MultiCarrier Transmission over Mobile Radio Channels

1
Multi-Carrier Transmission over Mobile Radio
Channels

• Jean-Paul M.G. Linnartz
• Nat.Lab., Philips Research

2
Outline

• Introduction to OFDM
• Introduction to multipath reception
• Discussion of receivers for OFDM and MC-CDMA
• Introduction to Doppler channels
• Intercarrier Interference, FFT Leakage
• New receiver designs
• Simulation of Performance
• Conclusions

3
OFDM

• OFDM a form of MultiCarrier Modulation.
• Different symbols are transmitted over different
  subcarriers
• Spectra overlap, but signals are orthogonal.
• Example Rectangular waveform -gt Sinc spectrum

4
I-FFT OFDM Transmission

• Transmission of QAM symbols on parallel
  subcarriers
• Overlapping, yet orthogonal subcarriers

5
OFDM Subcarrier Spectra

• OFDM signal strength versus frequency.
• Rectangle lt- FFT -gt Sinc
• before channel
• after channel

Frequency
6
Applications

• Fixed / Wireline
• ADSL Asymmetric Digital Subscriber Line
• Mobile / Radio
• Digital Audio Broadcasting (DAB)
• Digital Video Broadcasting - Terrestrial (DVB-T)
• Hiperlan II
• Wireless 1394
• 4G (?)

7
The Wireless Multipath Channel
8
(No Transcript)
9
The Mobile Multipath Channel

• Delay spread

• Doppler spread

10
Effects of Multipath Delay and Doppler
11
Effects of Multipath (II)
12
Multi-Carrier CDMA

• Various different proposals.
• (1) DS-CDMA followed by OFDM
• (2) OFDM followed by DS-CDMA
• (3) DS-CDMA on multiple parallel carriers
• First research papers on system (1) in 1993
• Fettweis, Linnartz, Yee (U.C. Berkeley)
• Fazel (Germany)
• Chouly (Philips LEP)
• System (2) Vandendorpe (LLN)
• System (3) Milstein (UCSD) Sourour and Nakagawa

13
Multi-Carrier CDM Transmitter

• What is MC-CDMA (System 1)?
• a form of Direct Sequence CDMA, but after
  spreading a Fourier Transform (FFT) is performed.
  
• a form of Orthogonal Frequency Division
  Multiplexing (OFDM), but with an orthogonal
  matrix operation on the bits.
• a form of Direct Sequence CDMA, but the code
  sequence is the Fourier Transform of the code.
• a form of frequency diversity. Each bit is
  transmitted simultaneously (in parallel) on many
  different subcarriers.

14
MC-CDM (Code Division Multiplexing) in Downlink

• In the forward or downlink (base-to-mobile)
  all signals originate at the base station and
  travel over the same path.
• One can easily exploit orthogonality of user
  signals. It is fairly simple to reduce mutual
  interference from users within the same cell, by
  assigning orthogonal Walsh-Hadamard codes.

BS
MS 1
MS 2
15
Synchronous MC-CDM receiver

• The MC-CDM receiver
• separates the various subcarrier signals (FFT)
• weights these subcarriers in W, and
• does a code despreading in C-1
• (linear matrix over the complex numbers)
• Compare to C-OFDM
• W equalization or AGC per subcarrier
• C-1 Error correction decoder (non-linear
  operation)

16
Synchronous MC-CDM receiver

• Receiver strategies (How to pick W ?)
• equalization (MUI reduction) w 1/b
• maximum ratio combining (noise reduction) w b
• Wiener Filtering (joint optimization) w b/(b2
  c)
• Next step W can be reduced to an automatic gain
  control, per subcarrier, if no ICI occurs

17
Synchronous MC-CDM receiver

• Optimum estimate per symbol B is obtained from B
  EBY
• C-1EAY C-1A.
• Thus optimum linear receiver can implement FFT -
  W - C-1
• Orthogonality Principle E(A-A)YH 0N, where A
  WYH
• Wiener Filtering W E AYH (EYYH)-1
• EAYH diagonal matrix of signal power
• EYYH diagonal matrix of signal plus noise power
• W can be reduced to an AGC, per subcarrier

Weigh
I-Code
N
N
N
N
S/P
P/S
FFT
Matrix
Matrix
Y
W
A
C
B
-1
18
MC-CDM BER analysis

• Rayleigh fading channel
• Exponential delay spread
• Doppler spread with uniform angle of arrival
• Perfect synchronisation
• Perfect channel estimation, no estimation of ICI
• Orthogonal codes
• Pseudo MMSE (no cancellation of ICI)

19
Composite received signal

• Wanted signal
• Multi-user Interference (MUI)
• Intercarrier interference (ICI)

20
Composite received signal

• Wanted signal
• Multi-User Interference (MUI)
• Intercarrier interference (ICI)

21
BER for MC-CDMA

• BER for BPSK versus Eb/N0
• (1) 8 subcarriers
• (2) 64 subcarriers
• (3) infinitely many subcarriers
• (4) 8 subc., short delay spread
• (5) 8 subc., typical delay spread

Local-mean Eb/N0
22
Capacity relative to non-fading channel

• Coded-OFDM
• same as N fading channels
• For large P0Ts/N0 on a Rayleigh fading channel,
  OFDM has 0.4 bit less capacity per dimension than
  a non-fading channel.

