Design of path searcher for WCDMA receiver and implementation in DSP

2008:090

M A S T E R ' S T H E S I S

Design of path searcher for WCDMA receiver and

implementation in DSP

Kai Chen

Luleå University of Technology Master Thesis, Continuation Courses

Electrical engineering

Department of Computer Science and Electrical Engineering Division of Signal Processing

2008:090 - ISSN: 1653-0187 - ISRN: LTU-PB-EX--08/090--SE

Master thesis

Design of path searcher for WCDMA receiver and implementation in DSP

Kai Chen

Abstract ...4

Introduction to project...5

1. Review of WCDMA theory ...6

1.1 Spreading Spectrum Communications ...6

1.1.1 M-array constellation model ...6

1.1.2 Random noise sequence as basis function...8

1.1.3 The advantage of spread spectrum communication ...10

1.2 Detector in spread spectrum communication ... 11

1.2.1 Review of MAP and ML detector ... 11

1.2.2 Detector with non-orthogonal basis in CDMA ...12

1.2.3 Detector with orthogonal basis in CDMA...13

1.2.4 Why apply orthogonal detector in CDMA system? ...13

1.2.5 Summary of model, detector and delimitation ...14

1.3 Wireless channel model...15

1.3.1 Multi-tap delay model ...15

1.3.2 Fading model...16

1.3.3 Time varied channel model ...19

1.3.4 Summary of Channel model...19

1.4 WCDMA introduction...20

1.4.1 Background of WCDMA ...20

1.4.2 Structure of physical lay in WCDMA handset receiver ...21

2. Time synchronization in WCDMA ...23

2.1 Introduction to ML phase estimation and PLL ...23

2.2 Path searcher detection theory ...24

2.2.1 Signal of path searcher with orthogonal basis function...25

2.2.2 Basic classifier of receiver signal in path searcher...26

2.2.3 Neyman - Pearson classifier-without prior probability: ...27

2.2.4 Sequence Detector for Path searcher...28

2.3 PDP path searcher theory ...30

2.3.1 Introduction to PDP path searcher ...30

2.3.2 Non coherent ML detector ...30

2.4 PDP path searcher design ...31

2.4.1 Structure of PDP path searcher...31

2.4.2 Parameters choice...32

3 Simulation results...34

4. Theory of DSP implementation...36

4.1 Characters of DSP ...36

4.2 Introduction of ADI tiger-SHARC...40

4.2.1 Basic feature...40

4.2.2 The hardware accelerator instruction for CDMA-XCORR...41

4.2.3 Pipeline in ADSP-TS201S Tiger-SHARC processor ...44

5. Fixed point algorithm optimization...45

6. Implementation in tiger SHARC DSP ...47

6.1 How to get the best performance of DSP ...47

6.1.1 Parallel computing ...47

6.1.2 Software pipeline and Eliminate delay/stalls ...47

6.2 Optimal key loop for Path searcher...48

6.2.1 Parallel computation unit ...48

6.2.2 Memory management...48

6.2.3 Software pipeline ...49

7. Benchmarks Result of DSP...49

8 Conclusion ...50

8.1 Algorithm design...50

8.2 Software implementation ...50

9 Reference ...51

Abstract

Code Division Multiple Access (CDMA) is a widely used wireless access technology that requires completing huge correlations in real-time, especially at the receiver. Most baseband receivers are hence implemented in hardware to fit this requirement. Meanwhile, the wireless technologies develop so quickly that implementation has to be modified to add new development. This kind of modification is especially costly in hardware design. The purpose of this thesis is to take advantage of Digital Signal Processors (DSP) and to complete a software solution of Path search in Wideband Code Division Multiple Access (WCDMA) receivers. In general, the DSP still can not achieve the same powerful calculation ability as hardware solutions and we will try to modify the inherent algorithms if required.

The purpose is to design the algorithm and implement a path searcher following the WCDMA standard. Path searcher is one of the main components in WCDMA receiver.

It can be use to detect the many signals in WCDMA channel.

Introduction to project

Background and target of project

The wireless communication technology develops very quickly and it demand engineers to modify the function to catch up with those developments. Since the design and implementation of hardware is so costly and it’s so easy in software, software implementation may be a good alternative for the wireless industry.

Meanwhile, since software is not capable of completing large number of calculation in shot time, this character limits the application of software solutions in wireless communication physical layer where the component have to complete large number of calculation, such as 1000 times of correlation or FFT, in less than 1/100 second.

To make the software implementation possible for wireless physical layer applications, low complex algorithms and powerful Digital Signal Processor (DSP) are two main ingredients.

The target of this project is completing a software implementation of the path searcher, which is a component in Wideband Code Division Multiple Access (WCDMA) receiver systems.

Delimitation:

In this project, a WCDMA system will be analyzed as an orthogonal system

Summary of project

Firstly, a simplified model and detector with orthogonal basis function, instead of very complex multi-input and multi-output (MIMO) ones with non-orthogonal basis function will be reviewed. The character of typical wireless channels and their effect on design will also be discussed.

Secondly, Path searcher strategies will be discussed based on the simplified model and detector. Further, for practical application environment and wireless channels, the details of design will be investigated.

At last, the path searcher will be implemented in an ADI tiger-SHARC DSP.

