Talk:Code division multiple access

From Wikipedia, the free encyclopedia

Contents 1 CDMA history 2 TDMA/GSM are DIGITAL cellular/PCS technologies – very poor CDMA Comparisons 3 Dot Product Problems 4 Dot Product Problems and MORE 5 Two meaning of CDMA 6 Vector components 7 Power control and more 8 Where do I begin... 9 comment 10 Comparision of CDM and CDMA is not satisfactory 11 Re: comment 12 Perspective from someone who just wants the basics, not the thesis 13 A little bit of historical perspective 14 See "Re: comment" above 15 why no sims? 16 Copy editing to improve clarity 17 Use of talk pages 18 What? 19 (See also the Market situation section of GSM.)

[edit] CDMA history

"CDMA is a military technology first used during World War II by English allies to foil German attempts at jamming transmissions. The allies decided to transmit over several frequencies, instead of one, making it difficult for the Germans to pick up the complete signal."

ok, first of all, CDMA as such did not come out until the 90s.

The concept of spread spectrum as it is understood today, originally invented by an American, Heady LaMarr (spelling), was never used in WW II.

Finally, it is usually referred to as "Allied forces" or "American allies" not "English allies".71.116.106.31 00:50, 9 July 2006 (UTC)

The CDMA was analysed in the late 1970 as technology for even Arpanet. It was prposed and analysed by the GSM as one alternative, and rejected as I say - because it does not have a finite time to deliver: Simple, when the number of users exceed a threshold, the time spend identifying and managing the packets is to high to be able to send everyone, so then you start to retransmit. Put it blunt: What do you consider will happen in a town where every time there was a read light request was issued for every car in the queue to fine a new car to line up for them? Yes - you would very soon run out of street and road space to hold the queue, and after that - run out of cars.

Yes, Qualcomm has supresses a slight error in their math equation. As long as there are few users, CDMA is a good technology - but once the air gets crowded, the O-residual that they claim is "insignificant" just shows when they fell asleep during Calulus in high school.

—The preceding unsigned comment was added by Khflottorp (talk • contribs) 12:43, 9 July 2006.

[edit] TDMA/GSM are DIGITAL cellular/PCS technologies – very poor CDMA Comparisons

It's my suspicion that people employed from certain carriers contributed to this article and would like a reader to believe TDMA and GSM are analog multiple access technologies. In fact they are both completely DIGITAL, which then concerns me about many of the other explanations – to include many of the other comparisons, which are plagued by incorrect explanations and inconsistencies. It’s in technical articles like this one where Wiki will always fall short of factual documentation. Reader beware and scrutinize what you take out of here.

OK. Yes, it was highly biased on the US understanding - afterall they invented the names "CDMA" and "TDMA". Outside the US it has several different names - mostly "Code Division Multiplexing" - replacing the "MA" with "mulitplexing" - which is the term applied in telecom for many logical streams sharing one physical - not only on the "Access Network" link.

The Nordic countries developed the NMT system soon after SS7 had been finalised (1978). This served as prototype for GSM - as it was fully digital in the network and call management, while the voice codec was insufficient to support fully digital service (full service 1982?).

The readers needs to be made aware that telecom was one of the first areas to be completely computerised - in Europe. Here the telecom companies had at the time protected national monopoly on the service, and was liable only to the government. Their last and final effort to withstand the expected competition was to digitise all the network - fibre in the ground, and digital service in the air - with a suite of services for computer networks based on IBM's then HDLC/LU6.2 - and a proposed network hierarchy/stack - refered to a s OSI - "Open System interconnect". We still refer to these "layers" - and honstly, they may come back and haunt the US. IP-level interfacing needs routing as a service, as found in SS7 connection set-up and routing. Here, the Europeans defined routing as a service. The net owner may set up own routing, but since the dominant capacity was available to lease to new operators, they had to allow "others" to define own routing - using foreign nets. This is the same as "Soft Handover" really - it is just that the routing table at the BSC will use not only one "next station" - but can also interroagate and find that you radio link quality is alsmost as good by another BST - but here there are better capacity, and move you to this to optimise the network.

