fbmc/oqam transceivers for 5g mobile communication systems · investigate the applicability of...
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FBMC/OQAM transceivers for 5G mobile
communication systemsFrançois Rottenberg
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“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
2
Digital modulations here
Modulation
0,1,1,0,1 …
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Evolution of telecommunicationstandards
2
2010… 2030
4G modulation format might not bethe best to address 5G challenges
2020… 2040
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Outline
Some basics
Single-carrier systems
Classical multicarrier systems
FBMC-OQAM systems
Principle
Pros and cons
My research
4
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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?”
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Outline
Some basics
Single-carrier systems
Classical multicarrier systems
FBMC-OQAM systems
Principle
Pros and cons
My research
6
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Outline
Some basics
Single-carrier systems
“How are old systems working?”
Classical multicarrier systems
FBMC-OQAM systems
Principle
Pros and cons
My research
7
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“Modulation”
“Someone I know” definition:
Convert bits of information into an electromagnetic wave
8
Digital modulations here
Modulation
0,1,1,0,1 …
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Bits to symbols mapping
Bits to symbols mapping
0,1,1,0,1 … 𝑑[𝑛]
1/𝑇𝑠
𝑇𝑠 is called the sampling period
Symbols d 𝑛 might be complex, contain one or more bits of information
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Bits to symbols mapping
𝑑 𝑛 might be complex, contain one or more bits of information
ℜ
ℑ
ℜ
ℑ
+1−1
+1 − 𝑗
2−1 − 𝑗
2
−1 + 𝑗
2
+1 + 𝑗
2
1 bit of information2 bits of information
Incoming bits Symbol 𝑑[𝑛]
0 -1
1 +1
00 −1 − 𝑗
2
01 −1 + 𝑗
2
10 +1 − 𝑗
2
11 +1 + 𝑗
2
10
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Bits to symbols mapping
𝑑 𝑛 might be complex, contain one or more bits of information, depending on “link quality”…
ℜ
ℑ
ℜ
ℑ
2 bits of information 4 bits of information
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Digital to analog conversion (DAC)
𝑑[𝑛]
1/𝑇𝑠
𝑢(𝑡)𝑠(𝑡)
𝑓
1
2𝑇𝑠
−1
2𝑇𝑠
𝛾𝑠(𝑓)
System bandwidth 𝐵𝑠 𝑡 =
𝑛
𝑑 𝑛 𝛿 𝑡 − 𝑛𝑇𝑠 ⊗ 𝑢(𝑡)
=
𝑛
𝑑 𝑛 𝑢(𝑡 − 𝑛𝑇𝑠)
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Wait… 𝑠(𝑡) complex?!
𝑠(𝑡) is called the baseband equivalent of the transmitted signal
𝑓
𝛾𝑠(𝑓)
𝑓
𝐵
𝑓𝑐−𝑓𝑐
Real passband transmitted signal 𝑠𝑝𝑏(𝑡)
is obtained by modulation around carrier frequency 𝑓𝑐
𝐵 𝐵13
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How in practice?
Analog mixer/oscillator/modulator…
𝑑[𝑛]
1/𝑇𝑠
𝑢(𝑡)𝑠(𝑡)
ℜ
𝑠𝑝𝑏(𝑡)
𝑠𝑝𝑏 𝑡 = ℜ 𝑠 𝑡 𝑒𝑗𝜔𝑐𝑡 = ℜ 𝑠 𝑡 cos 𝜔𝑐𝑡 − ℑ 𝑠 𝑡 sin(𝜔𝑐𝑡)
𝑒𝑗𝜔𝑐𝑡
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What about the receiver?
