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orthogonal frequency-division multiplexing In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a type of digital transmission and a method of encoding digital data on multiple carrier frequencies. OFDM has developed into a popular scheme for wideband digital co ...
(OFDM), which typically makes it very robust and efficient (and equipping them with accurate ranging capabilities, which is difficult without CDMA). Other schemes use subcarriers based on binary offset carrier modulation (BOC modulation), which is inspired by Manchester codes and enable a larger gap between the virtual center frequency and the subcarriers, which is not the case for OFDM subcarriers. Many carriers (such as AT&T and Verizon) will shut down 3G CDMA networks in 2022.

# History

The technology of code-division multiple access channels has long been known.

## USA

In the US, one of the earliest descriptions of CDMA can be found in the summary report of Project Hartwell on "The Security of Overseas Transport", which was a summer research project carried out at the
Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private Land-grant university, land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern t ...
from June to August 1950. Further research in the context of jamming and anti-jamming was carried out in 1952 at Lincoln Lab.

## USSR

In the
Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nati ...
(USSR), the first work devoted to this subject was published in 1935 by Dmitry Ageev. It was shown that through the use of linear methods, there are three types of signal separation: frequency, time and compensatory. The technology of CDMA was used in 1957, when the young military radio engineer Leonid Kupriyanovich in Moscow made an experimental model of a wearable automatic mobile phone, called LK-1 by him, with a base station. LK-1 has a weight of 3 kg, 20–30 km operating distance, and 20–30 hours of battery life. The base station, as described by the author, could serve several customers. In 1958, Kupriyanovich made the new experimental "pocket" model of mobile phone. This phone weighed 0.5 kg. To serve more customers, Kupriyanovich proposed the device, which he called "correlator." In 1958, the USSR also started the development of the " Altai" national civil mobile phone service for cars, based on the Soviet MRT-1327 standard. The phone system weighed . It was placed in the trunk of the vehicles of high-ranking officials and used a standard handset in the passenger compartment. The main developers of the Altai system were VNIIS (Voronezh Science Research Institute of Communications) and GSPI (State Specialized Project Institute). In 1963 this service started in Moscow, and in 1970 Altai service was used in 30 USSR cities.

# Uses

* Synchronous CDM (code-division 'multiplexing', an early generation of CDMA) was implemented in the Global Positioning System (GPS). This predates and is distinct from its use in
mobile phone A mobile phone, cellular phone, cell phone, cellphone, handphone, hand phone or pocket phone, sometimes shortened to simply mobile, cell, or just phone, is a portable telephone that can make and receive calls over a radio frequency link wh ...
s. * The Qualcomm standard IS-95, marketed as cdmaOne. * The Qualcomm standard IS-2000, known as CDMA2000, is used by several mobile phone companies, including the Globalstar network. * The UMTS 3G mobile phone standard, which uses W-CDMA. * CDMA has been used in the OmniTRACS satellite system for transportation logistics.

# Steps in CDMA modulation

CDMA is a spread-spectrum multiple-access technique. A spread-spectrum technique spreads the bandwidth of the data uniformly for the same transmitted power. A spreading code is a pseudo-random code that has a narrow ambiguity function, unlike other narrow pulse codes. In CDMA a locally generated code runs at a much higher rate than the data to be transmitted. Data for transmission is combined by bitwise XOR (exclusive OR) with the faster code. The figure shows how a spread-spectrum signal is generated. The data signal with pulse duration of $T_b$ (symbol period) is XORed with the code signal with pulse duration of $T_c$ (chip period). (Note: bandwidth is proportional to $1/T$, where $T$ = bit time.) Therefore, the bandwidth of the data signal is $1/T_b$ and the bandwidth of the spread spectrum signal is $1/T_c$. Since $T_c$ is much smaller than $T_b$, the bandwidth of the spread-spectrum signal is much larger than the bandwidth of the original signal. The ratio $T_b/T_c$ is called the spreading factor or processing gain and determines to a certain extent the upper limit of the total number of users supported simultaneously by a base station. Each user in a CDMA system uses a different code to modulate their signal. Choosing the codes used to modulate the signal is very important in the performance of CDMA systems. The best performance occurs when there is good separation between the signal of a desired user and the signals of other users. The separation of the signals is made by correlating the received signal with the locally generated code of the desired user. If the signal matches the desired user's code, then the correlation function will be high and the system can extract that signal. If the desired user's code has nothing in common with the signal, the correlation should be as close to zero as possible (thus eliminating the signal); this is referred to as cross-correlation. If the code is correlated with the signal at any time offset other than zero, the correlation should be as close to zero as possible. This is referred to as auto-correlation and is used to reject multi-path interference. An analogy to the problem of multiple access is a room (channel) in which people wish to talk to each other simultaneously. To avoid confusion, people could take turns speaking (time division), speak at different pitches (frequency division), or speak in different languages (code division). CDMA is analogous to the last example where people speaking the same language can understand each other, but other languages are perceived as noise and rejected. 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 communicate. In general, CDMA belongs to two basic categories: synchronous (orthogonal codes) and asynchronous (pseudorandom codes).