I would like the article to state that: "CDMA was made by Qualcomm on behalf of the US telephone companies following the HR decision, and later sanction by the US president as the law to "Liberate the frequencies". This basically bars GSM usage in the US, and protects the US companies to make something different (not better). The observation was that there was a severe danger at the time, that the US operators would be an easy prey for European takeovers."

Qualcommwas most likely unaware that the GSM consortium had studied Code Division Mutliplexing" and rejected it. They hired some Indians to help them with the math, and the poor professor has published and article where he completes the calculation of the O-residual, but this is never refered to by them. Participants from Nokia/Finland argued strongly for CDMA indicating that they had reached very far in investigating this and exploring other properties. I cannot find the papers, but if I remember right, it is multi-channel code division, with the capability to cut-off to time-division when the network was congested. The terrain in the Nordic countries require extensive cell overlay, thus multiple channels had to be used (coverage is considered more important than a few as possible base stations - to allow the consumer later to be loyal to the first network and not move on to competitors that needed to provide the same coverage).

The GSM network also has muliple frequncy bands to support different cell sizes. These systems are defined by engineers and not by company directors. The engineers knows the basic laws of physics and use them to acheive specific properties. By using the SS7, it is possible for GSM to use special modulation for data - know as EDGE, and also paves the way for easy upgrade to 3G - with new modulation technology already in place making the first specifications outdated. I know that a comittee is a beast with 1 head and 12 legs - but it is better then no head at all (where 2 ignorant corporate managers decide based on how they believe they can acheive a higher profit. I know give the people tin cans with a wire between - but that is not "wire less")

I have tried to tidy up some. Most important is that Americans need to understand that regardless of numerous attempts to offer CDMA even for free - the rest of the world has choosen GSM. They also need to understand that the ITU is the holder of standards, and as long as the US decides to ignore important work going on in the ITU, they loose business opportunities - and the rest of the world goes on very well without their intereference. (See first wimper...:-) --KH Flottorp 12:23, 9 July 2006 (UTC)

[edit] Dot Product Problems

It's been a while since I've done it, but I'm fairly confident the dot products on this page are incorrect.

[edit] Dot Product Problems and MORE

<sigh> Those aren't the only problems on this page. Ah, the wonder of Wikipedia! Any amateur who knows just enough to be dangerous can spread his errors far and wide and claim to have authored an encyclopdia article on the subject! Corrections are futile because the amateur simply returns and re-errorizes the information.

• • The dot products are correct in that they are normalized dot products (i.e. divide the result of the dot product by the number of terms in the respective vectors). I edited the description to reflect this, as it confused me a lot when I was reading it as well.

How broadcasting +1.2/-1.2 or +0.8/-0.8 change the calculations or the orthogonality between the walsh codes? To me the dot products between the presented codes don't seem to suffer from power difference between the transmissions at all. Crosstalk between the codes comes from totally different phenomena. There is no infinite amount of CDMA codes; presented four chip long code has only four.

[edit] Two meaning of CDMA

The article does a good deal of explaining the two meaning of the initials. See this post for more info [1]

[edit] Vector components

"Most generally these vectors are specially constructed for ease of decoding -- they are columns or rows from Walsh matrices that are constructed from Walsh functions, but strictly mathematically the only restriction on these vectors are that they have no nonzero components". That means they are null vectors doesn't it? Thats the way I read, so maybe its a mistake.

Agh. Yes, it was a mistake, and the statement was wrong anyway. I've fixed it. I don't know what I was thinking. Dysprosia 14:04, 10 July 2005 (UTC)

[edit] Power control and more

The article has improved a lot but still the explanation why the orthogonality is lost is missing. Power difference would require better orthogonality but it doesn't remove the orthogonality as can be understood from the article now. All the shown equations apply to any power level. In real systems no 1's or -1's can be transmitted since they would require infinite bandwidth. On the other hand limited bandwidth chips would require infinite time. So waveforms somewhere in between must be used. They are unfortunately both non-orthogonal and sensitive to timing.

If infinite amount of CDMA codes would be used one bit would be infinite chips long and bit rate would be zero bps. In practice the amount of CDMA codes in most applications is very limited. There is also other CDMA systems than the described direct sequence.

Maybe someone familiar with these issues could rewrite this article one more time?

With respect to the first problem, this is dependent on whether the receiver is detecting for sign or for value. For sign, it isn't a problem, but for value, it is. In implementation, I don't know what is more common/used. If you do know, please be bold, go ahead and rectify the article directly. It is a wiki after all.

