Code division multiple access

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Code division multiple access (CDMA) is a form of multiplexing (not a modulation scheme) and a method of multiple access that does not divide up the channel by time (as in TDMA), or frequency (as in FDMA), but instead encodes data with a special code associated with each channel and uses the constructive interference properties of the special codes to perform the multiplexing. CDMA also refers to digital cellular telephony systems that make use of this multiple access scheme, such as those pioneered by Qualcomm, and W-CDMA by the International Telecommunication Union or ITU.

CDMA has since been used in many communications systems, including the Global Positioning System (GPS) and in the OmniTRACS satellite system for transportation logistics.

Contents

[edit] Usage in mobile telephony

A number of different terms are used to refer to CDMA implementations. The original U.S. standard defined by QUALCOMM was known as IS-95, the IS referring to an Interim Standard of the Telecommunications Industry Association (TIA). IS-95 is often referred to as 2G or second generation cellular. The QUALCOMM brand name cdmaOne may also be used to refer to the 2G CDMA standard. The CDMA has been submitted for approval as a mobile air interface standard to the ITU International Telecommunication Union.

Whereas the Global System for Mobile Communications (GSM) standard is a specification of an entire network infrastructure, the CDMA interface relates only to the air interface—the radio part of the technology. For example GSM specifies an infrastructure based on internationally approved standard while CDMA allows each operator to provide the network features as it finds suited. On the air interface, the signalling suite (GSM: ISDN SS7) work has been progressing to harmonise these.

After a couple of revisions, IS-95 was superseded by the IS-2000 standard. This standard was introduced to meet some of the criteria laid out in the IMT-2000 specification for 3G, or third generation, cellular. It is also referred to as 1xRTT which simply means "1 times Radio Transmission Technology" and indicates that IS-2000 uses the same 1.25 MHz shared channel as the original IS-95 standard. A related scheme called 3xRTT uses three 1.25 MHz carriers for a 3.75 MHz bandwidth that would allow higher data burst rates for an individual user, but the 3xRTT scheme has not been commercially deployed. More recently, QUALCOMM has led the creation of a new CDMA-based technology called 1xEV-DO, or IS-856, which provides the higher packet data transmission rates required by IMT-2000 and desired by wireless network operators.

The QUALCOMM CDMA system includes highly accurate time signals (usually referenced to a GPS receiver in the cell base station), so cell phone CDMA-based clocks are an increasingly popular type of radio clock for use in computer networks. The main advantage of using CDMA cell phone signals for reference clock purposes is that they work better inside buildings, thus often eliminating the need to mount a GPS antenna on the outside of a building.

This CDMA system is frequently confused with a similar but incompatible technology called Wideband Code Division Multiple Access (W-CDMA) which forms the basis of the W-CDMA air interface. The W-CDMA air interface is used in the global 3G standard UMTS and the Japanese 3G standard FOMA, by NTT DoCoMo and Vodafone; however, the CDMA family of US national standards (including cdmaOne and CDMA2000) are not compatible with the W-CDMA family of International Telecommunication Union (ITU) standards.

Another important application of CDMA — predating and entirely distinct from CDMA cellular — is the Global Positioning System, GPS.

[edit] Coverage and Applications

The size of a given cell depends on the power of the signal transmitted by the handset, the terrain, and the radio frequency being used. Various algorithms can reduce the noise introduced by variations in terrain, but require extra information be sent to validate the transfer. Hence, the radio frequency and power of the handset effectively determine the cell size. Long wavelengths need less energy to travel a given distance vs. short wavelengths, so lower frequencies generally result in greater coverage while higher frequencies result in shorter coverage. These characteristics are used by mobile network planners in determining the size and placement of the cells in the network. In cities, many small cells are needed; the use of high frequencies allows sites to be placed more-closely together, with more subscribers provided service. In rural areas with a lower density of subscribers, use of lower frequencies allows each site to provide broader coverage. (See also the Market situation section of GSM.)

