{"id":146,"date":"2018-07-13T07:29:27","date_gmt":"2018-07-13T07:29:27","guid":{"rendered":"http:\/\/itp12.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=146"},"modified":"2019-05-15T09:34:01","modified_gmt":"2019-05-15T09:34:01","slug":"spread-spectrum-technology-direct-sequence-spread-spectrum","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/itp12\/chapter\/spread-spectrum-technology-direct-sequence-spread-spectrum\/","title":{"rendered":"Spread Spectrum Technology: Direct Sequence Spread Spectrum"},"content":{"raw":"<div><span style=\"float: right;\"><a href=\"https:\/\/youtu.be\/h_j6TS-Y95s\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n<strong>Learning Objectives<\/strong>\r\n<ul>\r\n \t<li style=\"text-align: justify;\">Understand the principle of Direct Sequence Spread Spectrum<\/li>\r\n \t<li style=\"text-align: justify;\">Understand the concept of spreading codes and study their properties<\/li>\r\n \t<li style=\"text-align: justify;\">Discuss orthogonal codes<\/li>\r\n \t<li style=\"text-align: justify;\">By illustration understand how data is transmitted using codes and how it is recovered back at receiving station<\/li>\r\n<\/ul>\r\n<p class=\"hanging-indent\"><strong>Introduction<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">In Direct Sequence spread spectrum, Each bit in the original signal is represented by multiple bits in transmitted signal with the help of a code known as spreading code. The code appears to be pseudo random in nature while actually it is deterministic. The P-R code is also called pseudo codes. The signal is spreaded in proportion with the number of bits in the code. For example 11-bit code spreads the signal 11 times greater than 1 bit code. The code is independent of data to be transmitted. This is intercepted by only those receivers who know the code, for rest it is rejected as noise. Therefore the code is also known as pseudo-random noise.<\/p>\r\n&nbsp;\r\n<p class=\"hanging-indent\"><img class=\"aligncenter size-full wp-image-147\" src=\"http:\/\/itp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic1.jpg\" alt=\"\" width=\"829\" height=\"455\" \/><\/p>\r\n<p style=\"text-align: center;\"><strong>Figure 1: Spreading of bandwidth<\/strong><\/p>\r\n&nbsp;\r\n<div>\r\n\r\n<strong>The magical codes<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify;\">Let us understand the concept of codes via the given example.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">Let us assume that there are two users. They transmit two symbols d1 and d2. A symbol is a bit obtained after encoding and decoding of noise and data. User 1 transmits symbol d1 and user 2 transmits symbol d2. The two users are assigned distinct codes as:<\/p>\r\n&nbsp;\r\n\r\n<strong>User 1: &lt;1, 1, 1, 1&gt;<\/strong>\r\n\r\n<strong style=\"text-align: initial; text-indent: 1em; font-size: 1em;\">User 2: &lt;1, 1, -1, -1&gt;<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">To transmit the symbol with the code, the symbol is multiplied with the code. Therefore symbol of user 1 is transmitted as<\/span><\/p>\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">&lt;d1, d1, d1, d1&gt;<\/span><\/p>\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">and of user2 is transmitted as<\/span><\/p>\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">&lt;d2, d2, -d2, -d2&gt;<\/span><\/p>\r\n&nbsp;\r\n<p class=\"hanging-indent\"><strong style=\"text-align: initial; text-indent: -1em; font-size: 1em;\">Therefore a single symbol is transmitted as a sequence of symbols.<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">These sub-symbols are known as chips and the sequence as known as chipping sequence. Now the two users transmit simultaneously. Their signals will linearly add up. Therefore resultant signal is:<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">S = &lt;d1, d1, d1, d1&gt; + &lt;d2, d2, -d2, -d2&gt;= &lt;d1+d2, d1+d2, d1-d2, d1-d2&gt;<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">At the receiving end, to recover the symbol of the user, it is multiplied with the code and correspondingly add the products. This technique is known as finding the correlation.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">S. &lt;1, 1, 1, 1&gt; = &lt;d1+d2, d1+d2, d1-d2, d1-d2&gt;. &lt;1, 1, 1, 1&gt;= d1+d1+d1+d1 = \u00a04d1<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-indent: -1em; font-size: 1em;\">Signal of user 2 has disappeared!!!!<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">S. &lt;1, 1, 1, 1&gt; = &lt;d1+d2, d1+d2, d1-d2, d1-d2&gt;. &lt;1, 1, -1, -1&gt;= d2+d2+d2+d2 = \u00a04d2<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-indent: -1em; font-size: 1em;\">Signal of user 1 has disappeared!!!!<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><strong style=\"font-size: 1em;\"><em>So we see that by finding the correlation of the resultant signal with the code of the user, we are able to retrieve its data.<\/em><\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">The interference from the other user is surprisingly nullified. This is the beauty of the codes.