Comparing with other programming, DSP programming focus on parallel computing

and cache miss reducing.

1. Review of WCDMA theory

WCDMA is a widely recognized 3G wireless communication standard based on spread spectrum communication. The basic analysis of spread spectrum communications model, Maximum a posteriori (MAP), Maximum Likelihood (ML) detector and simplified ones with orthogonal basis will be explored and applied in WCDMA system analysis. Further the character of wireless channels and their effect on the design of WCDMA system and the receive model in this project will be introduced. At last, the structure of WCDMA system will be investigated.

1.1 Spread Spectrum Communications

Analysis of spread spectrum communication is based on signal space theory, which applies basis functions to separate different users. In this chapter, a general analysis of an M-ary communication model and a simplified one will be introduced. Moreover, this model will be applied in spread spectrum communication with random noise. At last, the advantage of spreading spectrum communication will be explained.

1.1.1 M-ary constellation model

The basic structure of an M-dimensioned constellation model and its simplification representation with orthogonal basis function will be shown here:

Consider a communication system model with an M-dimensioned constellation using basis functions θ

^. The geometrical representation for the source symbols are

s

m=1….M, the theoretic model is shown figure 1:

Figure.1 M-array communication model The receiver signal will be:

∫

∑ ∫

∫ ^{+ +}

=

≠

= T

k T

k l l m

k T l

k k k

k

s t t dt s t t dt n t t dt

r ( ) ( ) ( ) ( ) ( ) ( )

, 1

θ θ

θ θ

θ

In general, the received signal will be affected by all input signal in the second term, i.e. ∑ ∫

≠

= T

k l l m

k l

dt t t s ( ) ( )

, 1

θ

θ ^, which make the model very complex.

A simplified model can be achieved if the basis functions are orthogonal.

Given orthogonal basis functions θ

 



≠

= =

∫

^{( t )}

^{( t ) d 1} ₀ ⁽ ₍ ^k _k ^l _l ⁾ ₎

T

τ θ θ

And ⁼ ∫ ⁺ ∑ ∫ ⁺ ∫

≠

= T

k T

k l l m

k T l

k k k

k

s t t dt s t t dt n t t dt

r ( ) ( ) ( ) ( ) ( ) ( )

, 1

θ θ

θ θ

θ

Having orthogonal basis functions cancel the second term θ

^(t)

θ

^(t)

θ

^(t)

θ

^(t)

θ

^(t)

θ

^(t)

n(t)

r(t)

∫ ^{() dt}

∫ ^{() dt}

∫ ^{() dt}

s(t)

r

r

s

r

Detector

s

s

k k T

k k

k

s n t t dt s n

r = + ∫ ^{( ) θ ( )} = + with Cov ( n

, n

)

 



≠

= =

) ( 0

) ( 2 /

1

l k

l k N

This means the model can be simplified as figure 2:

Figure 2. Orthogonal basis communication model And r

= s

+ n

1.1.2 Random noise sequence as basis function

Spread spectrum communication applies a pseudo-random noise sequences as basis functions. Because of the characters of uncorrelated random sequences, they are similar to those of orthogonal basis functions.

Uncorrelated random sequence as orthogonal basis function

Usually the bandwidth of a typical basis function is very limited. But what if we take uncorrelated random noise sequences _θ

as basis function? Since they are uncorrelated noise sequence, we can get

 



≠

= =

∫

^{( t )}

^{( t ) d} ₀ ^C ₍ ⁽ _k ^k _l ^l ₎ ⁾

T

τ θ

θ by their autocorrelation and cross-correlation definition

It fits the definition of orthogonal basis function and we can apply it as basis function. Compared with normal basis function, the bandwidth of noise sequence is very large since it is a noise sequence. Therefore, we call those noise sequences as spread spectrum signal.

s

r

n

Detector

Example of spread spectrum signal communication

Compared with other communication system, there is a unique part in spread spectrum communication system which would generate Pseudo noise (PN) sequences as random noise sequence. We would take this PN sequences as basis function. The PN sequences would spread the spectrum of source sequences. Pseudo noise sequences are ‘almost random’ sequences, their autocorrelation and cross-correlation character resembles independent noise sequence. The common model of spread spectrum communication system shows in Figure 3

Figure 3 Example of spread spectrum system Figure 4 will give us a picture of how spread spectrum system works

Figure 4 Example of spread and de-spread Source

Coding

Channel

Spread De-spread decoding

PN PN

Sequence 1 is source before spread; the interval of it is Ts

Sequence 2 is PN sequence with interval Tc. The rate L= Ts/Tc=4 is a integer and normally L>>1

Sequence 3 is the spreaded sequence

If we assume that there is no noise in the channel, the receive sequence is sequence 3. If we multiply same PN sequence 2 with Sequence 3, we get source sequence (Sequence 1) again.

1.1.3 The advantage of spread spectrum communication

Spread spectrum signal will expand the bandwidth of the original information signal greatly with the spread signal’s bandwidth B. This character seems waste bandwidth when transmit those signal, but from Shannon–Hartley theorem

C = B ( 1 + S / N )

We can know if we keep the same channel capacity C, introduce redundancy bandwidth means we can lower the energy of signal bit, so we can get a wide band but low S/N signal. Spread spectrum signal are used in following field, as [1] introduced:

1. Anti-jamming ,low detectable and secrecy communication

This is a military application. Compared with FSK or other modulation technologies, the bandwidth of spread spectrum signal is often larger than l0 MHz .It is hard for the enemy to suppressing the whole bandwidth and interrupt the communication by interference (jamming). Also, the S/N of this spread spectrum signal is very low and hard to detect. At last, when de-spreading the spread spectrum signal, we require the original spread signal. This character make the information private without knowing those codes.

