An Experimental Approach to CDMA and Interference Mitigation phần 6 docx

It is seen that in a first stage the frequency error is quite large QT s 0.10, the CPRU has no way to lock in, and the lock metrics initialized at l0 1.75have a short acquisition and set

20 10

0

Normalized Time (Symbols)

L=64, K=32 C/I=-6 dB, P/C=6 dB

10

10 8 6 4 2 0

Eb/N0 (dB)

L=64, K=32 C/I=-6 dB, P/C=6 dB

J BAID =2-15

Figure 3-38 Accuracy of CPRU phase estimates

2 3 4 5

0.01

2 3 4 5

0.1

2 3 4 5

1

10 8 6 4 2 0

Eb/N0 (dB)

L=64, K=32 C/I=-6 dB, P/C=6 dB

J BAID =2-15

AFC, PLL on ideal

Figure 3-39 BER performance in the presence of frequency and phase errors

where 'T( )k T( )k  Tˆ( )k is the residual phase error at step k, and

{±1±j}

k

c  is the kth transmitted QPSK symbol on the useful traffic

channel If we look at ( ) as a function of 'T( )k we easily find that it is

not dependent on the particular value of c , and it is periodic with period k

(recall that A ! by definition) As is seen from the plot of (3.99) in Figure 0

3-40, ( ) attains its maximum value 2A when the phase error is a multiple

of S/ 2, i.e., when the phase loop is in lock Re-considering noise and MAI,

( )

 needs filtering to yield a reliable lock metrics as in (3.97)

Before the AFCU and the CPRU have attained lock ( ) is affected by a

frequency offset In such a condition 'T( )k has a linear evolution with time,

and therefore the oscillating plot in Figure 3.40 is in a sense ‘swept’ on the

phase x-axis If the forgetting factor is small, i.e., J  , the lock metrics 1

Figure 3-40 z k vs the phase error 'T k .

Our lock detection criterion will be a comparison of l k with a suited ( )

threshold ranging between 1.8A and 2A If the threshold is crossed, the phase

error should be stable and close to one of the four lock point multiples of

ʌ/2

Figures 3-41 and 3-42 show the evolution of the lock metrics and of the

AFCU frequency estimate starting from receiver switch on in the following

J , QT s 0.1 The frequency step size is intentionally

set from the very start to its steady state value This has the effect of

lengthening the frequency acquisition time to show better the two

different DC levels attained by l k in the two different out of lock and ( )

in lock conditions;

2

J U ;

300 200

100 0

Normalized Time (Symbols)

L=64, K=32 C/I=-6 dB, P/C=6 dB

300 200

100 0

Normalized Time (Symbols)

L=64, K=32 C/I=-6 dB, P/C=6 dB

E b /N 0 =0 dB

QT s =0.1

Figure 3-42 Frequency acquisition @ E b/N dB 0 0

Joint evaluation of Figures 3-41 and 3-42 is quite instructive It is seen that in a first stage the frequency error is quite large (QT s 0.10), the CPRU has no way to lock in, and the lock metrics (initialized at l(0) 1.75)have a short acquisition and settles at the expected out of lock value 1.8 As soon as the AFCU acquisition is over, and thus the frequency error is small

(roughly k ˜2 105), the CPRU starts acquiring lock, and in parallel (after a

short CPRU acquisition time) the lock metrics rapidly attains the lock value

1.82 Unfortunately this value is substantially smaller than the theoretical

peak value of 2 in Figure 3-40 owed to noise induced biasing We can

therefore use a strategy of comparison with hysteresis to detect “out of

lockoin lock” and “in lockoout of lock” transitions based on the two

threshold values O L 1.8 and O H 1.815 This prevents the circuit to detect

false events like the one we would find in Figure 3-43 at 5

4.2 10

k # ushould we use a single threshold at O with no hysteresis H

300 200

100 0

Normalized Time (Symbols)

L=64, K=32 C/I=-6 dB, P/C=6 dB

E b /N 0 =4 dB

O H

O L

lock det.

Figure 3-43 Lock metrics evolution @ E b/N dB 0 0

Concerning the bias phenomenon for the out of lock and in lock values of

( )

l k mentioned above, we found that the out of lock value 1.8 is very

marginally affected by the operating condition in terms of SNIR, probably

owing to the implicit time averaging effect on ( ) we have discussed

Instead, the in lock value tends to grow when the SNIR improves Thus, the

same threshold values determined for the worst case in Figure 3-43 can be

safely re-used in conditions of better SNIR

MITIGATION

Implementation of a single-channel interference mitigating CDMA

detector represents the main novelty of the MUSIC project In this Section

we present the interference mitigating feature of the MUSIC receiver which

is based on the EC-BAID algorithm to be detailed hereafter

3.1 EC-BAID Architecture

We start with the analytical description of the signal at the receiver input,

assuming that K user traffic channels in DS/SS format are code multiplexed

in A-CDMA mode (see Chapter 2) The generic kth CDMA user transmits a

stream of complex-valued information bearing symbols, denoted as

( ) ( ) j ( )

k k p k q

a u a u  a u The symbols, which belong to a QPSK alphabet

(i.e., a k p, ( ),u a k q, ( ) { 1}u  r ) and run at symbol rate R s 1/T s, are spread

over the frequency spectrum by multiplication with a binary signature code,

denoted as ( ) { 1}c k A  r , with period L and running at chip rate R c 1/T c

The signature is actually a short code as its repetition period L spans exactly

one symbol interval: T s ˜L T c Chip rate symbols are eventually shaped by

a transmit filter with SRRC impulse response g t At the receiver side, T( )

after baseband conversion, the overall signal, denoted as r t , is made of K( )

