Cdma what is the spreading factor in this example

The four states are phase shifts of the carrier spaced 90degrees apart. By convention, the phase shifts are 45, , , and degrees.

Since there are four possible states used to encode binary information, each state represents two bits. Algebraically, a carrier wave with an applied phase shift, Y t , can be expressed as a sum of two components, a Cosine wave and a Sine wave, as:. I t is called the real, or In-phase, component of the data, and Q t is called the imaginary, or Quadrature-phase, component of the data. We end up with two Binary PSK waves superimposed. These are easier to modulate and later demodulate.

The transmitter generates two carrier waves of the same frequency, a sine and cosine. I t and Q t are binary, modulating each component by phase shifting it either 0 or degrees. Both components are then summed together. The receiver generates the two reference waves, and demodulates each component. It is easier to detect degrees phase shifts than 90degrees phase shifts. The following table summarizes this modulation scheme.

Note that I and Q are normalized to 1. In order to make full use of the efficiency of Digital Signal Processing, the conversion of the Information data into complex symbols occurs before the modulation. To spread the Information data the system performs complex multiplication between the complex PN codes and the complex data.

Many channels are added together and transmitted simultaneously. This addition happens digitally at the chip rate. Since I and Q are no longer limited to 1 or -1, the phase shift of the composite carrier is not limited to the four states, the phase and amplitude vary as. Since the PN-code has the statistical properties of random noise, it averages to zero over long periods of time such as the symbol period.

Therefore, fluctuations in I and Q, and hence the phase modulation of the carrier, that occur at the chip frequency, average to zero. Over the symbol period the modulation averages to one of the four states of QPSK, which determine what the symbol is. The receiver performs the following steps to extract the Information:. The receiver generates two reference waves, a Cosine wave and a Sine wave.

Separately mixing each with the received carrier, the receiver extracts I t and Q t. Analog to Digital converters restore the 8-bit words representing the I and Q chips. The receiver, as described earlier, generates its own complex PN code that matches the code generated by the transmitter.

However, the local code must be phase-locked to the encoded data. Each method will be covered in more detail in later sections. Once the PN code is phase-locked to the pilot, the received signal is sent to a correlator that multiplies it with the complex PN code, extracting the I and Q data meant for that receiver.

The receiver reconstructs the Information data from the I and Q data. CDMA is typically used for wireless systems with fixed base stations and many mobile stations at varying distances from it. The power level received at the base station depend on how far away the transmitters are.

The receiver base station can listen to all senders at once by running the decoding algorithm for each of them in parallel. The base station gets bombarded by signals from many mobile stations. Some of these mobile stations are close and their signals are much stronger than mobile stations farther away. System Capacity is also dependant on signal power.

The output of the correlator consists of two components:. Mathematically, if we are trying to decode the k th signal, we have:. A j is the amplitude of the j th signal, r jk is the cross-correlation between the k th and j th signal, and S is the sum over all the j signals excluding k.

Since the cross-correlation is small ideally, it is zero , the sum of cross-correlation terms should be much less than the amplitude of the desired signal. However, if the desired signal is broadcast from far away, and undesired signals are broadcast from much closer, the desired signal may be so small as to be drowned out by the cross-correlation terms. Note that this problem only exists in the reverse direction.

The base station is receiving signals from many mobile stations at different distances, but the mobile station is receiving all signals from one base station. The base station controls the power of each mobile station so that the signals received from all mobile stations are the same strength.

GPS is a satellite based radio navigation system. There are 24 GPS satellites orbiting the Earth and transmitting radio signals. Based on measurements of the amount of time that the radio signals travel from a satellite to a receiver, GPS receivers calculate the distance and determine the locations in terms of longitude, latitude and altitude. DSSS provides the structure for the transmission of ranging signal and essential navigation data such as satellite co-ordinates and health.

P-code can be denied to SPS users if the anti-spoofing code is activated in the satellite vehicle. In that case, P-code is encrypted and known as Y-code. Y-code has same chipping rate as P-code. GPS satellites transmit two carrier frequencies: the primary frequency L1 and the secondary frequency L2. Satellites transmit at two frequencies simultaneously, but, their signals do not interfere significantly with each other due to PRN code code modulation.

Since each satellite is assigned a unique PRN code and all of the PRN code sequences are nearly uncorrelated with respect to each other, the satellite signals can be separated and detected by CDMA technique. In order to track one satellite in common view with several other satellites by the CDMA technique, a GPS receiver must replicate the PRN sequence for the desired satellite along with the replica carrier signal. Two carrier frequencies are provided to permit the two frequency user to measure the ionospheric delay since this delay is related by a scale factor to the difference in signal time of arrival TOA for the tow carrier frequencies.

Single frequency L1 users must estimate the ionospheric delay using modeling parameters that are broadcast to the user in navigation message.

This combination uses the XOR process. There fore there 90 degrees phase shift between these two combined carrier frequencies. PPS users have classified algorithms and the classifies key to remove certain errors.

However, differential GPS techniques have successfully mitigated these effects. At each phase of operation, the system satellite broadcasts pilot signals. These pilot signals are the unmodulated PN codes associated with each channel, used to synchronize and track the locally generated PN codes for despreading.

At the receivers, the PRN code is derived by combination of two code generators. Code generators are nothing but linear feedback shift registers.

After derivation, the receiver must shift the phase of the replica code until it correlates with the satellite PRN code. The same correlation properties occur when cross correlating the transmitted PRN code with a replica code as occurs for the mathematical autocorrelation process for a given PRN code. When the phase of the GPS receiver replica code matches the phase of the incoming satellite code, there is maximum correlation. When the phase of the replica code is offset by more than one chip on either side of the incoming satellite code, there is minimum correlation.

Instead the CDMA codes create a uniqueness to enable call identification. CDMA codes should not correlate to other codes or time shifted version of itself for optimum performance. Spreading codes are noise like pseudo-random codes, channel codes are designed for maximum separation from each other and cell identification codes are arranged not to correlate to other codes of itself.

There are several types of codes that can be used within a CDMA system for providing the spreading function:. A figure known as the Spreading Factor is the ratio of the chips to baseband information rate.

The orthogonal spreading codes used within CDMA play a vital role in ensuring that the maximum efficiency and number of users can be gained. The use of orthogonal codes against random codes provide a useful increase in effectiveness of the system, reducing mutual interference between users.

CDMA codes and correlation The concept of CDMA is based around the fact that a data sequence is multiplied by a spreading code or sequence which increases the bandwidth of the signal. These codes will sum to zero over a period of time. Although the sequence is deterministic because of the limited length of the linear shift register used to generate the sequence, they provide a PN code that can be used within a CDMA system to provide the spreading code required.

They are used within many systems as there is a very large number that can be used. A feature of PN codes is that if the same versions of the PN code are time shifted, then they become almost orthogonal, and can be used as virtually orthogonal codes within a CDMA system. Truly orthogonal codes: Two codes are said to be orthogonal if when they are multiplied together the result is added over a period of time they sum to zero.

For example a codes 1 -1 -1 1 and 1 -1 1 -1 when multiplied together give 1 1 -1 -1 which gives the sum zero. Shopping on Electronics Notes Electronics Notes offers a host of products are very good prices from our shopping pages in association with Amazon.