Code division multiple access (CDMA) is a channel access method utilized by various radio communication technologies. It should not be confused with cdmaOne (often referred to as simply "CDMA"), which is a mobile phone standard that uses CDMA as its underlying channel access method.
CDMA employs spread-spectrum technology and a special coding scheme (where each transmitter is assigned a code) to allow multiple users to be multiplexed over the same physical channel. By contrast, time division multiple access (TDMA) divides access by time, while frequency-division multiple access (FDMA) divides it by frequency. CDMA is a form of "spread-spectrum" signaling, since the modulated coded signal has a much higher bandwidth than the data being communicated.
An analogy to the problem of multiple access is a room (channel) in which people wish to communicate with each other. To avoid confusion, people could take turns speaking (time division), speak at different pitches (frequency division), or speak in different directions (spatial division). In CDMA, they would speak different languages. People speaking the same language can understand each other, but not other people. Similarly, in radio CDMA, each group of users is given a shared code. Many codes occupy the same channel, but only users associated with a particular code can understand each other.
CDMA has been used in many communications and navigation systems, including the Global Positioning System and the OmniTRACS satellite system for transportation logistics.
Code Division Multiplexing (Synchronous CDMA)
Synchronous CDMA exploits mathematical properties of orthogonality between vectors representing the data strings. For example, binary string "1011" is represented by the vector (1, 0, 1, 1). Vectors can be multiplied by taking their dot product, by summing the products of their respective components. If the dot product is zero, the two vectors are said to be orthogonal to each other. Some properties of the dot product help to understand how WCDMA works. If vectors a and b are orthogonal, then
Example
Start with a set of vectors that are mutually orthogonal. (Although mutual orthogonality is the only condition, these vectors are usually constructed for ease of decoding, for example columns or rows from Walsh matrices.) An example of orthogonal functions is shown in the picture on the left.
An example of four mutually orthogonal digital signals.Now, associate with one sender a vector from this set, say v, which is called the "code", "chipping code" or "chip code". Associate a zero digit with the vector –v, and a one digit with the vector v. For example, if v=(1,–1), then the binary vector (1, 0, 1, 1) would correspond to (v, –v, v, v) which is then constructed in binary as ((1,–1),(–1,1),(1,–1),(1,–1)). For the purposes of this article, we call this constructed vector the transmitted vector.
Each sender has a different, unique vector v chosen from that set, but the construction method of the transmitted vector is identical.
Now, due to physical properties of interference, if two signals at a point are in phase, they add to give twice the amplitude of each signal, but if they are out of phase, they "subtract" and give a signal that is the difference of the amplitudes. Digitally, this behaviour can be modelled by the addition of the transmission vectors, component by component.
If sender0 has code (1,–1) and data (1,0,1,1), and sender1 has code (1,1) and data (0,0,1,1), and both senders transmit simultaneously, then this table describes the coding steps:
Step Encode sender0 Encode sender1
0 vector0=(1,–1), data0=(1,0,1,1)=(1,–1,1,1) vector1=(1,1), data1=(0,0,1,1)=(–1,–1,1,1)
1 encode0=vector0.data0 encode1=vector1.data1
2 encode0=(1,–1).(1,–1,1,1) encode1=(1,1).(–1,–1,1,1)
3 encode0=((1,–1),(–1,1),(1,–1),(1,–1)) encode1=((–1,–1),(–1,–1),(1,1),(1,1))
4 signal0=(1,–1,–1,1,1,–1,1,–1) signal1=(–1,–1,–1,–1,1,1,1,1)
Because signal0 and signal1 are transmitted at the same time into the air, they add to produce the raw signal:
(1,–1,–1,1,1,–1,1,–1) + (–1,–1,–1,–1,1,1,1,1) = (0,–2,–2,0,2,0,2,0)
This raw signal is called an interference pattern. The receiver then extracts an intelligible signal for any known sender by combining the sender's code with the interference pattern, the receiver combines it with the codes of the senders. The following table explains how this works.