The article says that the amount of CDMA codes are infinite in that, for example, if there are two senders, one can use chip codes of "length" 2, if there are up to four senders, one can use chip codes of "length" 4, and so on, so theoretically there is no hard protocol-imposed limit to how many senders can use the system, but practically there may need to be caps placed on the number of senders.

I'll try and add a clarification here and there in regards to these matters, and the article would probably be served by a few more passes over it -- but again, if you see problems, go ahead and edit. Dysprosia 06:53, 11 July 2005 (UTC)

[edit] Where do I begin...

I would completely re-write this article if I had time. It is wrong on so many levels. Perhaps after I finish my doctoral thesis. Until then, here are the important points that need to be made:

CDM vs. CDMA:

The biggest fundamental error with this article is there is no distinction drawn between CDM (Code Division Multiplexing) and CDMA (Code Division Multiple Access). This article discusses CDM, not CDMA! CDM is synchronous, and is used for all of the Base-to-Mobile links. These can be synchronized because the base-stations are completely stationary and the clocks can be synchronized with extremely fine precision. Orthogonality is only possible in this synchronous *multiplexed* scenario.

CDMA vs. TDMA and FDMA:

The entire point of using CDMA is so that the mobiles do not need to be synchronized to the base-station. If you could perfectly synchronize all of the users, you might as well use TDMA. To a first order, TDMA, FDMA and CDMA are all equivalent in the sense that they all provide a means of of orthogonally separating multiple users under ideal conditions. However, in practice they all have pros and cons. In FDMA, doppler spreading and imperfect filters creates a need for guard bands. In TDMA, the inability to perfectly synchronize the users creates a need for guard times. In CDMA, orthogonality is only mathematically possible if the users are perfectly synchronized. Thus in practice, TDMA and FDMA can never be made perfectly efficient, while the mobile-to-base links in CDMA can never be made orthogonal.

Asynchronous CDMA:

True CDMA (asynchronous mobile-to-base links) comes in two flavors, short code and long code CDMA. The long code CDMA is the most common type, typically a pseudo-random shift register sequence (a.k.a, an "m-sequence") that is longer than the code length (number of chips per symbol, a.k.a the "Processing Gain"). Solomon Golomb's book "Shift Register Sequences" is a classic reference for these sequences.

Multiple Access Interference (MAI):

In an asynchronous system, the users are *not*, and *cannot* be orthogonal, merely *uncorrelated*, i.e., the average cross-correlation is zero. The variance of the correlation, on the other hand, is inversely proportional to the code length, and directly proportional to the number of users. This is known as Multiple Access Interference (MAI), and is an asymptotically stationary zero-mean Gaussian noise process for a large number of users (via the central limit theorem). Sarwate and Pursely's 1977 paper is a classic reference for this result. Each user adds a small amount of additional interference, which is known as "soft degradation".

Power-Control and Capacity This can be significant since each base station typically picks up transmissions from all of the users in the cell, plus a large number of interfering mobiles from adjacent cell sites. The near-far problem with power control is that the mobiles close to the base station must use significantly lower power than mobiles far from it. In effect, if a user transmits twice as much power, they generate twice as much interference as they are supposed to. The use of FEC (Forward Error Correction) is to mitigate the number of errors incurred from the total of all the sources of degradation (thermal noise, MAI, co-site interference, narrowband interference, etc.). The capacity is essentially constrained by the strength of the FEC and ability to control the power. The FEC can only tolerate interference down to a signal-to-interference ratio (SIR) where the bit error rate (BER) becomes unacceptably high. Thus, the capacity (number of users) is maximized by keeping the level of interference generated by each user the same. If the power control is imperfect, then this inefficiency leads to a degradation in capacity.

There are so many concepts here that need to be properly explained, I could probably spend a month on this!

Complete your PhD - and then get cracking! But beware the readers of Wikipedia are many-fold: Some require high-level abstracts that easy to read, others need toi reference parts to allow them to understand the text books they read. Just beware:"interference generated by each user" is not a uniform distribution - best a poission - probably an expotential since they all use the same frequency - making your assumptions a dangerous one. —The preceding unsigned comment was added by Khflottorp (talk • contribs) 12:43, 2006 July 9.

