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You may think the algorithm should be complex, but you would be wrong. For each sample of the pattern, multiply the corresponding pattern and signal values, then sum all these results.
Then, shift the pattern by one sample on the right and do the same calculation again to find the second point of the correlation, and so on. You then just have to locate the peaks on the calculated correlation. Their position shows where the pattern is located in the signal, and their amplitudes are directly proportional to the amplitude of the replica.
An example is shown in Figure 1. The middle plot shows an arbitrary pattern. Here I took a pattern made with a saw-tooth, then a small step. The top plot shows a signal. It is noisy, but includes two replicas of the pattern, with different amplitudes.
Where are these replications? Do you see them? If not, then simply calculate the correlation of the signal and pattern. I did that for you, and the result is shown in the bottom plot. Two peaks are clearly visible, and they directly indicate the beginning of each replica of the pattern in the signal, along with their respective levels.
A last word on correlations. In my example, both the signal and pattern are analog values. The multiplication operation has simply to be replaced by a negated XOR 1 if both logic levels are equal, otherwise 0 , which is even simpler.
One again, this was just a refresher, but now you have enough information on correlation to understand what DSSS is. Imagine that you have a bit stream to transmit. Rather than transmitting each bit individually, you can implement a DSSS transmitter. For that, you have simply to replace each bit by a given sequence of 1s and 0s—a pattern.
By calculating a correlation between the received signal and each of the two patterns. The advantages of DSSS over a direct transmission of the bit stream are numerous, especially if the patterns are long and complex. This is, of course, why its first applications were military. Of course, the patterns should be selected with care. First their length must be decided. Long patterns will increase the noise resilience, but will reduce the transmission speed.
So long patterns should be preferred when noise immunity is a must, whereas shorter ones should be used for high-speed transmission. Then, for a given length, not all patterns are equal in performance. If not, the correlation with a real signal will show plenty of additional peaks, and this will reduce the performance of the transmission. Similarly, the two distinct patterns used for 0s and 1s, when correlated with each other, must not show any significant peak.
If they do, 1s may be understood as 0s or vice-versa. Mathematicians solved this problem for us a long time ago. We engineers have just to know what pattern to use. Gold sequences are long, binary patterns that have low auto-correlation and low cross-correlation between any two sequences—perfect for this application.
We will see later that they are heavily used for high-performance communications. This pattern could be used to transmit logic 1s, and its negation to transmit 0s. The correlation between the signal and the pattern will give a maximum positive value for 1s and a maximum negative value for 0s.
Such a signal is then sent to a BPSK demodulator. Although these signals appear to be noisy in the frequency domain, bandwidth provided by the PN code permits the signal power to drop below the noise threshold without any loss of information.
By: Dr. By: Kaushik Pal Contributor. Dictionary Dictionary Term of the Day. Random Forest. Techopedia Terms.
Connect with us. Sign up. Term of the Day. Direct sequence spread spectrum basics Direct sequence spread spectrum is a form of transmission that looks very similar to white noise over the bandwidth of the transmission. The use of direct sequence spread spectrum is a powerful principle and has many advantages. DSSS spreading gain The bandwidth of the spread spectrum signal will be much wider than the original data stream.
Read more about. CDMA cellphone multiple access technology. Shopping on Electronics Notes Electronics Notes offers a host of products are very good prices from our shopping pages in association with Amazon. Note: Electronics Notes receives a small commission on sales at no cost to you. Supplier Directory For everything from distribution to test equipment, components and more, our directory covers it. Featured articles. The received signal is correlated with the generated code, extracting the Information data.
To recover the bit stream of an individual station, the receiver must know that station's chip sequence in advance. It does the recovery by computing the normalized inner product of the received chip sequence and the chip sequence of the station whose bit stream it is trying to recover.
The reason is,. In an ideal noiseless CDMA system, the capacity no. In practice, physical limitations reduce the capacity considerably. First, we have assumed that all the chips are synchronized in time.
In reality, doing so is impossible. What can be done is that sender and receiver synchronize by having the sender transmit a long enough known chip sequence that the receiver can lock onto.
All the other unsynchronized transmissions are seen as random noise. The longer the chip sequence the higher is the probability of detecting in presence of noise. For extra security, bit sequences can use error correcting codes.
Chip sequences never use error correcting codes. For each channel the base station generates a unique code that changes for every connection. The pseudo-random code must have the following properties:. It must be deterministic. The subscriber station must be able to independently generate the code that matches the base station code.
It must appear random to a listener without prior knowledge of the code i. The cross-correlation between any two codes must be small see below for more information on code correlation. The code must have a long period i. In this context, correlation has a specific mathematical meaning. In general the correlation function has these properties:.
Intermediate values indicate how much the codes have in common. The more they have in common, the harder it is for the receiver to extract the appropriate signal.
There are two correlation functions:. The receiver uses cross-correlation to separate the appropriate signal from signals meant for other receivers, and auto-correlation to reject multi-path interference. Some terminology related to the pseudo-random code:. Transmitting Data. QPSK uses four different states to encode each symbol. 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.
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