Various companies use different variants of CDMA to provide fixed-line networks using Wireless local loop (WLL) technology. Since they can plan with a specific number of subscribers per cell in mind, and these are all stationary, this application of CDMA can be found in most parts of the world.

CDMA is suited for data transfer with bursty behaviour and where delays can be accepted. It is therefore used in Wireless LAN applications; the cell size here is 500 feet because of the high frequency (2.4 GHz) and low power. The suitability for data transfer is the reason for why W-CDMA seems to be "winning technology" for the data portion of third-generation (3G) mobile cellular networks.

[edit] Technical details

[edit] Code Division Multiplexing (Synchronous CDMA)

Synchronous CDMA, also known as Code Division Multiplexing (CDM), exploits at its core mathematical properties of orthogonality. Suppose we represent data signals as vectors. For example, the binary string "1011" would be represented by the vector (1, 0, 1, 1). We may wish to give a vector a name, we may do so by using boldface letters, e.g. a. We also use an operation on vectors, known as the dot product, to "multiply" vectors, by summing the product of the components. The operation is denoted with a dot between the vectors. For example, the dot product of \mathbf a=(1, 0, 1, 1) and \mathbf b=(1, -1, -1, 0), written as \mathbf a\cdot \mathbf b, would be (1)\times(1)+(0)\times(-1)+(1)\times(-1)+(1)\times(0)=1+(-1)=0. For the special case when the dot product of two vectors is identically 0, the two vectors are said to be orthogonal to each other.

The dot product has a number of properties, which will aid in understanding how CDM works. For vectors a, b, c:

\mathbf{a}\cdot(\mathbf{b}+\mathbf{c})=\mathbf{a}\cdot\mathbf{b}+\mathbf{a}\cdot\mathbf{c},\quad\mathrm{and}
\mathbf{a}\cdot k\mathbf{b}=k(\mathbf{a}\cdot\mathbf{b})., where k is an arbitrary constant, and not a vector

The square root of \mathbf a\cdot\mathbf a is a real number, and is called the magnitude of the vector \mathbf a. It is denoted as

||\mathbf{a}||=\sqrt{\mathbf{a}\cdot\mathbf{a}}.

Suppose vectors a and b are orthogonal. Then:

\mathbf{a}\cdot(\mathbf{a}+\mathbf{b})=||\mathbf{a}||^2\quad\mathrm{since}\quad\mathbf{a}\cdot\mathbf{a}+\mathbf{a}\cdot\mathbf{b}= ||a||^2+0,
\mathbf{a}\cdot(-\mathbf{a}+\mathbf{b})=-||\mathbf{a}||^2\quad\mathrm{since}\quad-\mathbf{a}\cdot\mathbf{a}+\mathbf{a}\cdot\mathbf{b}= -||a||^2+0,
\mathbf{b}\cdot(\mathbf{a}+\mathbf{b})=||\mathbf{b}||^2\quad\mathrm{since}\quad\mathbf{b}\cdot\mathbf{a}+\mathbf{b}\cdot\mathbf{b}= 0+||b||^2,
\mathbf{b}\cdot(\mathbf{a}-\mathbf{b})=-||\mathbf{b}||^2\quad\mathrm{since}\quad\mathbf{b}\cdot\mathbf{a}-\mathbf{b}\cdot\mathbf{b}=0 -||b||^2.

[edit] Example

An example of 4 orthogonal digital signals.
Enlarge
An example of 4 orthogonal digital signals.

Suppose we have a set of vectors that are mutually orthogonal (though mutual orthogonality is mathematically speaking the only constraint, these vectors are usually constructed for ease of decoding — columns or rows from Walsh matrices constructed from Walsh functions). An example of orthogonal functions is shown in the picture on the right. Now, associate with one sender a vector from this set, say v, which is called the 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 ((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 chosen from that set, but the construction of the transmitted vector is identical.