2. Anti-frequency selective or time selective fading

There are always some deep but narrow fading in particular frequency/time in moving channel .It is easy to understand that a wide band signal can easily handle this problem when fading only occur in a narrow frequency/time

3. Multi-user Access

Due to the low power of spread signal and its way of demodulation and

orthogonality among sequences, it is possible for more than one user to transmit the

signal in the same time via the same frequency band. In this case other users’ signal

can be viewed as noise. This type of Multi-user Access is called Code Division

Multiple Access, well known as CDMA

1.2 Detector in spread spectrum communication

Based on the formal analysis, MAP detector theory will be applied here to figure out the optimal detector for spread spectrum systems. At first, the MAP/ML detector will be reviewed; secondly, I will discuss the general case: detectors for non-orthogonal basis functions; and then a simple detector in the orthogonal basis case will be developed. This will later be applied in the path searcher. At last, I will explain why this simplification can be applied in the project.

1.2.1 Review of the MAP and ML detector

The purpose of the detector is to find out the original source signal from the received signal; for example, as figure 1, if the receive signal are recorded, the detector will try to find out the source signal [ s

, s

.... s

] .

The MAP detector will get the optimal performance [3] by calculating the conditional probability of all possible source signals P[s | r] on the condition of r to find out the largest one sˆ ,which will maximum the P[s | r]. s and r are the vectors

] ....

,

[ s

s

s

and to represent a combination of source or receiver signals ,and sˆ is the best decision in this case.

Sk

max

= arg p [ s

| r ] By Bayes’ theorem, for any source signal s

( ) ) ( )

| ) (

|

( r

s s r r

s p

p

p

= p

p(r) is the same and positive for all s and can be neglected,

p s (

) is the prior probability of each source symbol s and should be known before, and only

)

|

(

p r s need to be calculated to find out the best decision sˆ .

For the orthogonal basis function case, white Gaussian channel noise and equal prior probability p s (

) for all symbols, the result is:

] ..

, [ r

r

r

] ..

, [ r

r

r

sˆ



 





 

 − −

−

= 2

] [

] exp [

|

| ) 2 ( ) 1

|

(

T k k m

p r s K r s

s K

r π

And this is known as the Maximum Likelihood (ML) detector.

1.2.2 Detector for non-orthogonal basis in CDMA

Basic analysis of detector for non-orthogonal basis function CDMA system will be explored here. The details can be found in [2]. Again, we will consider a system containing m users, assuming that source signal from user m is s

(k ) . Further, the random noise sequence acting as basis function for this user is θ

(t ) , as Figure 1a

Figure 1a CDMA system

∫

∑ ∫

∫ ^{+ +}

=

≠

= T

k T

k l l m

k T l

k k k

k

s t t dt s t t dt n t t dt

r ( ) ( ) ( ) ( ) ( ) ( )

, 1

θ θ

θ θ

θ

Applying the MAP detector in the CDMA multi-users case, the detector will try to find out a set of [ s

, s

.... s

] to maximum the posterior probability P ([ s

, s

... s

] | [ r

, r

.. r

]) , as [4] introduced. By Bayes’

theorem, ( )

) ( )

| ) (

|

( r

s s r r

s p

p

p

= p

, where p ( s

| r ) need to be calculated. If the

noise is jointed Gaussian distributed.

2 ]

] [

] exp[ [

|

| ) 2 ( ) 1 (

1

2 / 1 2 /

s θ r Κ s θ r r Κ

|

s

T k k m

p = − −

−

π

K is the covariance matrix decided by Gaussian noise and basis function vector θ . It’s easy to known the results only decided by the term

] [

]

[ r s

θ

Κ

r s

θ

Q = − −

− ^,

Q is the metric variable need to be maximum, detail analysis of CDMA detector can be found in [5] and [6].

1.2.3 Detector with orthogonal basis in CDMA

Detector with orthogonal basis function will be discussed in this paragraph With orthogonal basis functions, it is easy to get the signal mode as following:

k k

k

s n

r = +

So instead of finding out a signal vector [ s

, s

.... s

] from all possible source signal vector combination [ s

, s

.... s

] to maximum the posterior P ([ s

, s

... s

] | [ r

, r

.. r

]) , the detector for orthogonal basis functions only need to consider the signal from one user s to maximin.

p ( s

| r

) . To find out the best decision sˆ , it can hence neglect

the effect of the other signals. The ML detector would hence maximin the likelihood:

 



 

 − −

=

2 ) exp (

2 ) 1

|

( π σ σ

i k i

k

s s r

r P

To achieve this only requires the following calculation

i k

s r Q = −

1.2.4 Why apply orthogonal detector in CDMA system?

The basis function of practical CDMA system is not orthogonal, but under some assumptions, orthogonal detector can applied in CDMA systems.