𝑑[𝑛]
1/𝑇𝑠
𝑢(𝑡)𝑠(𝑡)
ℜ
𝑠𝑝𝑏(𝑡)
𝑢(𝑡)
1/𝑇𝑠𝑟 [𝑛]
𝑝(𝑡)
If 𝑝 𝑡 = 𝛿(𝑡) and several conditions, we will have 𝑟 𝑛 = 𝑑[𝑛]. In practice, not really equality…
15
−Δ𝑓𝑡CFO
𝜖𝜏 TO
𝑛(𝑡)Additive noise
𝑟(𝑡) 𝑟𝑝𝑏(𝑡)
𝑒𝑗𝜔𝑐𝑡
𝑒−𝑗𝜔𝑐𝑡
ADC low-pass
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Noise and impairments
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ℜ
ℑ
+1 − 𝑗
2−1 − 𝑗
2
−1 + 𝑗
2
+1 + 𝑗
2
𝑑[𝑛]𝑟[𝑛]
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Equivalent transmission chain
𝑑[𝑛]
1/𝑇𝑠
𝑢(𝑡)𝑠(𝑡)
ℜ
𝑠𝑝𝑏(𝑡)
𝑢(𝑡)
1/𝑇𝑠
ADC
𝑟 [𝑛]
𝑝(𝑡)
DAC
17
ℎ[𝑛]
𝑟(𝑡) 𝑟𝑝𝑏(𝑡)
𝑒𝑗𝜔𝑐𝑡
𝑒−𝑗𝜔𝑐𝑡
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All discrete baseband equivalentmodel, why?
𝑑[𝑛]
1/𝑇𝑠
ℎ[𝑛]
𝑟[𝑛]
Abstraction model
Easy to simulate
How it is done in practice
Easy to understand, more tractable
Very accurate18
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What are the disadvantages of single-carrier systems?
𝑑[𝑛]
1/𝑇𝑠
ℎ𝑒𝑞[𝑛]
𝑑 [𝑛]
In practice, multipath channel, intersymbol interference, 𝑅 𝜔 = 𝐻 𝜔 𝐷(𝜔)
Need for channel « equalization », might require long filters…
𝐻 𝜔 𝐻𝑒𝑞 𝜔 ≈ 1 ↔ 𝐷 𝜔 ≈ 𝐷 𝜔 ↔ ℎ ⊗ ℎ𝑒𝑞 𝑛 ≈ 𝛿[𝑛]
𝑛
|ℎ 𝑛 ||𝐻(𝜔)|
𝑓
ℎ[𝑛]𝑟[𝑛]
19
𝑅 𝜔 = 𝐻 𝜔 𝐷(𝜔)
𝐷 𝜔 = 𝐻𝑒𝑞 𝜔 𝐻 𝜔 𝐷(𝜔)
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Outline
Some basics
Single-carrier systems
Classical multicarrier systems "4G-like"
FBMC-OQAM systems
Principle
Pros and cons
My research
20
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Multicarrier systems
𝑑[𝑛]
1/𝑇𝑠
S/P
𝑑0,𝑙
𝑑2𝑀−1,𝑙
1/𝑇
1/𝑇
1/𝑇
𝑑1,𝑙
𝑔0,𝑙[𝑛]
𝑔1,𝑙[𝑛]
𝑔2𝑀−1,𝑙[𝑛]
Symbol mapping
𝑠[𝑛]
1/𝑇𝑠
0,1,1,0,1 …
Baseband equivalent of the transmitted signal
Multicarrier symbol index
Subcarrier index
21
𝑇 = 2𝑀𝑇𝑠
𝑇 is the multicarrier symbol period
1/𝑇𝑠
1/𝑇𝑠
1/𝑇𝑠
𝑔𝑚,𝑙 𝑛 = 𝑔 𝑛 − 𝑙2𝑀 𝑒𝑗2𝜋2𝑀𝑚𝑛
𝑠 𝑛 =
𝑚=0
2𝑀−1
𝑙=−∞
+∞
𝑑𝑚,𝑙 𝑔𝑚,𝑙[𝑛]
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Time-frequency lattice𝑠 𝑛 =
𝑚=0
2𝑀−1
𝑙=−∞
+∞
𝑑𝑚,𝑙 𝑔𝑚,𝑙[𝑛]
𝑔𝑚,𝑙 𝑛 = 𝑔 𝑛 − 𝑙2𝑀 𝑒𝑗2𝜋2𝑀𝑚𝑛
Lattice density: 1
ΔtΔ𝑓=
11
𝑇𝑇
symbol per second per Hertz
1
𝑇
𝑇𝑡
𝑓
22
Exactly the same throughput rate as SC system 1
𝑇𝑠1
𝑇𝑠