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: center;\"><span style=\"font-family: 'Cormorant Garamond', serif; font-size: 1em; font-weight: bold; text-align: center;\">What is the magic behind this? Would the same thing happen if I change the codes?<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">The answer is NO. Because these codes are unique. What is the uniqueness? Just find dot product\/correlation between these codes.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">&lt;1, 1, 1, 1&gt;\u00a0 \u00a0. \u00a0&lt;1, 1, -1, -1&gt; \u00a0= \u00a01+1-1-1 = 0<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: center;\"><span style=\"font-family: 'Cormorant Garamond', serif; font-size: 1em; font-weight: bold; text-align: center;\">It comes out to be 0. Such codes are called orthogonal codes.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Therefore using orthogonal codes, we have been able to able to send symbols of two users simultaneously on the same channel without interference. This is the basic technology used in CDMA, CDMAone, IS-95 and so on. The code appears to be random hence the name pseudo- random sequence. The receiver should know the code to retrieve the symbol. For those who do not know the code, it appears as noise hence the name pseudo-random noise.<\/span><\/p>\r\n&nbsp;\r\n<p class=\"hanging-indent\" style=\"text-align: justify;\"><strong style=\"text-align: initial; text-indent: -1em; font-size: 1em;\">Spreading of Bandwidth<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Let us see how the signal is spreaded. Before spreading, Suppose the bit rate is 1 kbps. To\u00a0<\/span><span style=\"font-size: 1em;\">transmit a single bit, time required =\u00a0<\/span><span style=\"font-size: 1em;\">After spreading to keep the bit rate constant, time required to send a chip or sub symbol is\u00a0<\/span><span style=\"font-size: 1em;\">hence\u00a0<\/span><\/p>\r\n&nbsp;\r\n<p class=\"hanging-indent\" style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Frequency<\/span><\/p>\r\n&nbsp;\r\n<p class=\"hanging-indent\" style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">We see that BW has spreaded by 4 times (Fig. 2)<\/span><\/p>\r\n\r\n<\/div>\r\n<img class=\"aligncenter size-full wp-image-149\" src=\"http:\/\/itp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic2.jpg\" alt=\"\" width=\"354\" height=\"180\" \/>\r\n<p style=\"text-align: center;\"><strong>Figure 2 Spreading of Bandwidth<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">Therefore the code is also known as \u201cspreading code\u201d .You can see in the Fig. 1 that bit 1 is transmitted as sequence of bits using the code \u201c1011011100\u201d<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">This code is known as Barker code &amp; is used in IEEE 802.11.Now you have seen that now the chipping sequence or the PN sequence spreads the symbol by a factor of 11 which is also length of code. This is known as spreading factors<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: center;\">Spreading factor =\u00a0<span style=\"text-align: initial; text-indent: 1em; font-size: 1em;\">\u00a0__<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">Civil application use spreading factor between 10 and 100 military application use upto 10,000. Wireless LAN IEEE 802.11 uses sequence 10110111000 as barker code with spreading factor of 11.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">We just saw in example that using 4 bit chipping sequence 2 users are able to transmit. Actually with 4 bit code, 4 orthogonal codes are possible. They are<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">&lt;1, 1, 1, 1&gt;<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">&lt;1, -1, -1, 1&gt;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a04 pairs of orthogonal codes<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">&lt;1, -1, 1, -1&gt;<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">&lt;1, 1, -1, -1&gt;<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">There are N possible orthogonal codes of length N. Hence N users can access the medium simultaneously.<\/p>\r\n&nbsp;\r\n<p class=\"hanging-indent\" style=\"text-align: justify;\"><strong>Principle of DSSS<\/strong><\/p>\r\n\r\n<ol>\r\n \t<li style=\"text-align: justify;\">BW is spreaded with help of a code called spreading code. The code is independent of data<\/li>\r\n \t<li style=\"text-align: justify;\">If m is length of code, the signal is spreaded by a factor of m<\/li>\r\n \t<li style=\"text-align: justify;\">By using unique code, all users transmit using entire BW. During transmission, the signals of all users add up linearly instead of being garbled<\/li>\r\n \t<li style=\"text-align: justify;\">The receiver receives sum of all signals. It is synchronizes with code of sender<\/li>\r\n \t<li style=\"text-align: justify;\">To recover the data, the receiver correlates the received signal with user code<\/li>\r\n<\/ol>\r\n<p style=\"text-align: justify;\"><strong>Illustration<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">Let us see a signal is spreaded and transmitted<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">Let us suppose four stations have been assigned 4 bit code<\/p>\r\n&nbsp;\r\n\r\nA: &lt;1, 1, 1, 1&gt;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0C: &lt;1, -1, 1, -1&gt;\r\n\r\n&nbsp;\r\n\r\n<strong>B: &lt;1, -1, -1, 1&gt;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0D: &lt;1, 1, -1, -1&gt;<\/strong>\r\n\r\n&nbsp;\r\n\r\nThis representation is a bipolar notation.