To see this, we look at received signal in an orthogonal basis system

∫

∑ ∫

∫ ^{+ +}

=

≠

= T

k T

k l l m

k T l

k k k

k

s t t dt s t t dt n t t dt

r ( ) ( ) ( ) ( ) ( ) ( )

, 1

θ θ

θ θ

θ

For CDMA systems, if we are only interested in decoding user k(single user detector), the second term is seen as a sum of a large number of random source signals ∫

T

k l

l

t t dt

s θ ( ) θ ( ) ^{. By} the central limit theorem, the second term is a Gaussian random variable. Meanwhile the third term is also Gaussian random variable whereby the sum of the second and third term should also be a Gaussian random variable.

Hence, in this case the received signal turn out to be:

)

( )

( t t dt n s

r

T

k k k

k

= ∫ ^{θ θ} +

For sequence with known energy, ∫

T

k k

( t ) θ ( t ) dt

θ can be normalized and we get

r

= s

+ n

In this case, we can consider the CDMA system as an orthogonal basis system and apply the orthogonal detector

1.2.5 Summary of model, detector and delimitation

As discussed in the previous section, under the assumption that the CDMA system is an orthogonal system, a simplified detector can be applied. The results are listed as following:

1. CDMA system as a orthogonal system 2. signal model is

k k

k

s n

r = +

3. MAP and ML detector

2 ) )) ( ) ( exp ( 2

max( 1 arg

and )) (

| ) ( ( max arg

2 2

 



 

 − −

σ σ π

k s k r k r k s p

i k

k i

1.3 Wireless channel model

A wireless channel model will be introduced, including multi-tap delay model and fast fading model in order to support the design of path searcher. At first, a multi-tap delay model, which determines the structure of CDMA receiver, will be introduced;

secondly, a fading model, which determines the channel coefficient, will be investigated. At last, the time variable channel will be presented.

The wireless channel will introduce channel coefficient A ( kT ) e

in the received signal s

) ( )

( ) ( )

( k s k A kT e

n

k

r

=

+

And the received signals may be accumulation of many overlaping signals r ( k ) = ∑ r

( k ) ^θ

( t − kT

)

If the basis functions θ

are orthogonal in time, we can neglect the overlap. In path searcher design, the overlap will be neglected.

1.3.1 Multi-tap delay model

When the wireless signal travels from transmitter to receiver, it may go directly from

start point to end point, as path2; or it will be reflected, as path 1 and path 3, see

figure 5. In those cases, the time delays τ of different paths are different, and all those

paths will be added together to generate the received signal. This is hence a multi-tap

delay model of wireless transmission. The different delays τ will let the signal overlap

and render inter-symbol interference (ISI).

Figure 5. Example of Multi-tap delay The signal after overlap is:

) (

) ( )

( k r

k

t kT

r = ∑ θ −

1.3.2 Fading model

Real life wireless channels have various kinds of propagation effects; one of the most important ones in cellar phone systems is fading. Fading is due to the relative movement of transmitter, receiver or obstacle. Jakes give a very good model to explain this phenomenon in [7], and I will explore it here.

The wireless channel will introduce the coefficient A ( kT ) e

in the receive signal )

( )

( ) ( )

( k s k A kT e

n

k

r =

+

The channel coefficient A ( kT ) e

is a random variable whose character is the following:

1. Amplify A(t) is Gaussian random processing with autocorrelation function )

2 ( )

(

XX

τ ^J π ^f τ

R = ∆

λ f = v

∆ v is the speed between the transmitter and receiver; λ is wavelength

is A(t) of function density

spectral Power

Normalized and

kind first the of function Bessel

order - zeroth is J

Path 1

Path 3

Path 2

1 ) 1

(

 

 



 ∆

−

•

=

λ π λ

v f v

f s

2. Phase e

is uniform distributed random processing in [ 0 , 2 π ]

The basic idea behind Jakes model is following. Fading is generated because the radio signal reflected by obstacles between the transmitter and receiver. If there is no Line of Sign (LOS) and all the paths propels indirectly from the transmitter to the receiver, they all are reflected by different kinds of obstacles

Figure 6 Example of Fading

Furthermore, if the transmitter, receiver and obstacles are all or at least one of them are moving during transmission. The spectrum of the received signal will experience a a Doppler frequency shift f ∆ .

λ f = v

∆ v is the speed between the transmitter and receiver; λ is wavelength It’s easy to understand that this process is random because the obstacle may be a car, a bus, a ship or cloud whose properties are unknown. This makes fading a random process. Jakes’ model [8] believe that there are a huge number of reflected paths between the transmitter and receiver, all arriving with uniform distribution in arrive angle ϕ

and the amplitude k

Rx

Tx

Figure 7 Example of Doppler frequency shift

The relate Doppler shift is then given by

v cos(

)

f ϕ

= λ

∆

If we assume the arrived angle ϕ

is uniform distribution and the amplitude k

is Gaussian distribution. The envelop of the receive signal is Rayleigh distribution with density:

2 2 /2 2

)

/ ( ) 0

( ^α

ϕ α ^e

p a

 

= 

We can also get the spectral spread due to fading, the details is in [9]

2

1 ) 1

(

 



 

 ∆

−

•

=

λ π λ

v f v

f s

Power spectral density s ( f ) w ill give information about the autocorrelation function R