Step Decode sender0 Decode sender1
0 vector0=(1,–1), pattern=(0,–2,–2,0,2,0,2,0) vector1=(1,1), pattern=(0,–2,–2,0,2,0,2,0)
1 decode0=pattern.vector0 decode1=pattern.vector1
2 decode0=((0,–2),(–2,0),(2,0),(2,0)).(1,–1) decode1=((0,–2),(–2,0),(2,0),(2,0)).(1,1)
3 decode0=((0+2),(–2+0),(2+0),(2+0)) decode1=((0–2),(–2+0),(2+0),(2+0))
4 data0=(2,–2,2,2)=(1,0,1,1) data1=(–2,–2,2,2)=(0,0,1,1)
Further, after decoding, all values greater than 0 are interpreted as 1 while all values less than zero are interpreted as 0. For example, after decoding, data0 is (2,–2,2,2), but the receiver interprets this as (1,0,1,1).
Asynchronous CDMA
See also: Direct-sequence spread spectrum
The previous example of orthogonal Walsh sequences describes how 2 users can be multiplexed together in a synchronous system, a technique that is commonly referred to as Code Division Multiplexing (CDM). The set of 4 Walsh sequences shown in the figure will afford up to 4 users, and in general, an NxN Walsh matrix can be used to multiplex N users. Multiplexing requires all of the users to be coordinated so that each transmits their assigned sequence v (or the complement, -v) starting at exactly the same time. Thus, this technique finds use in base-to-mobile links, where all of the transmissions originate from the same transmitter and can be perfectly coordinated.
On the other hand, the mobile-to-base links cannot be precisely coordinated, particularly due to the mobility of the handsets, and require a somewhat different approach. Since it is not mathematically possible to create signature sequences that are orthogonal for arbitrarily random starting points, unique "pseudo-random" or "pseudo-noise" (PN) sequences are used in Asynchronous CDMA systems. These PN sequences are statistically uncorrelated, and the sum of a large number of PN sequences results in Multiple Access Interference (MAI) that is approximated by a Gaussian noise process (following the "central limit theorem" in statistics). If all of the users are received with the same power level, then the variance (e.g., the noise power) of the MAI increases in direct proportion to the number of users.
All forms of CDMA use spread spectrum process gain to allow receivers to partially discriminate against unwanted signals. Signals encoded with the specified PN sequence (code) are received, while signals with different codes (or the same code but a different timing offset) appear as wideband noise reduced by the process gain.
Since each user generates MAI, controlling the signal strength is an important issue with CDMA transmitters. A CDM (Synchronous CDMA), TDMA or FDMA receiver can in theory completely reject arbitrarily strong signals using different codes, time slots or frequency channels due to the orthogonality of these systems. This is not true for Asynchronous CDMA; rejection of unwanted signals is only partial. If any or all of the unwanted signals are much stronger than the desired signal, they will overwhelm it. This leads to a general requirement in any Asynchronous CDMA system to approximately match the various signal power levels as seen at the receiver. In CDMA cellular, the base station uses a fast closed-loop power control scheme to tightly control each mobile's transmit power.
Advantages of Asynchronous CDMA over other techniques
Asynchronous CDMA's main advantage over CDM (Synchronous CDMA), TDMA and FDMA is that it can use the spectrum more efficiently in mobile telephony applications. (In theory, CDMA, TDMA and FDMA have exactly the same spectral efficiency but practically, each has its own challenges - timing in the case of TDMA, and power control in the case of CDMA and frequency generation/filtering in the case of FDMA.). TDMA systems must carefully synchronize the transmission times of all the users to ensure that they are received in the correct timeslot and do not cause interference. Since this cannot be perfectly controlled in a mobile environment, each timeslot must have a guard-time, which reduces the probability that users will interfere, but decreases the spectral efficiency. Similarly, FDMA systems must use a guard-band between adjacent channels, due to the random doppler shift of the signal spectrum which occurs due to the user's mobility. The guard-bands will reduce the probability that adjacent channels will interfere, but decrease the utilization of the spectrum.
Most importantly, Asynchronous CDMA offers a key advantage in the flexible allocation of resources. There are a fixed number of orthogonal codes, timeslots or frequency bands that can be allocated for CDM, TDMA and FDMA systems, which remain underutilized due to the bursty nature of telephony and packetized data transmissions. There is no strict limit to the number of users that can be supported in an Asynchronous CDMA system, only a practical limit governed by the desired bit error probability, since the SIR (Signal to Interference Ratio) varies inversely with the number of users. In a bursty traffic environment like mobile telephony, the advantage afforded by Asynchronous CDMA is that the performance (bit error rate) is allowed to fluctuate randomly, with an average value determined by the number of users times the percentage of utilization. Suppose there are 2N users t