# Code-division multiplexing (synchronous CDMA)

The digital modulation method is analogous to those used in simple radio transceivers. In the analog case, a low-frequency data signal is time-multiplied with a high-frequency pure sine-wave carrier and transmitted. This is effectively a frequency convolution ( Wiener–Khinchin theorem) of the two signals, resulting in a carrier with narrow sidebands. In the digital case, the sinusoidal carrier is replaced by Walsh functions. These are binary square waves that form a complete orthonormal set. The data signal is also binary and the time multiplication is achieved with a simple XOR function. This is usually a Gilbert cell mixer in the circuitry. Synchronous CDMA exploits mathematical properties of orthogonality between vectors representing the data strings. For example, the 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 (for example, if u = (''a'', ''b'') and v = (''c'', ''d''), then their dot product u·v = ''ac'' + ''bd''). If the dot product is zero, the two vectors are said to be ''orthogonal'' to each other. Some properties of the dot product aid understanding of how W-CDMA works. If vectors a and b are orthogonal, then $\mathbf\cdot\mathbf = 0$ and: :$\mathbf\cdot\left(\mathbf + \mathbf\right) = \, \mathbf\, ^2,\ \text\ \mathbf\cdot\mathbf + \mathbf\cdot\mathbf = \, \mathbf\, ^2 + 0,$ :$\mathbf\cdot\left(-\mathbf + \mathbf\right) = -\, \mathbf\, ^2,\ \text\ \cdot\mathbf + \mathbf\cdot\mathbf = -\, \mathbf\, ^2 + 0,$ :$\mathbf\cdot\left(\mathbf + \mathbf\right) = \, \mathbf\, ^2,\ \text\ \mathbf\cdot\mathbf + \mathbf\cdot\mathbf = 0 + \, \mathbf\, ^2,$ :$\mathbf\cdot\left(\mathbf - \mathbf\right) = -\, \mathbf\, ^2,\ \text\ \mathbf\cdot\mathbf - \mathbf\cdot\mathbf = 0 - \, \mathbf\, ^2.$ Each user in synchronous CDMA uses a code orthogonal to the others' codes to modulate their signal. An example of 4 mutually orthogonal digital signals is shown in the figure below. Orthogonal codes have a cross-correlation equal to zero; in other words, they do not interfere with each other. In the case of IS-95, 64-bit Walsh codes are used to encode the signal to separate different users. Since each of the 64 Walsh codes is orthogonal to all other, the signals are channelized into 64 orthogonal signals. The following example demonstrates how each user's signal can be encoded and decoded.

## Example

orthogonal In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in ...
. (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 adjacent picture. These vectors will be assigned to individual users and are called the ''code'', '' chip code'', or ''chipping code''. In the interest of brevity, the rest of this example uses codes v with only two bits. Each user is associated with a different code, say v. A 1 bit is represented by transmitting a positive code v, and a 0 bit is represented by a negative code −v. For example, if v = (''v''0, ''v''1) = (1, −1) and the data that the user wishes to transmit is (1, 0, 1, 1), then the transmitted symbols would be :(v, −v, v, v) = (''v''0, ''v''1, −''v''0, −''v''1, ''v''0, ''v''1, ''v''0, ''v''1) = (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: 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 following table explains how this works and shows that the signals do not interfere with one another: 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). Values of exactly 0 mean that the sender did not transmit any data, as in the following example: Assume signal0 = (1, −1, −1, 1, 1, −1, 1, −1) is transmitted alone. The following table shows the decode at the receiver: When the receiver attempts to decode the signal using sender1's code, the data is all zeros; therefore the cross-correlation is equal to zero and it is clear that sender1 did not transmit any data.

# Asynchronous CDMA

## Advantages of asynchronous CDMA over other techniques

### Efficient practical utilization of the fixed frequency spectrum

In theory CDMA, TDMA and FDMA have exactly the same spectral efficiency, but, in practice, each has its own challenges – power control in the case of CDMA, timing in the case of TDMA, 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 time slot and do not cause interference. Since this cannot be perfectly controlled in a mobile environment, each time slot 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 unpredictable Doppler shift of the signal spectrum because of user mobility. The guard bands will reduce the probability that adjacent channels will interfere, but decrease the utilization of the spectrum.

### Flexible allocation of resources

Asynchronous CDMA offers a key advantage in the flexible allocation of resources i.e. allocation of spreading sequences to active users. In the case of CDM (synchronous CDMA), TDMA, and FDMA the number of simultaneous orthogonal codes, time slots, and frequency slots respectively are fixed, hence the capacity in terms of the number of simultaneous users is limited. There are a fixed number of orthogonal codes, time slots 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 2''N'' users that only talk half of the time, then 2''N'' users can be accommodated with the same ''average'' bit error probability as ''N'' users that talk all of the time. The key difference here is that the bit error probability for ''N'' users talking all of the time is constant, whereas it is a ''random'' quantity (with the same mean) for 2''N'' users talking half of the time. In other words, asynchronous CDMA is ideally suited to a mobile network where large numbers of transmitters each generate a relatively small amount of traffic at irregular intervals. CDM (synchronous CDMA), TDMA, and FDMA systems cannot recover the underutilized resources inherent to bursty traffic due to the fixed number of
orthogonal In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in ...
codes, time slots or frequency channels that can be assigned to individual transmitters. For instance, if there are ''N'' time slots in a TDMA system and 2''N'' users that talk half of the time, then half of the time there will be more than ''N'' users needing to use more than ''N'' time slots. Furthermore, it would require significant overhead to continually allocate and deallocate the orthogonal-code, time-slot or frequency-channel resources. By comparison, asynchronous CDMA transmitters simply send when they have something to say and go off the air when they do not, keeping the same signature sequence as long as they are connected to the system.

# Collaborative CDMA

* CDMA spectral efficiency * CDMA2000 * Comparison of mobile phone standards * cdmaOne * Orthogonal variable spreading factor (OVSF), an implementation of CDMA * Pseudo-random noise * Quadrature-division multiple access (QDMA), an implementation of CDMA * Rise over thermal * Spread spectrum * W-CDMA