\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify;\">To transmit a 1 the code is transmitted as it and to transmit a 0, complement of the code is to be transmitted. At the receiver all the signals of all the stations add up linearly (Fig. 4)<\/p>\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-151\" src=\"http:\/\/itp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic3.jpg\" alt=\"\" width=\"472\" height=\"242\" \/>\r\n<p style=\"text-align: center;\"><strong>Figure 3: Sending of data by adding chipping sequence<\/strong><\/p>\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-152\" src=\"http:\/\/itp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic4.jpg\" alt=\"\" width=\"561\" height=\"253\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\"><strong>Figure 4: Signals add up linearly<\/strong><\/p>\r\n\r\n<div>\r\n\r\nLet us consider four cases\r\n\r\n&nbsp;\r\n\r\nCase I: Only A transmits a 1\r\n\r\n&nbsp;\r\n<p class=\"hanging-indent\"><strong>Resultant signal at sender<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">S1 = &lt;1, 1, 1, 1&gt;<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\">Case II: A transmits a 1 &amp; B transmits 0A\u2019s signal will be spreaded as &lt;1, 1, 1, 1&gt;, B\u2019s signal as &lt;-1, +1, +1, -1&gt;<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">ResultantsignalatsenderS2 = &lt;0, +2, +2, 0&gt;<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Case III: A transmits a 1 \u00a0B transmits a 1 and\u00a0 C transmits a 0S3 =\u00a0\u00a0\u00a0 &lt;1, 1, 1, 1&gt;+ &lt;1, -1, -1, 1&gt;+ &lt;-1, +1, -1, +1&gt; = \u00a0&lt;1, 1, -1, 3&gt;<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Let us try to recover these signals at receiving side.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Let us recover the data stream of station <\/span><strong style=\"font-size: 1em;\">A<\/strong><span style=\"font-size: 1em;\">. For that find correlation of the received chip sequence with chip sequence or code of A. For that find inner product<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Case I: S1 . A&lt;1, 1, 1, 1&gt; . &lt;1, 1, 1, 1&gt; = \u00a0= 1<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Inner product perform pairwise summary of chip sequence of A and received signal so the correct bit sent is recovered<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">Case II<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">S2 . A<\/span><span style=\"text-align: initial; text-indent: 1em; font-size: 1em;\">&lt;0, +2, +2, 0&gt; &lt;1, 1, 1, 1&gt; = \u00a0= 1<\/span><\/p>\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">S2 . <\/span><span style=\"text-align: initial; font-size: 1em;\">B<\/span><span style=\"text-align: initial; font-size: 1em;\">&lt;0, +2, +2, 0&gt; &lt;1, -1, -1, 1&gt; =<\/span><span style=\"text-align: initial; font-size: 1em;\">= -1<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">(-1) indicates B has transmitted a zero.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">Case IIIS3 . A = &lt;1, 1, -1, 3&gt; &lt;1, 1, 1, 1&gt; =\u00a0\u00a0\u00a0 \u00a0= 1<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">S3 . B = &lt;1, 1, -1, 3&gt; &lt;1, -1,- 1, 1&gt; =\u00a0\u00a0\u00a0 \u00a0= 1<\/span><\/p>\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">S3 . C = &lt;1, 1, -1, 3&gt; &lt;1,- 1, 1,- 1&gt; =<\/span><span style=\"text-align: initial; font-size: 1em;\">= -1<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Now let us try to recover bit stream of a station when it has not transmitted at all. In all the three cases we can see that D has not transmitted. If we correlate the sequence of D with all three received signals, what do we get<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">S1 . D = &lt;1, 1, -1, 3&gt;. &lt;1, 1,- 1,- 1&gt; = 0<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">Similarly<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">S2 . D = &lt;0, +2, +2, 0&gt;. &lt;1, 1,- 1,- 1&gt; = 0<\/span><\/p>\r\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">S3 . D = &lt;1, 1, -1, 3&gt;. &lt;1, 1,- 1,- 1&gt; = 0<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">This applies that in all 3 cases D did not transmit at all.