[edit] comment

Comment on “Where do I begin”*** WARNING, he grossly overstates the inconstancies found in this article. You can tell he is someone who has only studied the technology from the outside in and does not actually know or understand some of the specific features found in the equipment itself - beyond the EE textbook – different vendors include different specifications which makes it hard to technically define a multiple access technology like CDMA – different carriers deploy different manufacturers’ solutions and then use different management techniques, which can also vary from market to market.

I came to this article looking for a reasonably concise and understandable explanation of CDMA after reading an article in the Wall Street Journal. I was impressed. While I understand the concerns of the editor (above), the article satisfied my needs and I commend those who have worked on it and who have tried to improve it. Walter Siegmund (talk) 20:02, 27 February 2006 (UTC)

[edit] Comparision of CDM and CDMA is not satisfactory

CDM/CDMA, code division CDM/CDMA is the orthogonal power distribution multiplex/demultiplex scheme. Different signals may coexist in the same frequency band at the same time. Existence of each signal means interference to other signals in channel. And this interference in determined by power distribution of all signals, phase difference, and correlation factors between random code of each signal. Hence we can conclude that CDM and CDMA is same and not different.—The preceding unsigned comment was added by 202.138.120.37 (talk • contribs) 10:38, 2006 May 6.

[edit] Re: comment

Again, the "Technical Details" section is only applicable to CDM. The statement that orthgonality is the heart of CDMA is *completely* wrong and totally misleading. I have removed some of the blatantly false statements, such as the nonsense about how the near-far effect "destroys the orthogonality". While it is true that 64-ary Walsh sequences are used in a particular M-ary CDMA scheme (IS-95, I beleive) to transmit multiple bits per symbol (64-ary -> 6 bits/symbol), the multiple-access capability comes from using different pseudo-random sequences (or at least different shifts of the same pseudo-random sequence), which *are not* and *cannot* be orthogonal. In general, however, Walsh sequences have *nothing* to do with the general concept of CDMA.

The entire point of this particular page is, in fact, to give a simple "textbook" overview of the *concept* of CDMA, eschewing the esoteric details of particular CDMA standards, each of which have their own pages. Therefore, I think the entire section about Walsh sequences and orthogonality should be done away with (or placed under an a proper explanation of either CDM or as a particular variant of M-ary CDMA). This page needs to bring home the point for the non-specialist audience that only a synchronous system, such as the base-to-mobile link, can have orthogonality (CDM, not CDMA), and that general asynchronous systems, such as the mobile-to-base link, (which is true CDMA) have Multiple Access Intereference (MAI) that is approximated by a Gaussian noise process, and requires power-control to reduce the near-far effect.

I have a doctorate in communications theory, wrote my dissertation on M-ary CDMA techniques for optical communications, have published several technical papers on CDMA in peer-reviewed journals, and my advisor was one of the pioneers of CDMA technology. So I definitely know what I am talking about here, and am probably more qualified than any other contributor to this page to assess the technical accuracy of this article (or the lack thereof, unfortunately). What I currently lack is loads of spare time to properly fix it. Until then, readers must be cautioned that the "Technical Details" section is very misleading.

You have also, however, removed rather pertinent details that need not have been removed. Dysprosia 01:08, 4 May 2006 (UTC)

Again, near-far has no effect on orthogonality! It's the very essence of what orthogonal means. Case in point, take any one of the 4 sequences S_i shown in the figure by a constant A, and then chose another sequence S_j and mutiply it by B (i = 0..3, k=0..3, i != k). When you correlate A*S_i with S_i, you get A. When you correlate B*S_k with S_k, you get B. If you correlate A*S_i with B*S_k, you get two positive A*B terms and two negative A*B terms that sum to zero. Period. This is the very essence of an orthogonal basis of functions. For instance, the FFT is an orthogonal basis of complex exponentials, and the whole point of signal processing is that you can use a linear filter to modify the weight of each spectral component indepdendently from any of the others. What destroys the orthogonality of a basis is to introduce non-linearities (like squaring) or to shift the time intervals of the components differently. As an example of a nonlinearity, it is clear that squaring any of the Walsh sequences produces the all ones sequence, destroying the orthogonality. As an example of shifting the time interval, it is evident that by cyclically rotating the third sequence to the right (move every chip over the right and carry back the right-most chip to the first (left-most) position), you obtain the second sequence, also destroying the orthogonality. In other words, linearity and orthogonality are like two sides of the same coin.

