1. Digital transmission over a fading channel
Narrowband system (introduction)
Wideband TDMA (introduction)
Wideband DS-CDMA (introduction)
Rake receiver (structure & analysis)

2. Propagation of Tx Signal
With low time-resolution,
different signal paths cannot be discriminated.
•••
These signals sometimes strengthen,
and sometimes cancel out each other,
depending on their phase relation.
••• This is “fading”.
In this case, signal quality is damaged
when signals cancel out each other.
In other words, signal quality is dominated
by the probability for detected power
to be weaker than minimum required level.
This probability exists with less than two paths.
Path Delay
Power
path-1
path-2
path-3
Time
Power
Detected Power

3. Fading in CDMA System ... ••• •••
Because CDMA has high time-resolution,
different path delay of CDMA signals
can be discriminated.
•••
Therefore, energy from all paths can be summed
by adjusting their phases and path delays.
••• This is a principle of RAKE receiver.
Path Delay
Power
path-1
path-2
path-3
Path Delay
Power
CODE A
with timing of path-1
path-1
interference from path-2 and path-3
CDMA
Receiver
path-3
しかし、CDMAシステムは、スペクトルを拡散するため速いチップレートの信号を使用しており、高い時間分解能を持っています。このため、時間差を持って到達するそれぞれのパスを分解して認識することができます。これより、違うパスの信号をそれぞれ別々に受信して、後でで足しあわせることにより、信号の劣化を防ぐことが出来ます。
これをRAKE受信機と呼びます。
path-2
Power
Synchronization
Adder
path-1
Path Delay
Power
CDMA
Receiver
CODE A
with timing of path-2
path-2
•••
•••

4. Fading in CDMA System (continued)
In CDMA system, multi-path propagation improves
the signal quality by use of RAKE receiver.
Power
path-1
path-2
path-3
Detected Power
このRAKE受信機を利用することにより、フェージングによる受信信号の落ち込みを緩和させることができ、安定した通信環境が確保できるようになります。それにより、ユーザへ安定した品質を保証することが出来ます。
Power
RAKE
receiver
Time
Less fluctuation of detected power, because of adding all energy .

5. Three kinds of systems (1)
Narrowband system:
Flat fading channel, single-tap channel model, performance enhancement through diversity (future lecture).
System bandwidth
D = delay spread of multipath channel
bit or symbol
T = bit or symbol duration

6. No intersymbol interference (ISI)
Narrowband system:
Adjacent bits (or symbols) do not affect decision process (in other words there is no intersymbol interference).
Received replicas of same bit overlap in multipath channel
No intersymbol interference at decision time instant
However:
Fading (destructive interference) possible

7. Decision circuit
In the binary case, the decision circuit compares the received signal with a threshold at specific time instants:
Distorted symbols
Clean symbols
Decision circuit
Decision threshold
Decision time instant

8. Three kinds of systems (2)
Wideband system (TDMA):
Selective fading channel, transversal filter channel model, good performance possible through adaptive equalization (future lecture).
Intersymbol interference
=> signal distortion
D = delay spread of multipath channel
T = bit or symbol duration

9. Receiver structure
The intersymbol interference of received bits (symbols) must be removed before decision making:
Symbols with ISI
Symbols without ISI
Clean symbols
Adaptive
equalizer
Decision
circuit

10. Three kinds of systems (3)
Wideband system (CDMA):
Selective fading channel, transversal filter channel model, good performance possible through use of Rake receiver (this lecture).
D = delay spread of multipath channel
Tc = Chip duration
...
bit or symbol
T = bit or symbol duration

11. Three kinds of systems: BER performance
Frequency-selective channel (equalization or Rake)
BER
Frequency-selective channel (no equalization or Rake)
“BER floor”
AWGN channel (no fading)
Flat fading channel
S/N

12. Rake receiver structure and operation
Rake receiver <=> a practical example that illustrates important concepts
Rake receiver is used in DS-CDMA (Direct Sequence Code Division Multiple Access) systems (like UMTS)
Rake “fingers” synchronize to signal components that are received through a wideband multipath channel
Important task of Rake receiver is channel estimation
Output signals from Rake fingers are combined, for instance using Maximum Ratio Combining (MRC)

13. To start with: multipath channel
Suppose a signal s (t) is transmitted. A multipath channel containing L paths can be presented (in equivalent low-pass signal domain) in form of its impulse response
in which case the received (equivalent low-pass) signal is of the form .

14. Impulse Response Measurement

15. Sampled channel impulse response
Wideband Channel Impulse Response (CIR)
Sampled CIR is presented in form of complex-valued samples spaced at most 1/W apart, where W is RF system bandwidth:
Uniformly spaced channel samples
Delay ( )
Generally: CIR sampling rate = sampling rate in receiver after A/D conversion.

16. Rake finger selection
Channel estimation circuit of Rake receiver selects strongest samples (paths) to be processed in the Rake fingers:
Only one path chosen, since adjacent paths may be correlated
L = 3
Only these paths are constructively utilized in Rake fingers
Delay ( )
In the Rake receiver example to follow, we assume L = 3.