<\/span><\/p>\r\n&nbsp;\r\n<p class=\"hanging-indent\" style=\"text-align: justify;\"><strong><span style=\"text-align: initial; font-size: 1em;\">DSSS Sender<\/span><\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Step 1:\u00a0 Spread the\u00a0 user data with the chipping sequence via digital modulation. Result is spreaded signal<\/span><\/p>\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Step 2: \u00a0Spread signal is again modulated via a radio modulation<\/span><\/p>\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Step 3: This shifts the signal to carrier frequency<\/span><\/p>\r\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Step 4: \u00a0Signal is transmitted<\/span><\/p>\r\n\r\n<\/div>\r\n<img class=\"aligncenter size-full wp-image-153\" src=\"http:\/\/itp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic5.jpg\" alt=\"\" width=\"448\" height=\"175\" \/>\r\n<p style=\"text-align: center;\"><strong>Figure 5: Block diagram of DSSS sender<\/strong><\/p>\r\n<p class=\"hanging-indent\" style=\"text-align: left;\"><strong style=\"text-align: initial; font-size: 1em;\">DSSS Receiver<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; text-indent: -1em; font-size: 1em;\">Step: 1 Demodulate the received signal<\/span><\/p>\r\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">Step: 2 Generate the same pseudo random sequence as the transmitter<\/span><\/p>\r\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">Step: 3 Find the correlation with the pseudo random sequence by finding the product and integrating the products<\/span><\/p>\r\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">Step: 4 Decision unit decides if this sum represent a binary 1 or 0<\/span><img class=\"aligncenter size-full wp-image-154\" src=\"http:\/\/itp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic6.jpg\" alt=\"\" width=\"610\" height=\"192\" \/><\/p>\r\n<p style=\"text-align: center;\"><strong>Figure 6: Block diagram of DSSS receiver<\/strong><\/p>\r\n<p class=\"hanging-indent\" style=\"text-align: left;\"><strong>Rake receivers<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">DSSS works well when transmitted and receiver and perfectly synchronized and the effect of noise or multipath propagation is not there. But in case of m path propagation there will be many paths of different delays between TX and RX. For this purpose rake receivers are used. They use n correlators for n paths. Each correlator is synchronized to the transmitter + delay of path. As soon as the receiver gets a new path which is stronger than current weak path, it assigns correlators to the new path. Output of all correlators will be combined to the decision unit.<\/span><\/p>\r\n&nbsp;\r\n<p class=\"hanging-indent\" style=\"text-align: left;\"><strong>Summary<\/strong><\/p>\r\n\r\n<ul>\r\n \t<li style=\"text-align: justify;\">Direct Sequence Spread Spectrum spreads the bandwidth by transmitting the data using PN code<\/li>\r\n \t<li style=\"text-align: justify;\">Only receivers who knows the code can intercept the data<\/li>\r\n \t<li style=\"text-align: justify;\">Codes are independent of data<\/li>\r\n \t<li style=\"text-align: justify;\">It provides built in security<\/li>\r\n \t<li style=\"text-align: justify;\">Bandwidth is spreaded by order of size of code<\/li>\r\n \t<li style=\"text-align: justify;\">Codes should be orthogonal<\/li>\r\n<\/ul>\r\n<p style=\"text-align: justify;\">At receiving end by finding correlation of signal with users code, data is retrieved back<\/p>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Spread Spectrum Technology: Direct Sequence Spread Spectrum<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/h_j6TS-Y95s\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n<p class=\"hanging-indent\"><strong>Suggested Reading:<\/strong><\/p>\r\n\r\n<ol>\r\n \t<li>Mobile Communication 2nd edition by Jochen Schiller, Pearson education<\/li>\r\n \t<li>Mobile Computing by Asoke Talukder, Roopa Yavagal (Tata McGraw Hill)<\/li>\r\n \t<li>\"Wireless communication and networking\" by William Stallings<\/li>\r\n \t<li>Mobile Cellular Telecommunications \u2014 W.C.Y. Lee, Mc Graw Hill<\/li>\r\n \t<li>Wireless Communications \u2013 Theodore. S. Rapport, Pearson Education<\/li>\r\n \t<li>Reza B'Far (Ed), \"Mobile Computing Principles\", Cambridge University Press.<\/li>\r\n<\/ol>","rendered":"<div><span style=\"float: right;\"><a href=\"https:\/\/youtu.be\/h_j6TS-Y95s\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p><strong>Learning Objectives<\/strong><\/p>\n<ul>\n<li style=\"text-align: justify;\">Understand the principle of Direct Sequence Spread Spectrum<\/li>\n<li style=\"text-align: justify;\">Understand the concept of spreading codes and study their properties<\/li>\n<li style=\"text-align: justify;\">Discuss orthogonal codes<\/li>\n<li style=\"text-align: justify;\">By illustration understand how data is transmitted using codes and how it is recovered back at receiving station<\/li>\n<\/ul>\n<p class=\"hanging-indent\"><strong>Introduction<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">In Direct Sequence spread spectrum, Each bit in the original signal is represented by multiple bits in transmitted signal with the help of a code known as spreading code. The code appears to be pseudo random in nature while actually it is deterministic. The P-R code is also called pseudo codes. The signal is spreaded in proportion with the number of bits in the code. For example 11-bit code spreads the signal 11 times greater than 1 bit code. The code is independent of data to be transmitted. This is intercepted by only those receivers who know the code, for rest it is rejected as noise. Therefore the code is also known as pseudo-random noise.