= 1
𝑑0,1
𝑑1,1𝑑1,0
𝑑0,0
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Single-carrier baseband and multicarrier spectrum comparison
1
2𝑇𝑆=
𝑀
𝑇
1
𝑇
1
𝑇subcarrier spacing
23
−1
2𝑇𝑆= −
𝑀
𝑇−
1
𝑇
1
2𝑇𝑆
−1
2𝑇𝑆 𝑓
𝑓
MC
SC 𝛾𝑠(𝑓)
𝛾𝑠(𝑓)
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Channel
𝑟 𝑛 = 𝑠 ⊗ ℎ [𝑛]𝑅 𝜔 = 𝑆 𝜔 𝐻(𝜔)
𝑠[𝑛]
1/𝑇𝑠
ℎ[𝑛]
𝑟 [𝑛]
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Receiver
𝑑[𝑛]
1/𝑇𝑠
P/S
𝑥0,𝑙0
𝑥2𝑀−1,𝑙0
1/𝑇
1/𝑇
𝑥1,𝑙0
𝑟[𝑛]
1/𝑇𝑠0,1,1,0,1 …
Demodulated symbol at subcarrier 𝑚0 and multicarrier symbol 𝑙0:
𝑥𝑚0,𝑙0 =< 𝑟 𝑛 , 𝑔𝑚0,𝑙0[𝑛] >
𝑛
𝑟 𝑛 𝑔𝑚0,𝑙0∗ 𝑛
25
Symbol demapping
𝑑0,𝑙0
𝑑1,𝑙0
𝑑2𝑀−1,𝑙0
𝑔0,𝑙∗ [𝑛]
𝑔1,𝑙∗ [𝑛]
𝑔2𝑀−1,𝑙∗ [𝑛]
1/𝑇
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Orthogonality conditions
Assume ideal condition, ℎ 𝑛 = 𝛿[𝑛] and 𝑟 𝑛 = 𝑠[𝑛]
𝑑𝑚0,𝑙0 =< 𝑠 𝑛 , 𝑔𝑚0,𝑙0 𝑛 >
= 𝑚=02𝑀−1 𝑙=−∞
+∞ 𝑑𝑚,𝑙 < 𝑔𝑚,𝑙 𝑛 , 𝑔𝑚0,𝑙0 𝑛 >
= 𝑑𝑚0,𝑙0
if « complex » orthogonality of the pulses is fullfilled, i.e.,
< 𝑔𝑚,𝑙 𝑛 , 𝑔𝑚0,𝑙0 𝑛 >= 𝛿𝑚−𝑚0,𝑙−𝑙0
for 𝑚0, 𝑚 = 0, . . , 2𝑀 − 1 and ∀𝑙, 𝑙0 (between symbols and subcarriers). “Generalized Nyquist constraint”.
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Generalized Nyquist constraint
1
𝑇
𝑇𝑡
𝑓
27
𝑑𝑚0,𝑙0
𝑑𝑚,𝑙
Where is the gain of multicarrier systems?!
< 𝑔𝑚,𝑙 𝑛 , 𝑔𝑚0,𝑙0 𝑛 >
< 𝑔𝑚,𝑙 𝑛 , 𝑔𝑚0,𝑙0 𝑛 >= 𝛿𝑚−𝑚0,𝑙−𝑙0
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Practical channel conditions
Channel approximated as flat at the subcarrier level𝑥𝑚0,𝑙0 =< 𝑟 𝑛 , 𝑔𝑚0,𝑙0 𝑛 >≈ 𝐻(𝜔𝑚0
)𝑑𝑚0,𝑙0
and 𝑑𝑚0,𝑙0 is simply recovered by 𝑑𝑚0,𝑙0 = 𝐻−1 𝜔𝑚0
𝑥𝑚0,𝑙0 ≈ 𝑑𝑚0,𝑙0
Very simple channel “equalization”
𝑛
|ℎ 𝑛 ||𝐻(𝜔)|
𝜔
28
𝐻(𝜔𝑚0)
𝜔𝑚0
𝑆(𝜔𝑚0)
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Receiver
𝑑[𝑛]
1/𝑇𝑠
P/S
𝑥0,𝑙0
𝑥2𝑀−1,𝑙0
1/𝑇
1/𝑇
𝑥1,𝑙0
0,1,1,0,1 …
Demodulated symbol at subcarrier 𝑚0 and multicarrier symbol 𝑙0:
𝑥𝑚0,𝑙0 =< 𝑟 𝑛 , 𝑔𝑚0,𝑙0[𝑛] >
𝑛
𝑟 𝑛 𝑔𝑚0,𝑙0∗ 𝑛
29
𝐻−1 𝜔0
Symbol demapping
𝐻−1 𝜔1
𝐻−1 𝜔𝑚
𝑑0,𝑙0
𝑑1,𝑙0
𝑑2𝑀−1,𝑙0
1/𝑇
𝑟[𝑛]
1/𝑇𝑠
𝑔2𝑀−1,𝑙∗ [𝑛]
𝑔0,𝑙∗ [𝑛]
𝑔1,𝑙∗ [𝑛]
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Multicarrier systems vs single-carrier systems?
