Contents
System Properties
We discuss signals and system properties with reference to the system below.
The system comprising of the hardware used to generate CDMA signal viz. low
pass filter followed by sampler, vocoder, encoder, interleaver, coder and
spreader.
The input signal is the voice signal. The output is the digital signal spread on the
whole frequency band.
1. Causality:
The system is causal as it cannot see the future inputs i.e. what voice message is coming next. The system transmits data at a rate depending on whether there is activity or not i.e. whether there is a pause or not. So the system looks at the input encountered a small interval earlier. It is important to note here that along with data signals, most CDMA signal applications such as cellular phones transmit an additional signal known as the Access signal. This signal is transmitted to the BTS to register the phone on the network and transmit overhead messages to the Base station. Recall that a system is said to be Causal if it generates an output.2. Memory:
Under normal circumstances one might expect the system to lack memory since it simply codes voice messages to digital form. Note however that recent handsets use an energy and- time-saving mechanism wherein sampling rate is fast for instances of time when the user is silent and slower when sampling speech. The system compresses the output signal for the instances of time occurring in the past i.e. a small interval earlier, so the system has memory.3. Invertibility:
The mobile handset at the other end through the hardware viz. digital to analog converter, decompressor, etc. is able to obtain the original voice signal so the system is invertible. The entire functionality of mobile systems depends on the fact that this system is invertible (It is rather illogical to picture a system where a user can talk all day long without anything being heard at the receiving end!).4. Shift Invariant:
A delay in the input signal produces the same delay in the output signal so the system is shift invariant. It ensures that input signals are not jumbled up oroutputs are different as compared to what they should have been at an earlier instant of time (Assuming that the noise levels are unchanging).5. Linearity:
a) Homogeneity: The system is one which receives an analog input waveform. The system converts this to digital codes and transmits another waveform of fixed amplitude but different phases to denote a ‘1’ or a ‘0’. Consider the user to give an input waveform of amplitude 10 (say). Now if the user speaks louder and gives an input of volume 20, this will not cause the output waveform to be doubled in amplitude (since CDMA uses choice amplitudes to propagate its signal). For example consider a decimal-to-binary converter: An input signal 2 to be converted to binary as 10. Now if this signal is, say, 8 then the output is expected to be 4 multiplied by ‘10’ i.e. ‘40’. However the transmitted signal can only transmit a ‘1’ or a ‘0’ not a ‘4’. Hence the system is not Homogeneous.b) Additivity: Similar to the above example, we can show that if an input of ‘2’ is encoded as ‘10’ then 4 (4 = 2+2) is not decoded as ‘20’. Since the amplitude is restricted to its assigned value, it cannot possibly relay this signal. Thus the system is not Additive since it always transmits in the form of 1’s and 0’s CDMA systems convert analog voice signals to binary codes. Hence the system is not Linear though after transmission the entire signal is reproduced almost exactly at the receiving system.