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"hanging-indent\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-147\" src=\"http:\/\/itp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic1.jpg\" alt=\"\" width=\"829\" height=\"455\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic1.jpg 829w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic1-300x165.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic1-768x422.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic1-65x36.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic1-225x123.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic1-350x192.jpg 350w\" sizes=\"auto, (max-width: 829px) 100vw, 829px\" \/><\/p>\n<p style=\"text-align: center;\"><strong>Figure 1: Spreading of bandwidth<\/strong><\/p>\n<p>&nbsp;<\/p>\n<div>\n<p><strong>The magical codes<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Let us understand the concept of codes via the given example.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Let us assume that there are two users. They transmit two symbols d1 and d2. A symbol is a bit obtained after encoding and decoding of noise and data. User 1 transmits symbol d1 and user 2 transmits symbol d2. The two users are assigned distinct codes as:<\/p>\n<p>&nbsp;<\/p>\n<p><strong>User 1: &lt;1, 1, 1, 1&gt;<\/strong><\/p>\n<p><strong style=\"text-align: initial; text-indent: 1em; font-size: 1em;\">User 2: &lt;1, 1, -1, -1&gt;<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">To transmit the symbol with the code, the symbol is multiplied with the code. Therefore symbol of user 1 is transmitted as<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">&lt;d1, d1, d1, d1&gt;<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">and of user2 is transmitted as<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">&lt;d2, d2, -d2, -d2&gt;<\/span><\/p>\n<p>&nbsp;<\/p>\n<p class=\"hanging-indent\"><strong style=\"text-align: initial; text-indent: -1em; font-size: 1em;\">Therefore a single symbol is transmitted as a sequence of symbols.<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">These sub-symbols are known as chips and the sequence as known as chipping sequence. Now the two users transmit simultaneously. Their signals will linearly add up. Therefore resultant signal is:<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">S = &lt;d1, d1, d1, d1&gt; + &lt;d2, d2, -d2, -d2&gt;= &lt;d1+d2, d1+d2, d1-d2, d1-d2&gt;<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">At the receiving end, to recover the symbol of the user, it is multiplied with the code and correspondingly add the products. This technique is known as finding the correlation.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">S. &lt;1, 1, 1, 1&gt; = &lt;d1+d2, d1+d2, d1-d2, d1-d2&gt;. &lt;1, 1, 1, 1&gt;= d1+d1+d1+d1 = \u00a04d1<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-indent: -1em; font-size: 1em;\">Signal of user 2 has disappeared!!!!<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">S. &lt;1, 1, 1, 1&gt; = &lt;d1+d2, d1+d2, d1-d2, d1-d2&gt;. &lt;1, 1, -1, -1&gt;= d2+d2+d2+d2 = \u00a04d2<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-indent: -1em; font-size: 1em;\">Signal of user 1 has disappeared!!!!<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong style=\"font-size: 1em;\"><em>So we see that by finding the correlation of the resultant signal with the code of the user, we are able to retrieve its data.<\/em><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">The interference from the other user is surprisingly nullified. This is the beauty of the codes.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: 'Cormorant Garamond', serif; font-size: 1em; font-weight: bold; text-align: center;\">What is the magic behind this? Would the same thing happen if I change the codes?<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">The answer is NO. Because these codes are unique. What is the uniqueness? Just find dot product\/correlation between these codes.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">&lt;1, 1, 1, 1&gt;\u00a0 \u00a0. \u00a0&lt;1, 1, -1, -1&gt; \u00a0= \u00a01+1-1-1 = 0<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><span style=\"font-family: 'Cormorant Garamond', serif; font-size: 1em; font-weight: bold; text-align: center;\">It comes out to be 0. Such codes are called orthogonal codes.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Therefore using orthogonal codes, we have been able to able to send symbols of two users simultaneously on the same channel without interference. This is the basic technology used in CDMA, CDMAone, IS-95 and so on. The code appears to be random hence the name pseudo- random sequence. The receiver should know the code to retrieve the symbol. For those who do not know the code, it appears as noise hence the name pseudo-random noise.