• MC-CDM
• Data Processing Theorem
• COFDM CMC-CDM
• In practise, we loose a little.
• In fact, for infinitely many subcarriers,
• CMC-CDM ½ log2(1 ?P0Ts/N0).
• where ? is MC-CDM figure of merit, typically -4
  .. -6 dB.

23
Capacity

• Capacity per dimension versus local-mean EN/N0,
• no Doppler.

24
MC-CDMA in uplink

• In the reverse or uplink (mobile-to-base), it
  is technically difficult to ensure that all
  signals arrive with perfect time alignment at the
  base station.
• Frame mis-alignments cause severe interference
• Different Doppler spectra for each signal
• Different channels for different signals
• Power control needed

BS
MS 1
MS 2
25
OFDM and MC-CDMA in a rapidly time-varying
channel

• Doppler spread is the Fourier-dual of a delay
  spread

26
Doppler Multipath Channel

• Describe the received signal with all its delayed
  and Doppler-shifted components
• Compact this model into a convenient form, based
  on time-varying amplitudes.
• Make a (discrete-frequency) vector channel
  representation
• Exploit this to design better receivers

27
Mobile Multipath Channel

• Collection of reflected waves, each with
• random angle of arrival
• random delay
• Angle of arrival is uniform
• Doppler shift is cos(angle)
• U-shaped power density spectrum

Doppler Spectrum
28
ICI caused by Doppler

Power or variance of ICI
3rd tier subcarrier
2nd tier subcarrier
Neighboring subcarrier
Doppler spread / Subcarrier Spacing
29
BER in a mobile channel

• Local-mean BER for BPSK, versus antenna speed.
• Local mean SNR of 10, 20 and 30 dB.
• Comparison between MC-CDMA and uncoded OFDM for
  fc 4 GHz
• Frame durationTs 896ms
• FFT size N 8192.
• Sub. spacing fs 1.17 kHz
• Data rate 9.14 Msymbol/s.

Antenna Speed m/s
30
Doppler Multipath Channel

• Received signal r(t)
• Channel model
• Iw reflected waves have
• the following properties
• Di is the amplitude
• ?I is the Doppler shift
• Ti is the delay

• OFDM parameters
• N is the number of subcarriers
• Ts is the frame duration
• an is the code-multiplexed data
• ?c is the carrier frequency
• ?s is the subcarrier spacing

31
Taylor Expansion of Amplitude

• Rewrite the Channel Model as follows
• Tayler expansion of the amplitude
• Vn(t) vn(0) vn(1) (t-?t) vn(2) (t-?t)2/2
  .. .
• vn(q) the q-th derivative of amplitude wrt
  time, at instant t ?t.
• vn(p) is a complex Gaussian random variable.

32
Random Complex-Gaussian Amplitude

• It can be shown that for p q is even
• and 0 for p q is odd.
• This defines the covariance matrix of subcarrier
  amplitudes and derivatives,
• allows system modeling and simulation between the
  input of the transmit I-FFT and output of the
  receive FFT.

33
DF Vector Channel Model

• Received signal Y y0, y1, yN-1 ,
• Lets ignore
• ?f frequency offset
• ?t timing offset
• We will denote ?? ?? (0) and ?? ?? (1)
• For integer ?, ?? ??0 (orthogonal subcarriers)
• ?? models ICI following from derivatives of
  amplitudes
• ?0 does not carry ICI but the wanted signal

System constants (eg sinc) determined by waveform
Complex amplitudes and derivatives
34
DF-Domain Simulation

• Simulation of complex-fading amplitudes of a
  Rayleigh channel with Doppler and delay spread
• Pre-compute an N-by-N matrix U, such that UUH is
  the channel covariance matrix ? with elements
  ?n,m Evn(0)vm(0)
• Simply use an I-FFT, multiply by exponential
  delay profile and FFT
• Generate two i.i.d vectors of complex Gaussian
  random variables, G and G, with unity variance
  and length N.
• Calculate V U G.
• Calculate V(1) 2?f?T U G.

35
DF Vector Channel Model

• Received signal Y y0, y1, yN-1 ,
• ?? models ICI following from derivatives of
  amplitudes
• ?0 does not carry ICI but the wanted signal

User data
Amplitudes Derivatives
FFT leakage
36
Possible Receiver Approaches

• Receiver
• 1) Try to invert adaptive matrix (Alexei
  Gorokhov)
• 2) See it as Multi-user detection (J.P.
  Linnartz, Ton Kalker)
• try to separate V . A and V(1). A
• 3) Decision Feedback (Jan Bergmans)
• estimate iteratively V, V (1) and A

