# Exercise 3.7Z: Spread Spectrum in UMTS

For UMTS/CDMA, the so-called  "PN modulation"  is applied:

• The rectangular digital signal  $q(t)$  is multiplied by the spread signal  $c(t)$  and gives the transmission signal  $s(t)$.
• This is by the spreading factor  $J$  of higher frequency than  $q(t)$;  this is called  "band spreading".

At the receiver the same spreading signal  $c(t)$  is added (namely in phase!).  This reverses the band spreading   ⇒   "band compression".

The graphic shows exemplary signal characteristics of  $q(t)$  und  $c(t)$.

Notes:

• This task refers to the chapter  Characteristics of UMTS.
• Reference is made to the chapter  Telecommunications Aspects of UMTS  in the book "Examples of Communication_Systems".
• For the calculation of the chip duration   $T_{\rm C}$,  please refer to page  Physical Channels .
• There you will find, among other things, the information important for this task, which is transmitted on the so-called  "Dedicated Physical Channel"  $\rm (DPCH)$  in ten milliseconds exactly  $15 \cdot 2560 \ \rm Chips$.
For example, the "transmitting chip"  $s_{3}$  denotes the constant signal value of  $s(t)$  in the time interval  $2T_{\rm C}$ ... $3T_{\rm C}$.

### Questionnaire

1

Which of the following statements are true?

 For UMTS the bit duration  $T_{\rm B}$  is fixed. For UMTS, the chip duration  $T_{\rm C}$  is fixed. Both values depend on the channel conditions.

2

Specify the chip duration  $T_{\rm C}$  and the chip rate  $R_{\rm C}$  in the downlink.

 $R_{\rm C} \ = \$ $\ \rm Mchip/s$ $T_{\rm C} \hspace{0.18cm} = \$ $\ \rm µ s$

3

Which spreading factor can be read from the graph on the data page?

 $J \ = \$

4

What is the bit rate with this spreading factor?

 $R_{\rm B} \ = \$ $\ \rm kbit/s$

5

What are the  "transmitting chips"  ⇒   of the signal  $s(t)$?

 $s_{3} \ = \$ $s_{4} \ = \$ $s_{5} \ = \$ $s_{6} \ = \$

### Musterlösung

#### Solution

(1)  Correct is the solution 2:

• For UMTS, the chip duration  $T_{\rm C}$, which is still to be calculated in the subtask  (2), is predefined.
• The greater the degree of spreading  $J$, the greater the bit duration.

(2)  According to the note on the information page, in  $10 \ \rm ms$  exactly  $15 \cdot 2560 = 38400 \ \rm chips$  are transferred.

• With this the chip rate:  $R_{\rm C} = 100 \cdot 38400 \ {\rm Chips/s} \ \underline{= 3.84 \ \rm Mchip/s}$.
• The chip duration is the reciprocal of this:   $T_{\rm C} \ \underline{\approx 0.26 \ \rm µ s}$.

(3)  Each data bit consists of four spreading chips   ⇒   $\underline{J = 4}$.

(4)  The bit rate is calculated with the spreading factor  $J = 4$  to  $R_{\rm B} = R_{\rm C}/J \ \underline{= 960 \ \rm kbit/s}$.

• With the maximum spreading factor  $J = 512$  for UMTS, the bit rate is only  $7.5 \ \rm kbit/s$.

(5)  The following applies to the transmission signal $s(t) = q(t) \cdot c(t)$.

• The chips  $s_{3}$  and  $s_{4}$  of the transmission signal belong to the first data bit  $(q_{1} = +1)$:
$$s_3 = c_3 \hspace{0.15cm}\underline {= -1},\hspace{0.4cm}s_4 = c_4 \hspace{0.15cm}\underline {= +1}\hspace{0.05cm}.$$
• On the other hand, the two other transmission chips sought are to be assigned to the second data bit $(q_{2} = -1)$:
$$s_5 = -c_5= -c_1 \hspace{0.15cm}\underline {= -1},\hspace{0.4cm}s_6 = -c_6= -c_2 \hspace{0.15cm}\underline {= +1}\hspace{0.05cm}.$$