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p class=\"hanging-indent\" style=\"text-align: justify;\"><strong style=\"text-align: initial; text-indent: -1em; font-size: 1em;\">Spreading of Bandwidth<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Let us see how the signal is spreaded. Before spreading, Suppose the bit rate is 1 kbps. To\u00a0<\/span><span style=\"font-size: 1em;\">transmit a single bit, time required =\u00a0<\/span><span style=\"font-size: 1em;\">After spreading to keep the bit rate constant, time required to send a chip or sub symbol is\u00a0<\/span><span style=\"font-size: 1em;\">hence\u00a0<\/span><\/p>\n<p>&nbsp;<\/p>\n<p class=\"hanging-indent\" style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Frequency<\/span><\/p>\n<p>&nbsp;<\/p>\n<p class=\"hanging-indent\" style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">We see that BW has spreaded by 4 times (Fig. 2)<\/span><\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-149\" src=\"http:\/\/itp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic2.jpg\" alt=\"\" width=\"354\" height=\"180\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic2.jpg 354w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic2-300x153.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic2-65x33.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic2-225x114.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic2-350x178.jpg 350w\" sizes=\"auto, (max-width: 354px) 100vw, 354px\" \/><\/p>\n<p style=\"text-align: center;\"><strong>Figure 2 Spreading of Bandwidth<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">Therefore the code is also known as \u201cspreading code\u201d .You can see in the Fig. 1 that bit 1 is transmitted as sequence of bits using the code \u201c1011011100\u201d<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">This code is known as Barker code &amp; is used in IEEE 802.11.Now you have seen that now the chipping sequence or the PN sequence spreads the symbol by a factor of 11 which is also length of code. This is known as spreading factors<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">Spreading factor =\u00a0<span style=\"text-align: initial; text-indent: 1em; font-size: 1em;\">\u00a0__<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Civil application use spreading factor between 10 and 100 military application use upto 10,000. Wireless LAN IEEE 802.11 uses sequence 10110111000 as barker code with spreading factor of 11.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">We just saw in example that using 4 bit chipping sequence 2 users are able to transmit. Actually with 4 bit code, 4 orthogonal codes are possible. They are<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">&lt;1, 1, 1, 1&gt;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">&lt;1, -1, -1, 1&gt;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a04 pairs of orthogonal codes<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">&lt;1, -1, 1, -1&gt;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">&lt;1, 1, -1, -1&gt;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">There are N possible orthogonal codes of length N. Hence N users can access the medium simultaneously.<\/p>\n<p>&nbsp;<\/p>\n<p class=\"hanging-indent\" style=\"text-align: justify;\"><strong>Principle of DSSS<\/strong><\/p>\n<ol>\n<li style=\"text-align: justify;\">BW is spreaded with help of a code called spreading code. The code is independent of data<\/li>\n<li style=\"text-align: justify;\">If m is length of code, the signal is spreaded by a factor of m<\/li>\n<li style=\"text-align: justify;\">By using unique code, all users transmit using entire BW. During transmission, the signals of all users add up linearly instead of being garbled<\/li>\n<li style=\"text-align: justify;\">The receiver receives sum of all signals. It is synchronizes with code of sender<\/li>\n<li style=\"text-align: justify;\">To recover the data, the receiver correlates the received signal with user code<\/li>\n<\/ol>\n<p style=\"text-align: justify;\"><strong>Illustration<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Let us see a signal is spreaded and transmitted<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Let us suppose four stations have been assigned 4 bit code<\/p>\n<p>&nbsp;<\/p>\n<p>A: &lt;1, 1, 1, 1&gt;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0C: &lt;1, -1, 1, -1&gt;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>B: &lt;1, -1, -1, 1&gt;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0D: &lt;1, 1, -1, -1&gt;<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>This representation is a bipolar notation.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">To transmit a 1 the code is transmitted as it and to transmit a 0, complement of the code is to be transmitted. At the receiver all the signals of all the stations add up linearly (Fig. 4)<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-151\" src=\"http:\/\/itp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic3.jpg\" alt=\"\" width=\"472\" height=\"242\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic3.jpg 472w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic3-300x154.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic3-65x33.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic3-225x115.