Easy channel equalization
Frequency division multiplexing
Resource allocation
Robust to timing offset
30
Used in most wireless communication standards ! Wi-Fi, DSL, LTE, DVB…
Sensitivity to carrier frequency offset and channel variation in timeHigh peak-to-average power ratio
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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
𝑔𝑚,𝑙 𝑡 = 𝑔 𝑡 − 𝑙Δ𝑡 𝑒𝑗2𝜋𝑚Δ𝑓𝑡
where 𝑚, 𝑙 ∈ ℤ. If Δ𝑡Δ𝑓 = 1, the Balian-Low theorem states that, if
{𝑔𝑚,𝑙 𝑡 , 𝑚, 𝑙 ∈ ℤ}
is an orthonormal basis for the Hilbert space 𝐿2(ℝ), then either
−∞
+∞𝑡2 𝑔 𝑡 2𝑑𝑡 = ∞ or −∞
+∞𝜔2 𝐺 𝜔 2𝑑𝜔 = ∞
where 𝐺(𝜔) is the Fourier transform of 𝑔(𝑡).
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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
< 𝑔𝑚,𝑙 , 𝑔𝑚0,𝑙0 > = 𝛿𝑚−𝑚0,𝑙−𝑙0 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.
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Bad for spectral efficiency, robustness, synchronization…
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OFDM leakage
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-𝑇
2𝑇
2
𝑔 𝑡
𝑡
|𝐺 𝜔 | = |sinc 𝜔𝑇 |
−∞
+∞
𝜔2 𝐺 𝜔 2𝑑𝜔 = ∞
−∞
+∞
𝑡2 𝑔 𝑡 2𝑑𝑡 ≤ 𝜉
Δ𝑡 = 𝑇, Δ𝑓 =1
𝑇and complex orthogonality (easy to show)
< 𝑔𝑚,𝑙 , 𝑔𝑚0,𝑙0 > = 𝑡
𝑔𝑚,𝑙(𝑡)𝑔𝑚0,𝑙0∗ (𝑡)𝑑𝑡 = 𝛿𝑚−𝑚0,𝑙−𝑙0
Wi-Fi, DSL, LTE, WiMAX, DVB…
Spectral leakage
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Spectral leakage leads to interference
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U1
U2
Frequency
Overlapping
U1
Synchronisation required to keep orthogonality
U2
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Time-frequency lattice of CP-OFDM
𝑠 𝑛 =
𝑚=0
2𝑀−1
𝑙=−∞
+∞
𝑑𝑚,𝑙 𝑔𝑚,𝑙[𝑛]
Undersampled lattice, loss in throughput rate
1
𝑇
𝑇 + 𝑇𝐶𝑃
𝑡
𝑓
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≈𝑇
10~
𝑇
4
Wi-Fi, DSL, LTE, WiMAX, DVB…
1
𝑇 + 𝑇𝐶𝑃1𝑇
=𝑇
𝑇 + 𝑇𝐶𝑃< 1
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Outline
Some basics
Single-carrier systems
Classical multicarrier systems
FBMC-OQAM systems
Principle
Pros and cons
My research
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Outline
Some basics
Single-carrier systems
Classical multicarrier systems
FBMC-OQAM systems
Principle “How does it work?”
Pros and cons
My research
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FBMC-OQAM principle
We want:
• Good time-frequency localization
• Full spectral efficiency
But how? Balian-Low…
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Use staggered lattices to circumvent the Balian-Low theoremIdea used by FBMC-OQAM modulations[Chang, 66], [Saltzberg, 67]Link to Wilson bases.