( τ ) of the received signal by Fourier transform; the details comes form [8]. The autocorrelation function of received signal is:

) 2 ( )

( τ ^J

π ^f τ

R

= ∆

J

is zeroth-order Bessel function of the first kind,

λ f = v

∆ v is the speed between the transmitter and receiver; λ is wavelength

v Path 1

Path 2

ϕ

1.3.3 Time varied channel model

The real life radio channel is not Wide Sense Stationary (WSS) in some case. The properties varies over time. 3GPP have shown some models to give the characters of some of them. They are birth-death channel and moving channel. The details can be found in 3GPP [10]

1.3.4 Summary of Channel model

After introducing the channel model and assuming invaried paths, see section 1.3, we can get the following channel model in Path searcher design:

) ( )

( ) ( )

( k s k A kT e

n

k

r =

+

The coefficient A ( kT ) e

is random variable whose character is following:

1. Amplitude A(t) is a Gaussian random process with autocorrelation function )

2 ( )

(

XX

τ ^J π ^f τ

R = ∆

is A(t) of function density

spectral Power

and

kind first the of function Bessel

order - zeroth is J

1 ) 1

(

 

 



 ∆

−

•

=

λ π λ

v f v

f s

λ f = v

∆ v is the speed between the transmitter and receiver. λ is wavelength.

2. Phase e

is uniform distributed random processing in [ 0 , 2 π ]

1.4 WCDMA introduction

1.4.1 Background of WCDMA

WCDMA is the abbreviation of ‘Wide band Code Division Multiple Access’. It is one kind of technology in 3G (third generation) mobile technology. There are some other standards in 3G, figure 8 show the relationship of them

Figure 8 3G communication standards

W-CDMA protocols are divided into 3 layers: layer 1 is physical layer; layer 2 includes MAC protocol, RLC protocol, PDCP protocol and BMC protocol; layer 3 includes RRC protocol. We concentrate on the physical layer. The protocols of the physical layers are 3GPP25.211-3GPP 25.215.

3G

CDMA2000

WCDMA

FDD TDD

1.4.2 Structure of physical lay in WCDMA handset receiver

Figure 9 Structure of the WCDMA handset receiver

The cell searcher completes the cell synchronization. The path searcher find out the delay of various source signals and the Rake receiver will use those delay to complete the de-spreading of source signal. Signal Interference Ratio (SIR) estimation and power control module will complete power estimating and control.

Multi-tap delay model and Rake receiver

The channel delays τ will spread and let the source signal overlap rendering the inter-symbol interference (ISI). In a CDMA system, the basis function is considered to be orthogonal or almost orthogonal, and rake receiver counteracts the ISI interference.

The Rake receiver would de-spread the receive sequence depending on their delay τ and make the combination by their SNR

Path searcher

Rake receiver

SIR est.

&

Power control Cell searcher

Basic handset function

Figure 10 Rake receiver

Time/phase synchronization and path searcher

The delays τ of the received signals must be known before we can apply the Rake receiver. The problem of timing these delays will be addressed in the next chapter.

Near-far effect and power control

As we have seen, orthogonal MAP/ML detectors are easier to be implemented in hardware or software, as they neglect the interference from other users. The interference depends on the covariance matrix of PN sequence and the energy of the source sequence. In a practical application, the energy of each source varies depending on the distance between the transmitter and receiver; if one source is very close to the receiver, it would generate a very large interference to other uses. Hence, to maintaining almost orthogonalities, we need to keep the receive power of this close transmitter and remote ones almost the same. This technology is called power control

Delay1

Delay2

Delay N

PN

2. Time synchronization in WCDMA

Time synchronization is one of the most complex parts in WCDMA receiver physical layer design. It would estimate the delay and phase φ of a local signal

)

; ( ^t φ

s to make ^s ( ^t ; φ ) be the best estimation of receive signal r (t ) .

The general method of phase ML estimation will be introduced at first, although it’s not suitable for our application; and then path searcher in discrete time, which transfer the problem of phase ML estimation to problem of MAP/ML detector for local signals ^s ( ^k ; φ

) ^{, s ( k ;} φ

^{) ……….} s ⁽ k ^; φ

⁾ in CDMA, will be investigated. Finally, I will introduce PDP path searcher which can avoid complex calculation.

2.1 Introduction to ML phase estimation and PLL

I will try to get the ML phase estimation rules, the detail analysis and following results in this page comes from [21].

Based on the ML estimation, the likelihood function of φ ^is

dt t

s t r

t

) ))

; ( ) ( ( exp(

)

( φ = − φ

Ψ ∫

We try to find out φ to minimum Ψ ( φ ) , which means maximizing

∫

= Ψ

t

l

( φ ) r ( t ) s ( t ; φ ) dt

And a necessary condition to get the maximum value of Ψ

( φ ) is

0 )

; ( ) (

∫ = φ

φ d

dt t s t r d

t

This can be achieved by a control loop or phase –lock loop ,see figure 11:

Figure 11 PLL structure (The figure comes from [22])

Why we can not directly use PLL here?

The first reason why we can not use PLL in WCDMA system time synchronization is multi-tap delays, there is more than one delay φ here, and the PLL can’t track more than one φ in the same time. It would lose the weak ones, or can’t track any of them, especially in fading cases.