To be very precise, the near-far effect makes the statistics of the MAI (and therefore, the performance) very difficult to analyze. Suppose there are 100 interferers with unity amplitude, and one extremely dominant interferer with an amplitude of 100. The 100 equal users combine to produce MAI that is approximately stationary Gaussian with zero mean and a variance of 100. Note that the tails aren't infinite though, the extreme values are +100 and -100. When you add this to a PN sequence with an amplitude of 100, you get a zero-mean process with a variance of 100^2 + 100 = 10100, but it is *not* stationary Gaussian. When a chip from the dominant sequence is positive, the values range between zero and 200. For a negative chip, the values range between -200 and zero. So you get a bi-modal distribution with one mode at +100, and the other at -100. To characterize it only by the mean and variance (which only completely describe a true stationary Gaussian distribution) is very misleading; the performance will be significantly worse than if you had 10100 users with unity amplitude.

Now, suppose that the processing gain is 100, so that the modes are at +1 and -1, with extreme values of -2 and +2. In this example, the error rate is 1/4 or 25% because the dominant MAI has equal power with the signal, destructively interfering half the time (to 0), and constructively interfering half the time (to -2 or +2). For a zero value, we'll get lucky half the time, and for +/-2, the remaining interference from the 100 users isn't strong enough to flip the sign (the extrema of this process are -1 and +1), so we'll always get it right. On the otherhand, for 10100 users we get Gaussian MAI with zero mean and a variance of 10100/100^2 = 1.01. The error probability in this case is erfc(sqrt(1.01)), which is 15.5%. So clearly, the near-far effect can have a far more drastic effect on the performance than simply decreasing the SIR, which is a reasonable assumption only when the power of the dominant interfer is close to the average power.

If by near-far you mean that the statement that differing signal strengths can disrupt orthogonality, I don't believe you are correct. Furthermore, I don't understand what you mean by "correlate". However, let me try and explain what is meant by using the example in the article. If we model signal fading by multiplication by a constant less than 1, suppose that v = (1,-1,-1,1,1,-1,1,-1) is transmitted by one sender V with chip code (1,-1), and w = (-1,-1,-1,-1,1,1,1,1) is sent by the other sender W with chip code (1,1). Suppose that V transmits less strongly than W, so we end up with 0.3v and w "adding up in the air" to get (-0.7, -1.3, -1.3, -0.7, 1.3, 0.7, 1.3, 0.7). Take the dot product of (-0.7, -1.3) and (1,-1) and we get 0.6 -- not 2 as expected. So something has gone wrong. If we take the dot product of (-0.7, -1.3) and (1,1), however, we get -2 as expected, so W is swamping V.

This is all according according to the mathematical model. Dysprosia 07:02, 4 May 2006 (UTC)

It dosen't matter what get's transmitted, it matters what the receiver is able to understand from the message. The receiver works by a process called correlation, which is the same as the dot-product for any orthogonal basis. Simply put, if user i has sequence S_i, and user k has sequence S_k, the receiver for user i(after synchronizing to know where the symbols start, which is not trivial) mutiplies each symbol by S_i, and takes the sum. If it is positive, decide 1. if negative, decide -1. So if you transmit (A S_i + B S_k), with A and B arbitrary constants, the receiver computes the correlation which is the dot-product (A S_i + B S_k) * S_i = A ||S_i||^2 + A*B (S_i * S_k). From the dot-product properties in the article, this gives you A + 0 since S_i and S_k are orthogonal. Similarly, the receiver for user k correlates with sequence S_k, producing the dot-product (A S_i + B S_k) * S_k = A*B (S_i * S_k) + B ||S_k||^2 = 0 + B.

Let's modify your example to see what I mean: I'm not sure your sequence for V is orthogonal to W, so let's pick two that we know are (from the Walsh basis): S_1 = {++++++++}, S_2 = {++++----}. Let A = 1 and B = 0.3. We transmit T = A S_1 + BS_2 = {++++++++} + 0.3{++++----} = {1.3, 1.3, 1.3, 1.3, 0.7, 0.7, 0.7, 0.7}.