CDMA channels plus additive noise n t as follows ( )

where P is the RF power of the kth channel and ( ) k s t is the relevant k

spreading signature defined as

In (3.101) W ,k I and k Q are the time delay, the carrier phase shift, and k

the frequency offset of the generic k-th traffic channel w.r.t the useful traffic

signal, which, without loss of generality is assumed to be channel 1 We

assume for now that the carrier frequency error relevant to channel 1 is

perfectly compensated for by means of an ideal AFC subsystem (i.e.,

f

' ) and that perfect chip timing recovery is performed (i.e., W ).1 0

The signal r t is then sent through a baseband filter with impulse response ( )

( )

R

g t performing Nyquist’s SRRC chip matched filtering, followed by chip

time sampling (or interpolation in the case of a digital implementation) The

signal samples taken at time t m m T˜ at the output of the CMF are thus c

R |t mT c

The chip time signal y m is then input to the EC-BAID data detector

that was introduced in Section 2-5 We will described here the detector in

more detail, starting back from the very fundamentals, just to make this

section as much self-contained as possible As detailed in [Rom97], the

EC-BAID uses a three-symbol observation window to detect one information

bearing symbol In the subsequent analytical description we will use the

superscript e to denote a 3L-dimensional vector (also termed ‘extended

vector’ as opposed to ‘non-extended’ L-dimensional vectors), the superscript

T

to denote transposition, and the asterisk *

to denote complex conjugation

The 3L-dimensional array of CMF samples observed by the detector is given

c c

with 1,0,1w  The EC-BAID is a linear detector operating on the chip rate

sampled received signal y(m) to yield the symbol rate signal b(r) as follows

1 e T e

where ( )he r is the 3L-dimensional array of the complex-valued detector

coefficients It is apparent that detection of each symbol calls for observation

of three symbol periods (i.e., the current, the leading, and the trailing ones)

which represent the so called observation window (W LEN) This suggests the

three-fold parallel implementation of the detector sketched in Figure 2-20,

and repetead here in Figure 3-44, wherein the first detector unit processes the

(r  th, the r th and the (1) r  th symbol periods for the detection of the 1)

rth symbol, the second unit processes the rth, the (r  th and the 1)

(r 2)th periods, for the detection of the (r  th symbol, and the third unit 1)

processes the (r  th, the (1) r 2)th and the (r  th periods, for the 3)

detection of the (r 2)th symbol The structure of the detector units will be

outlined in the sequel Also, in the algorithm description we will assume a

normalized observation window W LEN , whilst further considerations 3

about the selection of the optimum value of W LEN will be reported later in

Section 4.1

Figure 3-44 EC-BAID top level functional block

The output stream of soft values for data detection is obtained by

sequentially selecting the three detector unit outputs at rate 1/T s by means of

a multiplexer We need thus a further clock reference ticking at the so called

Super-Symbol rate RSS 1/(3 )T s , i.e., once every three symbols Taking this

into account, the sample at the output of the n-th detector unit (n 1, 2, 3) is

with s running at super-symbol rate To achieve blind adaptation the

complex coefficients he n, of each detector are anchored to the user signature

sequence, represented by the L–dimensional array c containing the chips

1( )

c A of the useful signal 1 The anchoring condition is obtained as follows

[Rom97] First, we decompose he n, in two parts

L

c c

,

,

0 ,

e n n

e n n

e n n L

with 1,0,1w  , and the optimum MMOE configuration of the detector is

found through application of a recursive update rule for the detector

coefficients As is detailed in [Rom97], the error signal in the recursion for

detector n is given by

1 e r T e r with e r e r e

e is orthogonal to c by construction (i.e., e

e c ), whilst the same consideration does not apply to the

quantization term ǻee( ) r In particular, taking into account that the LSB of

the term (ye*( ) 2r ˜ 7) in (3.119) is necessarily zero, ǻ ( ) ee r can be expressed

w has components with values +1 or –1 The product with D(r) then

gives two different possible results: if D(r) is even, 1 bit truncation does not

introduce any error and we have

if D( )r is odd, 1 bit truncation is equivalent, considering a 2’s complement

representation, to subtracting 1 to each non-zero vector element, thus

The vector ǻee( )r is made of a component which is orthogonal to ce

and of a component de which is not The first will have no effect on the e

overall performance, whilst the second, being characterized by elements all

of the same sign, will build up an accumulation error This will impair

algorithm convergence In particular, de is given by e

ǻ >111 1@

T T

c A So de is zero only if the sequence e c is balanced, that is, it contains an

equal number of 1 and 1 As previously stated, the MUSIC receiver

supports the use of extended PN sequences overlaid to WH signatures This

superposition generates unbalanced codes for almost all of the possible

combinations Thus it is very likely, in the case of 1 bit truncation, to have

d ( ) 0ee r z

Figure 3-49 shows the estimated BER performance of the EC-BAID

obtained with L 128, K 64, E N b/ 0 5 dB, C I / 6 dB and on a

simulation run of 20 Msymbols The lower (almost horizontal) curve was

obtained with no truncation in the evaluation of e

e , whilst the upper one was

obtained with just 1 bit error in the internal word length dimensioning In the

latter case, the term >111 1" @Tc of (3.125) is equal to 16, and so every time

drift and indefinitely increase, thus causing in the long run saturation and

failure of the detector To prevent this, it is mandatory to calculate the error

signal...

threshold ranging between 1.8A and 2A If the threshold is crossed, the phase

error should be stable and close to one of the four lock point multiples of

ʌ/2

Figures 3-41 and. .. ye and b, the processing

relevant to e (and so e xe) has to be performed with an internal word length