Another reason is that the delay and phase in baseband may go beyond the region of ]

2 , 0

[ π and PLL doesn’t work in this situation.

2.2 Path searcher detection theory

The problem can be settled in discrete time system by introducing a path searcher to transfer the problem of phase ML estimation to the problem of choose some ‘high probability’ signal by MAP/ML detector. Following the basic rules of detector in last chapter, also introducing Neyman-Pearson classifier, we can get the basic decision rules for path searcher.

The path searcher will generate the local signals ^s ( ^k ; φ

) ^{, s ( k ;} φ

^{) ……….}

)

; ( k

s φ within the possible time interval [ φ

^, φ

^... φ

] and calculate the likelihood function between ^s ( ^k ; φ ) and the received signal r(k) to determine the probability P[ ^s ( ^k ; φ ) |r(k)] and compare it with threshold to make the decision whether or not

∫ ^{() dt}

VCO )

; ( t φ s )

(t

r

those φ is ‘real’ delay of receive signal. The algorithm can be shown as following:

For(i=0;i<m;i++)

{ if (P[ s ( k ; φ

) |r(k)]> Threshold) { φ

is signal delay}

Else

{ φ

is NOT signal delay } }

The structure of path searcher shown figure 12A:

Figure 12A. Path searcher with ML detection

2.2.1 Signal of path searcher with orthogonal basis function

Following the receiver model using orthogonal basis function in 1.2.5 and 1.3.4, assuming the complex source signal is S ( k ) = iS

( k ) + S

( k ) , and that the complex channel coefficient due to Rayleigh fading is A ( kT ) e

, we can get the received signal after de-spread as:

)) ( )

( ) ( Re(

)

( k s k A kT e

n

k

r

=

^φ

+

)) ( )

( ) ( Im(

)

( k s k A kT e

n

k

r

=

^φ

+

Likelihood

function/match filter

Decision )

(k r

)

; ( k φ

s

)

; ( k

s φ

)

;

( k φ

s

Where n is independent Gaussian noise after de-spread. Furthermore, we assume

that the channel fading coefficients A ( kT ) e

will not change during a short time slot . The received signal would be

r

( k ) = Re( s ( k ) Ae

^φ + n

( k )) r

( k ) = Im( s ( k ) Ae

^φ + n

( k ))

2.2.2 Basic classifier of receiver signal in path searcher

The test of the path searcher is to find out the delay of signal by deciding whether the source signal s(k) exist or do not exist in a delay φ , it achieves this under investigation through the calculation of P[ s ( k ; φ

) |r(k)]. According to [11], this is a two class discrete time detection problem with class C1 which means a target exists in this delay, or C0, which means no target is present in this delay. The observed vector signal r(k) and in each class is then.

C1: S ( k ) = iS

( k ) + S

( k ) C0: S ( k ) = 0

We want to make the decision from observer vector r(k) . In ordinary case, we always calculate P(C1| r(k)) and P(C0| r(k));

if P(C1| r(k))> P(C0| r(k))

{decide C1: target (signal in this delay)}

else

{decide C0: no target(no signal in this delay)}

In order to calculate P(C1| r(k)) and P(C0| r(k)), we need to know the prior

probability P(C1) and P(C0) and apply Bayes’ theorem . In practical applications, we

can not know these. So we will introduce Neyman-Pearson classifier to settle this

problem

2.2.3 Neyman - Pearson classifier-without prior probability:

Using the Neyman-Pearson classifier in [12], we don’t require the prior probability of the targets P(C1) and P(C0). We can make the decision by following some performance guides in this case, the guide is:

Probability of Detection (Pd), which is the probability that the target is there and we make the right decision.

Probability of Detection False alarm (Pfa), which is the probability that there is no target but we make a wrong decision.

If P(r(k)|C1) and P(r(k)|C0) are known and an acceptable Pfa , ε

, is assigned, the decision rules is:

If = > λ

) 0

| ) ( (

) 1

| ) ( ) (

( P r k C

C k r r p

l decide C1, otherwise decide C0

With threshold λ ^{holds by} ε

and P(r(k)|C0)

)

0

|

( ε

λ

∫ =

∞

dx C x p

The details can be found in [13], we just take the results from [14]

It’s not easy to set λ in practical applications. The plots of Pd and Pfa in the same map from zero to infinity, called receive operating characteristic (ROC). It will show that the improvement of Pd also increase Pfa. ROC will help to set up suitable parameters such as ε

^, λ (the derivative of curve) and find out good operating point A typical ROC is shown here.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Pfa

Pd

ROC

Obviously, setting a very low threshold achieves very high Pd, but in this case, Pfa would be too high. We must trade off between the Pfa and Pd,

2.2.4 Sequence Detector for Path searcher

Now the problem is how to calculate P(r(k)|C1) and P(r(k)|C0). Since the received signal is a sequence r( k ) = r( k

, k

, k

... k

) with samples in discrete time, the decision must take all r( k

, k

, k

... k

) into consideration.

For a received signal r ( k ) = s ( k ) A ( kT ) e

+ n

( k ) in the practical system 1. s(k) is known by some protocols, such as all ‘1’s or other patterns.

2. Phase coefficients e

can be estimated and the receiver can cancel it from received signal.