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Classical multicarrier lattice
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1
𝑇
𝑇𝑡
𝑓
Complex symbol
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FBMC-OQAM lattice
1
𝑇
𝑇𝑡
𝑓𝑇
2
Lattice density 1
Δ𝑡Δ𝑓=
1𝑇
21/𝑇
= 2 real symbols per second per Hertz
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Orthogonality satisfied only in the real domain
Real symbol
Imag. symbol
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Good frequency localization
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No need for synchronization of the users
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USER 1
USER 2
Frequency
USER 1 USER 2
No overlapping
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FBMC-OQAM transmission model
Transmitted signal
𝑠 𝑛 =
𝑚=0
2𝑀−1
𝑙=−∞
+∞
𝑑𝑚,𝑙 𝑔𝑚,𝑙 𝑛
with 𝑔𝑚,𝑙 𝑛 = 𝒋𝒍+𝒎𝑔 𝑛 − 𝒍𝑴 𝑒𝑗2𝜋
2𝑀𝑚𝑛.
Assume ideal channel, i.e., 𝑟 𝑛 = 𝑠[𝑛]. The demodulated signal is
𝑑𝑚0,𝑙0 = ℜ < 𝑠 𝑛 , 𝑔𝑚0,𝑙0 𝑛 >
= 𝑚=02𝑀−1 𝑙=−∞
+∞ 𝑑𝑚,𝑙 ℜ < 𝑔𝑚,𝑙 𝑛 , 𝑔𝑚0,𝑙0 𝑛 >
= 𝑑𝑚0,𝑙0
if, ℜ < 𝑔𝑚,𝑙 𝑛 , 𝑔𝑚0,𝑙0 𝑛 > = 𝛿𝑚−𝑚0,𝑙−𝑙0∀𝑚, 𝑚0, 𝑙, 𝑙0.
Purely real now !
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ℜ-ℑ pattern
Interference from symbol 𝑑𝑚,𝑙
−𝑙2𝑀 symbols are closer in time
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FBMC-OQAM lattice
1
𝑇
𝑇𝑡
𝑓𝑇
2
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𝑑𝑚0,𝑙0
𝑑𝑚,𝑙
ℜ < 𝑔𝑚,𝑙 𝑛 , 𝑔𝑚0,𝑙0 𝑛 >
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Real orthogonality conditions
< 𝑔𝑚,𝑙 𝑛 , 𝑔𝑚0,𝑙0 𝑛 > = 𝑗Δ𝑚+Δ𝑙 𝑛 𝑔 𝑛 − 𝑙𝑀 𝑔 𝑛 − 𝑙0𝑀 𝑒𝑗2𝜋
2𝑀Δm𝑛
… (simple math. manipulations)
= 𝑗Δ𝑚+Δ𝑙+Δ𝑙Δ𝑚 −1 Δ𝑚𝑙0
𝑛
𝑔 𝑛 −Δ𝑙𝑀
2𝑔 𝑛 +
Δ𝑙𝑀
2𝑒
𝑗2𝜋2𝑀 Δm𝑛
ℜ < 𝑔𝑚,𝑙 𝑛 , 𝑔𝑚0,𝑙0 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.
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“Ambiguity function”: real for real and even pulse 𝑔[𝑛]
Δ𝑚 = 𝑚 − 𝑚0, Δ𝑙 = 𝑙 − 𝑙0
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FBMC-OQAM lattice
1
𝑇
𝑇𝑡
𝑓𝑇
2
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Real symbol
Imag. symbol
Purely imaginary interference, eliminated directly when 𝑔[𝑛] is even and real
Remaining interference, eliminated by filter design Δ𝑚 = Δ𝑙 = 0 mod 2
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Outline
Some basics
Single-carrier systems
Classical multicarrier systems
FBMC-OQAM systems
Principle
Pros and cons “Why is it better?”
My research
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Pros and cons
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.
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Wait… Good for us ! We like complex things ! That means that there is still a lot to do !
Pros and Pros “Le beurre et l’argent du beurre”
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Evolution of telecommunicationstandards
2
2010… 2030
4G modulation format might not bethe best to address 5G challenges
2020… 2040
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Flexible spectrum utilization in 5G
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Fragmented spectrum
2 MHz 20 MHz5 MHz150 KHz
840MHz
1285MHz
20 MHz
602MHz 604MHz 820MHz
1280MHz
1700MHz1680MHz
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Outline
Some basics
Single-carrier systems
Classical multicarrier systems
FBMC-OQAM systems
Principle
Pros and cons
My research “What am I doing?”
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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
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I hope I convinced you !We are note alone…
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