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic3-350x179.jpg 350w\" sizes=\"auto, (max-width: 472px) 100vw, 472px\" \/><\/p>\n<p style=\"text-align: center;\"><strong>Figure 3: Sending of data by adding chipping sequence<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-152\" src=\"http:\/\/itp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic4.jpg\" alt=\"\" width=\"561\" height=\"253\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic4.jpg 561w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic4-300x135.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic4-65x29.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic4-225x101.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic4-350x158.jpg 350w\" sizes=\"auto, (max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong>Figure 4: Signals add up linearly<\/strong><\/p>\n<div>\n<p>Let us consider four cases<\/p>\n<p>&nbsp;<\/p>\n<p>Case I: Only A transmits a 1<\/p>\n<p>&nbsp;<\/p>\n<p class=\"hanging-indent\"><strong>Resultant signal at sender<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">S1 = &lt;1, 1, 1, 1&gt;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Case II: A transmits a 1 &amp; B transmits 0A\u2019s signal will be spreaded as &lt;1, 1, 1, 1&gt;, B\u2019s signal as &lt;-1, +1, +1, -1&gt;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">ResultantsignalatsenderS2 = &lt;0, +2, +2, 0&gt;<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Case III: A transmits a 1 \u00a0B transmits a 1 and\u00a0 C transmits a 0S3 =\u00a0\u00a0\u00a0 &lt;1, 1, 1, 1&gt;+ &lt;1, -1, -1, 1&gt;+ &lt;-1, +1, -1, +1&gt; = \u00a0&lt;1, 1, -1, 3&gt;<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Let us try to recover these signals at receiving side.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Let us recover the data stream of station <\/span><strong style=\"font-size: 1em;\">A<\/strong><span style=\"font-size: 1em;\">. For that find correlation of the received chip sequence with chip sequence or code of A. For that find inner product<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Case I: S1 . A&lt;1, 1, 1, 1&gt; . &lt;1, 1, 1, 1&gt; = \u00a0= 1<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Inner product perform pairwise summary of chip sequence of A and received signal so the correct bit sent is recovered<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">Case II<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">S2 . A<\/span><span style=\"text-align: initial; text-indent: 1em; font-size: 1em;\">&lt;0, +2, +2, 0&gt; &lt;1, 1, 1, 1&gt; = \u00a0= 1<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">S2 . <\/span><span style=\"text-align: initial; font-size: 1em;\">B<\/span><span style=\"text-align: initial; font-size: 1em;\">&lt;0, +2, +2, 0&gt; &lt;1, -1, -1, 1&gt; =<\/span><span style=\"text-align: initial; font-size: 1em;\">= -1<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">(-1) indicates B has transmitted a zero.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">Case IIIS3 . A = &lt;1, 1, -1, 3&gt; &lt;1, 1, 1, 1&gt; =\u00a0\u00a0\u00a0 \u00a0= 1<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">S3 . B = &lt;1, 1, -1, 3&gt; &lt;1, -1,- 1, 1&gt; =\u00a0\u00a0\u00a0 \u00a0= 1<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">S3 . C = &lt;1, 1, -1, 3&gt; &lt;1,- 1, 1,- 1&gt; =<\/span><span style=\"text-align: initial; font-size: 1em;\">= -1<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Now let us try to recover bit stream of a station when it has not transmitted at all. In all the three cases we can see that D has not transmitted. If we correlate the sequence of D with all three received signals, what do we get<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">S1 . D = &lt;1, 1, -1, 3&gt;. &lt;1, 1,- 1,- 1&gt; = 0<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">Similarly<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">S2 . D = &lt;0, +2, +2, 0&gt;. &lt;1, 1,- 1,- 1&gt; = 0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: initial; font-size: 1em;\">S3 . D = &lt;1, 1, -1, 3&gt;. &lt;1, 1,- 1,- 1&gt; = 0<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">This applies that in all 3 cases D did not transmit at all.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p class=\"hanging-indent\" style=\"text-align: justify;\"><strong><span style=\"text-align: initial; font-size: 1em;\">DSSS Sender<\/span><\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Step 1:\u00a0 Spread the\u00a0 user data with the chipping sequence via digital modulation. Result is spreaded signal<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Step 2: \u00a0Spread signal is again modulated via a radio modulation<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Step 3: This shifts the signal to carrier frequency<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-size: 1em;\">Step 4: \u00a0Signal is transmitted<\/span><\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-153\" src=\"http:\/\/itp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic5.jpg\" alt=\"\" width=\"448\" height=\"175\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic5.jpg 448w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic5-300x117.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic5-65x25.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic5-225x88.