3. Amplified coefficients A(kT) is random but autocorrelation function of it is known.

The received signal is r ' ( k ) = A ( kT ) + n

( k ) after cancel s(k) and e

, Where P(r(k)|C1)= P(r’(k)|C1) and P(r(k)|C0)= P(r’(k)|C0).

If channel coefficients A(kT) is modeled as Gaussian processing as section 1.3.4 and )

0

( k

n is Gaussian noise processing, received signal r ' k ( ) ,the sum of them, is also Gaussian random processing. The covariance matrix K of r ' k ( ) is

 

 

 





 

 

 





=

nn ji

n

ij n

σ σ

σ

σ σ

σ σ

σ

...

...

...

..

..

...

...

...

1 01

1 10

00

K

If A(kT)=x(k), n

( k ) =y(k) and r ' k ( ) =z(k)=x(k)+y(k) , A(kT) and n

( k ) are zero means Gaussian processing, and they are WSS

 



=

= ≠

+

=

=

−

=

0 noise of variance

0 ) 0

(

) ( )

( )

( ) (

τ τ τ

τ τ

τ σ σ

σ

noise

noise XX

ji

R

R R

j i

) 2 ( )

(

XX

τ ^J π ^f τ

R = ∆

) ( τ

R

is autocorrelation function of amplify of channel coefficients in section 1.3.3

P(r’(k)|C1) and P(r’(k)|C0) can be calculated by jointed Gaussian distribution:

K is covariance matrix of receive signal r ' k ( )

The evaluation of probability can be approximated using a IIR filter when the input signal sequence is infinite long, as figure 12 B

Figure 12B Detector for sequence

Overall, we will get two step solutions for this problem

1 Estimate the phase channel coefficients e

and cancel the effect of them 2 Calculate the P(r(k)|C1) and P(r(k)|C0) and make the decision

The reason why only phase channel coefficients e

is estimated instead of estimating all of channel coefficients A ( kT ) e

is that the phase information can

calculated by

Q I

k S

k arctag S

) (

)

( and the receiver already do that in channel estimation

for Rake receiver meanwhile it’s hard to estimate A (kT ) because of amplify also depend on power control, antenna gain and other parameters.

IIR Decision

r’(k)

2 ]

)]

( ' [ )]

( ' exp[ [

|

| ) 2 ( ...) 1 3 , 2 , 1 (

1

2 / 1 2 /

k x k

x x P

T

m

r r Κ

Κ

−

= π

2.3 PDP path searcher theory

In this chapter, I will discuss the theory and structure of the PDP path searcher and how to choose the parameters in the PDP searcher algorithm to obtain good performance.

2.3.1 Introduction to PDP path searcher

Some path searchers apply the sequence detector to detect the different delays, but for most practical path searcher algorithms, it is not possible due to the delay introduced by estimating the channel coefficients. Crucial is also that path searcher must make the decision in very short time. In industrial application, they circumvent this by using non coherent ML detector to avoid channel estimation and simplify the calculation of the path searcher.

2.3.2 Non coherent ML detector

Non coherent ML detector achieves calculation of P(r(k)|C1) and P(r(k)|C0) without phase information e

, i.e., by assuming that the phase is random [15]. Hence the channel coefficient A ) ( t e

due to Rayleigh fading is random as introduced in 1.3.4 and we can use the Non coherent demodulation if we deny the effect of the slow change of A(t) by power control. In the two-class decision problem with

C1: S ( k ) = iS

( k ) + S

( k ) C0: S ( k ) = 0

the calculation of P(r(k)|C1 ) is

)

2 ( 2 2 )

exp( 4 2

) 1 1

| ,

(

2 1 2 1 2 0

2 1 2 1

2

σ

ε σ

ε πσ

ik qk qk

ik ik

qk

r I r

r C r

r r

p + + +

−

=

I here is the modified Bessel function of zero order,

r

, r

are the correlation

results between r ,

r

and c

.We could just calculate r

+ r

to simplify the

calculation. The structure of Non-coherent ML detector shown in Figure 12C

Figure.12C Path searcher with non-coherent ML detection

We only need to calculate P(r(k)|C1 ) in this project, as P(r(k)|C0 ) can be calculated off-line as will be discussed in the next section.

In conclusion the decision is based on the following strategy:

if P(r(k)|C1 ) > λ P(r(k)|C0 ) { φ

is signal delay}

Else

{ φ

is NOT signal delay}

2.4 PDP path searcher design

2.4.1 Structure of PDP path searcher

We can get the structure of the PDP path searcher in figure 13 and investigate the suitable parameters for components.

Likelihood

function/Match filter

()^2 )

(k r

)

; ( k φ

s

)

; ( k

s φ

)

; ( ^k φ

s

Decision

Figure 13 Structure of PDP path searcher

The matched filter evaluates the correlation between the received signal and differently local signals. After Non-coherent accumulation/detection, the signal is low pass filtered using an IIR filter to finally make the final decision. For handling time variable channel, the path searcher will also process the signal without the IIR filter to finger management. Finger management makes the decision depend on the signal without IIR low passing filter to catch the fast time-varied change signal.