The receiver for V correlates by multiplying by S_1, taking the sum and dividing by the length N (N = 8), which is the same thing as the normalized dot-product of T and S_1: T * S_1 = sum({1.3, 1.3, 1.3, 1.3, 0.7, 0.7, 0.7, 0.7})/8 = (2+2+2+2)/8 = 8/8 = 1 = A.

The receiver for W correlates by multiplying by S_2, taking the sum and dividing by the length, i.e., the normalized dot-product of T and S_2: T * S_2 = sum({1.3, 1.3, 1.3, 1.3, -0.7, -0.7, -0.7, -0.7})/8 = (0.6+0.6+0.6+0.6)/8 = 0.6/2 = 0.3 = B.

So the reciever for V correctly determines that T includes A S_1, and the receiver for W determines that T includes B S_2, and they have no bearing on eachother whatsoever. In practice, |A| and |B| are random variables due to fading, while sign(A) and sign(B) are random from the modulation. The receiver only needs knowledge of the signature sequence S_i (and synchronization!) to recover A. The larger |A| is, the more reliably it can determine sign(A) in the presence of noise. Same for knowlege of S_k to determine B. The value of B has no bearing whatsoever on the recieved value of A, and vice-versa, which is the very essence of the orthogonality of S_i and S_k. —The preceding unsigned comment was added by 71.136.55.139 (talk • contribs) 09:11, 2006 May 4.

[edit] Perspective from someone who just wants the basics, not the thesis

None of this does the topic any good. Most of the information in the article is too detailed for the Wikipedia reader. Keep the super-detailed stuff to the textbooks and standards and take your political views about various cellular technologies and standards to another forum. —The preceding unsigned comment was added by 204.181.181.9 (talk • contribs) 21:03, 2006 June 28.

I agree. I was lost after 2 paragrgaphs, although im only 17 doing senior high school physics. It would be nice if you could please explain some of the jargon (if not all) that is used. Also providing a summary in simple language to give an overview for the people that dont want the specifics would be nice.

Its ok to have the detailed version aswell, but have this simple stuff in there as well.

I came here looking for "the frequency of CDMA" as pertaining in my assessment questions but could not find the answer in the article. --202.139.23.75 07:51, 26 July 2006 (UTC) Nick

[edit] A little bit of historical perspective

While many people give actress Hedy Lamar credit for having "invented" CDMA during WWII, there was no digital transmission taking place, unless you count Morse code as a digital method. During WWII the Allied forces did use a code system which would transmit dashes on one frequency, and dots on another in an attempt to fool their enemies.

My understanding is that the first military use of digital radio transmissions took place during the Cuban Missile crisis in 1962.

Hedy's patent for a frequency agile transmission scheme, designed to avoid frequency jamming on torpedoes was certainly a breakthrough concept at the time, but as far as I know, it was never put into use during WWII. 03:45, 1 July 2006 (UTC) —The preceding unsigned comment was added by 70.20.208.13 (talk • contribs) 03:45, 2006 July 1.

[edit] See "Re: comment" above

If by near-far you mean that the statement that differing signal strengths can disrupt orthogonality, I don't believe you are correct. Furthermore, I don't understand what you mean by "correlate". However, let me try and explain what is meant by using the example in the article. If we model signal fading by multiplication by a constant less than 1, suppose that v = (1,-1,-1,1,1,-1,1,-1) is transmitted by one sender V with chip code (1,-1), and w = (-1,-1,-1,-1,1,1,1,1) is sent by the other sender W with chip code (1,1). Suppose that V transmits less strongly than W, so we end up with 0.3v and w "adding up in the air" to get (-0.7, -1.3, -1.3, -0.7, 1.3, 0.7, 1.3, 0.7). Take the dot product of (-0.7, -1.3) and (1,-1) and we get 0.6 -- not 2 as expected. So something has gone wrong. If we take the dot product of (-0.7, -1.3) and (1,1), however, we get -2 as expected, so W is swamping V. This is all according according to the mathematical model. Dysprosia 07:02, 4 May 2006 (UTC)