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic5-350x137.jpg 350w\" sizes=\"auto, (max-width: 448px) 100vw, 448px\" \/><\/p>\n<p style=\"text-align: center;\"><strong>Figure 5: Block diagram of DSSS sender<\/strong><\/p>\n<p class=\"hanging-indent\" style=\"text-align: left;\"><strong style=\"text-align: initial; font-size: 1em;\">DSSS Receiver<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; text-indent: -1em; font-size: 1em;\">Step: 1 Demodulate the received signal<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">Step: 2 Generate the same pseudo random sequence as the transmitter<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">Step: 3 Find the correlation with the pseudo random sequence by finding the product and integrating the products<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">Step: 4 Decision unit decides if this sum represent a binary 1 or 0<\/span><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-154\" src=\"http:\/\/itp12.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic6.jpg\" alt=\"\" width=\"610\" height=\"192\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic6.jpg 610w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic6-300x94.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic6-65x20.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic6-225x71.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-content\/uploads\/sites\/27\/2018\/07\/M09Pic6-350x110.jpg 350w\" sizes=\"auto, (max-width: 610px) 100vw, 610px\" \/><\/p>\n<p style=\"text-align: center;\"><strong>Figure 6: Block diagram of DSSS receiver<\/strong><\/p>\n<p class=\"hanging-indent\" style=\"text-align: left;\"><strong>Rake receivers<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">DSSS works well when transmitted and receiver and perfectly synchronized and the effect of noise or multipath propagation is not there. But in case of m path propagation there will be many paths of different delays between TX and RX. For this purpose rake receivers are used. They use n correlators for n paths. Each correlator is synchronized to the transmitter + delay of path. As soon as the receiver gets a new path which is stronger than current weak path, it assigns correlators to the new path. Output of all correlators will be combined to the decision unit.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p class=\"hanging-indent\" style=\"text-align: left;\"><strong>Summary<\/strong><\/p>\n<ul>\n<li style=\"text-align: justify;\">Direct Sequence Spread Spectrum spreads the bandwidth by transmitting the data using PN code<\/li>\n<li style=\"text-align: justify;\">Only receivers who knows the code can intercept the data<\/li>\n<li style=\"text-align: justify;\">Codes are independent of data<\/li>\n<li style=\"text-align: justify;\">It provides built in security<\/li>\n<li style=\"text-align: justify;\">Bandwidth is spreaded by order of size of code<\/li>\n<li style=\"text-align: justify;\">Codes should be orthogonal<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">At receiving end by finding correlation of signal with users code, data is retrieved back<\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Spread Spectrum Technology: Direct Sequence Spread Spectrum<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/h_j6TS-Y95s\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"hanging-indent\"><strong>Suggested Reading:<\/strong><\/p>\n<ol>\n<li>Mobile Communication 2nd edition by Jochen Schiller, Pearson education<\/li>\n<li>Mobile Computing by Asoke Talukder, Roopa Yavagal (Tata McGraw Hill)<\/li>\n<li>&#8220;Wireless communication and networking&#8221; by William Stallings<\/li>\n<li>Mobile Cellular Telecommunications \u2014 W.C.Y. Lee, Mc Graw Hill<\/li>\n<li>Wireless Communications \u2013 Theodore. S. Rapport, Pearson Education<\/li>\n<li>Reza B&#8217;Far (Ed), &#8220;Mobile Computing Principles&#8221;, Cambridge University Press.<\/li>\n<\/ol>\n","protected":false},"author":4,"menu_order":9,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["miss-suchit-purohit"],"pb_section_license":""},"chapter-type":[],"contributor":[59],"license":[],"class_list":["post-146","chapter","type-chapter","status-publish","hentry","contributor-miss-suchit-purohit"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-json\/pressbooks\/v2\/chapters\/146","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-json\/wp\/v2\/users\/4"}],"version-history":[{"count":8,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-json\/pressbooks\/v2\/chapters\/146\/revisions"}],"predecessor-version":[{"id":635,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-json\/pressbooks\/v2\/chapters\/146\/revisions\/635"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-json\/pressbooks\/v2\/chapters\/146\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-json\/wp\/v2\/media?parent=146"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-json\/pressbooks\/v2\/chapter-type?post=146"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-json\/wp\/v2\/contributor?post=146"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp12\/wp-json\/wp\/v2\/license?post=146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}