] Link to Wilson bases. 38
Classical multicarrier lattice f Complex symbol 1 T T t 39
FBMC-OQAM lattice f T 2 Real symbol Imag. symbol 1 T T t Lattice density 1 = 1 ΔtΔf T 2 1/T = 2 real symbols per second per Hertz Orthogonality satisfied only in the real domain 40
Good frequency localization 41
No need for synchronization of the users USER 1 No overlapping Frequency USER 1 USER 2 USER 2 42
FBMC-OQAM transmission model Transmitted signal R-I pattern 2M 1 + s n = d m,l g m,l n m=0 l= 2M mn. with g m,l n = j l+m g n lm e j2π Assume ideal channel, i.e., r n = s[n]. The demodulated signal is d m0,l 0 = R < s n, g m0,l 0 n > + d m,l R < g m,l n, g m0,l 0 n > 2M 1 = m=0 l= = d m0,l 0 Purely real now! if, R < g m,l n, g m0,l 0 n > = δ m m0,l l 0 m, m 0, l, l 0. l2m symbols are closer in time Interference from symbol d m,l 43
FBMC-OQAM lattice f T 2 d m,l R < g m,l n, g m0,l 0 n > 1 T d m0,l 0 T t 44
Real orthogonality conditions < g m,l n, g m0,l 0 n > = j Δm+Δl n g n lm g n l 0 M e j2π 2M Δmn (simple math. manipulations) = j Δm+Δl+ΔlΔm 1 Δml 0 n g n ΔlM 2 g n + ΔlM 2 e j2π 2M Δmn Δm = m m 0, Δl = l l 0 Ambiguity function : real for real and even pulse g[n] R < g m,l n, g m0,l 0 n > is only non zero if Δm + Δl + ΔlΔm = 0 mod 2, which only occurs when Δm = Δl = 0 mod 2. Hence, g[n] should be designed to cancel those terms. 45
FBMC-OQAM lattice f T 2 Real symbol Imag. symbol 1 T T t Purely imaginary interference, eliminated directly when g[n] is even and real Remaining interference, eliminated by filter design Δm = Δl = 0 mod 2 46
Outline Some basics Single-carrier systems Classical multicarrier systems FBMC-OQAM systems Principle Pros and cons Why is it better? My research 47
Pros Pros and and cons Pros Le beurre et l argent du beurre Advantages of MC systems: easy channel equalization High data rate Filter well time-frequency localized: Higher complexity especially in certain scenarios. Need for more investigation, many open issues. Wait Good for us! We like complex things! That means that there is still a lot to do! 48
Evolution of telecommunication standards 2010 2030 2020 2040 4G modulation format might not be the best to address 5G challenges 2
Flexible spectrum utilization in 5G Fragmented spectrum 1280MHz 1285MHz 2 MHz 20 MHz 5 MHz 20 MHz 150 KHz 602MHz 604MHz 820MHz 840MHz 1680MHz 1700MHz 50
Outline Some basics Single-carrier systems Classical multicarrier systems FBMC-OQAM systems Principle Pros and cons My research What am I doing? 51
My research Investigate the applicability of FBMC-OQAM modulations for 5G communication systems -Channel estimation -MIMO What if we use multiple antennas at transmitter and/or receiver? -Massive MIMO What if the number of those antennas grows very large? -High speed scenario: What if the channel changes quickly? -Application to optical fiber: other issues and challenges 52
I hope I convinced you! We are note alone 53