It dosen't matter what get's transmitted, it matters what the receiver is able to understand from the message. The receiver works by a process called correlation, which is the same as the dot-product for any orthogonal basis. Simply put, if user i has sequence S_i, and user k has sequence S_k, the receiver for user i(after synchronizing to know where the symbols start, which is not trivial) mutiplies each symbol by S_i, and takes the sum. If it is positive, decide 1. if negative, decide -1. So if you transmit (A S_i + B S_k), with A and B arbitrary constants, the receiver computes the correlation which is the dot-product (A S_i + B S_k) * S_i = A ||S_i||^2 + A*B (S_i * S_k). From the dot-product properties in the article, this gives you A + 0 since S_i and S_k are orthogonal. Similarly, the receiver for user k correlates with sequence S_k, producing the dot-product (A S_i + B S_k) * S_k = A*B (S_i * S_k) + B ||S_k||^2 = 0 + B.

Let's modify your example to see what I mean: I'm not sure your sequence for V is orthogonal to W, so let's pick two that we know are (from the Walsh basis): S_1 = {++++++++}, S_2 = {++++----}. Let A = 1 and B = 0.3. We transmit T = A S_1 + BS_2 = {++++++++} + 0.3{++++----} = {1.3, 1.3, 1.3, 1.3, 0.7, 0.7, 0.7, 0.7}.

The receiver for V correlates by multiplying by S_1, taking the sum and dividing by the length N (N = 8), which is the same thing as the normalized dot-product of T and S_1: T * S_1 = sum({1.3, 1.3, 1.3, 1.3, 0.7, 0.7, 0.7, 0.7})/8 = (2+2+2+2)/8 = 8/8 = 1 = A.

The receiver for W correlates by multiplying by S_2, taking the sum and dividing by the length, i.e., the normalized dot-product of T and S_2: T * S_2 = sum({1.3, 1.3, 1.3, 1.3, -0.7, -0.7, -0.7, -0.7})/8 = (0.6+0.6+0.6+0.6)/8 = 0.6/2 = 0.3 = B.

So the reciever for V correctly determines that T includes A S_1, and the receive" what the hell is this, i didn't come here to learn what "correlates", either simplifiy it or i will, manually. by cutting up this article. —The preceding unsigned comment was added by 71.160.54.34 (talk • contribs) 22:56, 2006 July 14.

[edit] why no sims?

Can someone with some knowledge on this subject explain why SIM cards arent used on CDMA phones? thanks 12.170.1.226 16:10, 10 August 2006 (UTC)LUID

Please its kind of confusing. Can anyone please explain this line to me how did he get the transmitted vector if v=(1,-1), then the binary vector (1, 0, 1, 1) would correspond to (1,-1,-1,1,1,-1,1,-1) —The preceding unsigned comment was added by HassanHaider (talk • contribs) 17:31, 2006 August 19.

[edit] Copy editing to improve clarity

After reading the article I could see why it had the "needs more clarity" tag on it. The greatest source of confusion seemed to be that it said 'CDMA' in many places where it actually meant 'CDM' (that is, Synchronous code division using Walsh vectors). What seemed to be needed was a better distinction between the 'CDM' Synchronous technique using Walsh vectors, and the 'CDMA' Asynchronous technique using pseudo-noise sequences as the vectors.

I also made some minor edits to header size and added a couple headers to mark the start of the Asynchronous discussion and the comparison of Asynchronous against the other techniques.

Still not 'perfect' but hopefully better. Randy549 05:18, 17 September 2006 (UTC)

[edit] Use of talk pages

The discussion above is hard to follow since many editors have not signed their comments using 4 tildes, ~~~~, at the end of their contributions. Also, please separate your comments from previous ones by indenting using ":", not tab or space or ---, at the beginning of each paragraph. Please see WP:TALK for more on using talk pages. Walter Siegmund (talk) 21:17, 9 July 2006 (UTC)

[edit] What?

I came here to learn what CDMA is, I read the whole page, and I still have no idea. I'm a fairly smart person but not a rocket scientist.--> —The preceding unsigned comment was added by 4.228.180.173 (talk • contribs) 08:07, 4 December 2006 (UTC).

[edit] (See also the Market situation section of GSM.)

The word Market doesn't appear in this article Global_System_for_Mobile_Communications. This article should list which cell phone operators use CDMA technology Mathiastck 23:08, 5 December 2006 (UTC)