2.4.2 Parameter choice

Coherent accumulation and Non coherent accumulation

The simulation and theoretical analysis show that the path searcher achieves better performance if we accumulate the signals before non-coherent detection. Here we expect that the channel coefficient A ( kT ) e

of signal doesn’t change. The length of accumulation depends on the time during which channel coefficient

)

)

( kT e

A

doesn’t change.

Match filter

Coherent Accumulator

Non-coher ent -Acc

IIR AGC

PN code with

different delay φ

Decision Threshold

Finger

management

IIR filter

As indicated in the last section, the properties of the IIR filter are decided by the characters of channel and involve the trade off between averaging and ability to catch changing channels. In the fast fading case, the delay would not change but there are changing channel coefficient depending on the moving speed. In time varying case, the delay would change and need some extra management to deal with it; I use one order IIR filter here and adjust the filter coefficient by simulation

Threshold calculation

It seems we need calculate both P(r(k)|C1) and P(r(k)|C0) , but P(r(k)|C0) which just decided by noise can be calculated within some knowledge of the whole system. We just need calculate P((r(k)|C1) online and compare it with theoretical P(r(k)|C0) metrics function.

Searcher without estimation of Doppler frequency shift

If the character of channel, characterized throw R

and depend on the Doppler frequency shift, is fixed, the procedure described above is sufficient to get good performance. Meanwhile the Doppler frequency shift would change with the speed of moving object. In such case, we have to estimate the Doppler frequency shift f to get parameters of coherent accumulation, Non coherent detector and IIR filter .Or in another way, we can average between all fading cases to set a suitable parameter to fit all the cases. For such approach, Doppler frequency shift estimation online is not required. This is what I do in this project because the estimation of Doppler frequency will cost complex in DSP implementation.

Time variable channel and finger management

The different delays would also change with time in some case, making the

channel non WSS. A typical case is the birth death channel, in which the signal will

appear in one time shot and disappear in another time slot, and appear in next slot

again. This makes the situation more complex and I have to add some finger

management in path searcher to handle this.

In the finger management, I will check the data after non-coherent detection but before the IIR filter. We observe that this data represents the probability of a signal in this time slot only. If the value is high enough, I will make the decision that there is signal in this time slot. Here we do not need the IIR filtering because the IIR filter will average the noise before with this value and make the result lower than the threshold.

This type of finger management lets the path searcher make decisions based on recently received signal and keep up with the change in time.

3 Simulation results

Simulation introduction:

The purpose of simulation is to test the baseband performance of algorithm using computer software simulation. The performance of PDP searcher is evaluated using guide PD and Pfa. Wireless channel is build following Jacks’ fading model;

transmitter is build following 3GPP standard; PDP path searcher is build as model introduced in section 2.4. The whole simulation channel is shown in figure 14

Figure 14 simulation channel

Following 3GPP standard, QPSK modulation will perform for baseband complex source signal.

As we have seen in section 1.3.4, amplify of fading is Gaussian processing with autocorrelation function ^R

( τ ) = ^J

( 2 π ∆ ^f τ ) , two independent filtered white Gaussian noise will serve as amplify of fading for complex signal.

The parameters of PDP path searcher will affect its performance. Critical parameters include Number of coherent-accumulation pilot bit (Nc), Number of Non coherent accumulation (Np) and coefficient of IIR filter. Those parameters will adjust depending on the PD and Pfa to select the best ones.

Transmitter Wireless channel PDP searcher

Results

record

Simulation results:

I simulate the algorithm in Matlab in moving case for V=120KM/H with different parameters and get the results in figure 15:

0 0.05 0.1 0.15 0.2 0.25

0.4 0.5 0.6 0.7 0.8 0.9 1

Pfa

P d

ROC of search v=120km/h

Np=6, Nc=10 Np=4,Nc=10

Figure 15 simulation results of path searcher In normal case, the acceptable Pfa is 0.02 and Pd>0.7 for V=120KM/H case

In the simulation results, we can find out that if we select Np=6 and Nc=10, we can get the performance Pd>0.75 when Pfa<0.02. It is very good performance for searcher.

But if we choose Np=4 and Nc=10, we can not guarantee that, although it can save

some resource.

4. Theory of DSP implementation

DSP (digital signal processors) is one kind of CPU enhanced with some special components to make it capable of huge calculation for signal processing while the functions still implemented in software. So, it can offer both calculation ability as hardware and flexibility as software by modifying the software functions in DSP.

With the development of IC(Integrated Circles) device, DSP becomes more powerful and start to be applied in wireless communication physical layer application.

Meanwhile, some restrictions in programming must be followed to get full power of the DSP.

I will introduce the general characters of DSP at first, giving the background knowledge of structure and software programming in DSP. Secondly, the specification of AD tiger-SHARC DSP from Analog device Inc., which I choose in this project, would be investigated. Last, following the characters of DSP, the key optimization of software implementation would be introduced.

4.1 Characters of DSP

Harvard architecture

In Harvard architecture, data loading and instruction loading have their own individual memory bus system and computation unit can access them in the same time without waiting.

VLIW (Very-long-instruction-word)

The VLIW instruction architecture can make the DSP run more than one instructions

in one clock cycle in multi-core structure. DSP usually have more than one

computation unit, which make the DSP can complete more than one computation

operation in one clock cycle. And DSP need more than one instruction in one cycle, so

more instructions have to be combined and get a very-long-instruction-word