17. Received multipath signal
Received signal consists of a sum of delayed (and weighted) replicas of transmitted signal.
Blue samples (paths) indicate signal replicas detected in Rake fingers
Green samples (paths) only cause interference
All replicas are contained in received signal and cause interference
Signal replicas: same signal at different delays, with different amplitudes and phases
Summation in channel <=> “smeared” end result :

18. (Generic structure, assuming 3 fingers)
Rake receiver
(Generic structure, assuming 3 fingers)
Received baseband multipath signal (in ELP signal domain)
Channel estimation
Weighting
Finger 1 
Output signal (to decision circuit)
Finger 2
Finger 3
Rake receiver
Combining (MRC)

19. RAKE Receiver Block Diagram

20. Another Block Diagram

21. Channel estimation Channel estimation A C B A B C
Amplitude, phase and delay of signal components detected in Rake fingers must be estimated. B
Each Rake finger requires delay (and often also phase) information of the signal component it is processing. C
Maximum Ratio Combining (MRC) requires amplitude (and phase if this is not utilized in Rake fingers) of components processed in Rake fingers.

22. Rake finger processing
Case 1: same code in I and Q branches
- for purpose of easy demonstration only
- no phase synchronization in Rake fingers
Case 2: different codes in I and Q branches
- the real case in IS-95 and WCDMA
- phase synchronization in Rake fingers

23.  Rake finger processing (Case 1: same code in I and Q branches)
Received signal
Stored code sequence
I branch 
To MRC
Delay
I/Q
Q branch
Output of finger: a complex signal value for each detected bit

24. Correlation vs. matched filtering
Basic idea of correlation:
Stored code sequence
Received
code sequence
Same end result !
Same result through matched filtering and sampling:
Received
code sequence
Matched
filter
Sampling
at t = T

25. Rake finger processing
Correlation with stored code sequence has different impact on different parts of the received signal
= desired signal component detected in i:th Rake finger
= other signal components causing interference
= other codes causing interference (+ noise ... )

26. Rake finger processing
Illustration of correlation (in one quadrature branch) with desired signal component (i.e. correctly aligned code sequence)
“1” bit
“0” bit
“0” bit
Desired component
Stored sequence
After multiplication
Strong positive/negative “correlation result” after integration

27. Rake finger processing
Illustration of correlation (in one quadrature branch) with some other signal component (i.e. non-aligned code sequence)
“1” bit
“0” bit
Other component
Stored sequence
After multiplication
Weak “correlation result” after integration

28. Rake finger processing
Mathematically:
Correlation result for bit between
Desired signal
Interference from same signal
Interference from other signals

29. Rake finger processing
Set of codes must have both:
- good autocorrelation properties (same code sequence)
- good cross-correlation properties (different sequences)
Large
Small
Small

30. Rake finger processing
(Case 2: different codes in I and Q branches)
Stored I code sequence
Received signal
To MRC for I signal
Delay
I/Q
I branch
To MRC for Q signal
Q branch
Required: phase synchronization
Stored Q code sequence

31. Phase synchronization
When different codes are used in the quadrature branches (as in practical systems such as IS-95 or WCDMA), phase synchronization is necessary.
I/Q
Phase synchronization is based on information within received signal (pilot signal or pilot channel).
Note: phase synchronization must be done for each finger separately!
Pilot signal Q
Signal in Q-branch I
Signal in I-branch

32. Weighting (Case 1: same code in I and Q branches)
Maximum Ratio Combining (MRC) means weighting each Rake finger output with a complex number after which the weighted components are summed “on the real axis”:
Component is weighted
Phase is aligned
Rake finger output is complex-valued
Instead of phase alignment: take absolute value of finger outputs ...
real-valued

33. Phasors representing complex-valued Rake finger outputs
Phase alignment
The complex-valued Rake finger outputs are phase-aligned using the following simple operation:
Before phase alignment:
Phasors representing complex-valued Rake finger outputs
After phase alignment:

34. Maximum Ratio Combining
(Case 1: same code in I and Q branches)
The signal value after Maximum Ratio Combining is:
The idea of MRC: strong signal components are given more weight than weak signal components.
Why is the performance of MRC better than that of Equal Gain Combining (EGC)?
The answer will be given in future lecture (diversity methods).

35. Maximum Ratio Combining of Symbols
MRC corrects channel phase rotation and weighs components with channel amplitude estimate.
The correlator outputs are weighted so that the correlators responding to strong paths in the multipath environment have their contributions accented, while the correlators not synchronizing with any significant path are suppressed.

36. Maximum Ratio Combining
(Case 2: different codes in I and Q branches)
Output signals from the Rake fingers are already phase aligned (this is a benefit of finger-wise phase synchronization).
Consequently, I and Q outputs are fed via separate MRC circuits to the quaternary decision circuit (e.g. QPSK demodulator).
MRC  I
Finger 1 I Q
Quaternary
decision
circuit I
Finger 2 Q
MRC  Q :