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

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

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 ••• •••

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 .

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

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

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

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

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

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

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

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)

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 .

Impulse Response Measurement

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.

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.

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 :

(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)

RAKE Receiver Block Diagram

Another Block Diagram

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.

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

 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

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

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 ... )

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

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

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

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

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

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

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

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:

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).

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.

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 :