37
Receiver 1 Matrix Inversion

• Estimate amplitudes V and complex derivatives V
  (1)
• create the matrix Q1 DIAG(V) T X DIAG(V(1))
• Invert Q1 to get Q1-1 (channel dependent)
• Compute Q1-1Y
• Zero-forcing
• For perfect estimates V and V (1), Q1-1Y A
  Q1-1N,
• i.e., you get enhanced noise.
• MMSE Wiener filtering inversion W

38
Receiver 1 MMSE Matrix Inversion

• Receiver sees Y Q A N, with QDIAG(V) TX
  DIAG(V(1))
• Calculate matrix Q DIAG(V) TX DIAG(V(1))
• Compute MMSE filter W QH Q QH ?n2 IN-1.
• Performance evaluation
• Signal power per subcarrier
• Residual ICI and Noise enhancement from W

39
Receiver 1 Matrix Inversion

• Simulation of channel for N 64, v 200 km/h
  fc 17 GHz, TRMS 1 ms, sampling at T 1ms.
  fDoppler 3.14 kHz, Subcarrier spacing fsr
  31.25 kHz, signal-to-ICI 18 dB

40
Receiver 1 Matrix Inversion

• SNR of decision variable. Simulation for N 64,
  MMSE Wiener filtering to cancel ICI

MMSE ICI canceller
Conventional OFDM
41
Simplified Matrix Inversion

• Rationale
• ICI diminishes with increasing subcarrier
  difference
• Approximate X by band matrix with 2k1 non-zero
  diagonals
• Matrix Q is approximately Q I D L
• D small, D X diag(V(1) ./ V)
• L diagonal of amplitudes V
• Approximate Q-1 I - D L-1
• Complexity 2kN

42
Performance of (Simplified) Matrix Inversion

• N 64, v 200 km/h, fc 17 GHz, TRMS 1 ms,
  sampling at T 1ms.
• fDoppler 3.15 kHz, Subc. spacing fsr 31.25
  kHz
• Compare to DVB-T v 140 km/h, fc 800MHz
  fdoppler 100 Hz while fsr 1.17 kHz

43
Receiver 1 Subconclusion

• Performance improvement of 4 .. 7
• Complexity can be reduced to 2kN, k 5 .. 10.
• Estimation of V(1) to be developed, V is already
  being estimated

44
Receiver 3 Decision Feedback

• Estimate
• data,
• amplitudes and
• derivatives
• iteratively

45
Receiver 3 Decision Feedback

• Iteratively do the following
• Compare the signal before and after the slicer
• Difference noise ICI decision errors
• Invert X to retrieve modulated derivatives from
  ICI
• V(1).A X-1 ICI
• MMSE to minimize noise enhancements
• Remove modulation 1/A
• Smooth to exploit correlation in V(1)
• Modulate with A
• Feed through X to estimate ICI
• Subtract estimated ICI

46
Receiver 3 DFE

• Estimate V(1) in side chain

Channel Model
47
Implementational Aspects

• Implementational considerations
• 1/A table lookup
• 20 taps FIR filter
• (select from library depending on Doppler)
• 2 taps IIR filter bi-directional
• (select from library depending on Delay)
• FFT - multiply - I-FFT

Estimated
Amplitudes
Pilot
Cancel
V
Doppler
Y
A
Y

0

2
Slicer
-
A
.
V

-
ICI
FIR
10X
x
weigh
1/
A
IIR
V

INT
A
x
48
Implementational Aspects
Estimated
Amplitudes
Pilot
Cancel
V
40
Doppler
Y
A
Y

0

30
2
Slicer
-
20
X
A
.
V

10
-
0
ICI
Optimal
-10
FFT
FIR
Amplitude of Filter Coefficients
-20
IIR
-30
x
weigh
1/
A
-40
-50
IIR
X-1
-60
FFT
V

-70
INT
-20
-15
-10
-5
0
5
10
15
20
A
Relative Subcarrier Number
x
Get derivatives modulation Smooth according to
delay profile Reconstruct ICI
49
Performance of Receiver 3 DFE

• Variance of decision variable after iterative ICI
  cancellation versus variance in conventional
  receiver

Variance of decision variable in DFE receiver
after ICI cancelling
Variance decision variable in conventional
receiver
50
Receiver 3 DFE

• N 64 out of 8192 subcarriers, v 30 m/s, fc
  600 MHz TRMS / NT 0.03, fDoppler 60 Hz,
  Subcarrier spacing fsr 1.17 kHz

51
Conclusions

• Modeling the Doppler channel as a set of
  time-varying subcarrier amplitudes leads to
  useful receiver designs.
• Estimation of V(1) is to be added, V is already
  being estimated
• Basic principle demonstrated by simulation
• Gain about
• 3 .. 6dB,
• factor of 2 or more in uncoded BER,
• factor 2 or more in velocity.
• Promising methods to cancel FFT leakage (DVB-T,
  4G)
• More at http//wireless.per.nl

52
Further Research Work

• Optimise the receiver design and estimation of
  derivatives
• Can we play with the waveform (or window) to make
  the tails of the filter X steeper?
• Can we interpret the derivatives as a diversity
  channel?
• Can estimation of derivatives be combined with
  synchronisation?
• Isnt this even more promising with MC-CDMA?
• Apply it to system design.