Now, the physical properties of interference say that if two signals at a point are in phase, they will "add up" to give twice the amplitude of each signal, but if they are out of phase, they will "subtract" and give a signal that is the difference of the amplitudes. Digitally, this behaviour can be modelled simply by the addition of the transmission vectors, component by component. So, if we have two senders, both sending simultaneously, one with the chip code (1, -1) and data vector (1, 0, 1, 1), and another with the chip code (1, 1), and data vector (0,0,1,1), the raw signal received would be the sum of the transmission vectors (1,-1,-1,1,1,-1,1,-1)+(-1,-1,-1,-1,1,1,1,1)=(0,-2,-2,0,2,0,2,0).

Suppose a receiver gets such a signal, and wants to detect what the transmitter with chip code (1, -1) is sending. The receiver will make use of the property described in the above foundation section, and take the dot product to the received vector in parts. Take the first two components of the received vector, that is, (0, -2). Now, (0, -2).(1, -1) = (0)(1)+(-2)(-1) = 2. Since this is positive, we can deduce that a one digit was sent. Taking the next two components, (-2, 0), (-2, 0).(1,-1)=(-2)(1)+(0)(-1)=-2. Since this is negative, we can deduce that a zero digit was sent. Continuing in this fashion, we can successfully decode what the transmitter with chip code (1, -1) was sending: (1, 0, 1, 1).

Likewise, applying the same process with chip code (1, 1): (1, 1).(0,-2) = -2 gives digit 0, (1, 1).(-2,0)=(1)(-2)+(1)(0)=-2 gives digit 0, and so on, to give us the data vector sent by the transmitter with chip code (1, 1): (0, 0, 1, 1).

[edit] Asynchronous CDMA

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 (via the theorem of the "law of large numbers" 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 with the desired chip code and timing are received, while signals with different chip codes (or the same spreading 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.

[edit] 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. 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 that only talk half of the time, then 2N 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 2N 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 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 2N 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 timeslots. 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 don't, keeping the same PN signature sequence as long as they are connected to the system.

[edit] Soft handoff

Soft handoff (or soft handover) is an innovation in mobility. It refers to the technique of adding additional base stations (in IS-95 as many as 5) to a connection to be certain that the next base is ready as you move through the terrain. However, it can also be used to move a call from one base station that is approaching congestion to another with better capacity. As a result, signal quality and handoff robustness is improved compared to TDMA systems.

In TDMA and analog systems, each cell transmits on its own frequency, different from those of its neighbouring cells. If a mobile device reaches the edge of the cell currently serving its call, it is told to break its radio link and quickly tune to the frequency of one of the neighbouring cells where the call has been moved by the network due to the mobile's movement. If the mobile is unable to tune to the new frequency in time the call is dropped.

In CDMA, a set of neighbouring cells all use the same frequency for transmission and distinguish cells (or base stations) by means of a number called the "PN offset", a time offset from the beginning of the well-known pseudo-random noise sequence that is used to spread the signal from the base station. Because all of the cells are on the same frequency, listening to different base stations is now an exercise in digital signal processing based on offsets from the PN sequence, not RF transmission and reception based on separate frequencies.

As the CDMA phone roams through the network, it detects the PN offsets of the neighbouring cells and reports the strength of each signal back to the reference cell of the call (usually the strongest cell). If the signal from a neighbouring cell is strong enough, the mobile will be directed to "add a leg" to its call and start transmitting and receiving to and from the new cell in addition to the cell (or cells) already hosting the call. Likewise, if a cell's signal becomes too weak the mobile is directed to drop that leg. In this way, the mobile can move from cell to cell and add and drop legs as necessary in order to keep the call up without ever dropping the link.

It should be noted that this "soft handoff" does not happen via CDMA from cell tower to cell tower. A group of cell sites are linked up with wire and the call is synced over wire, over TDM, ATM, or even IP.

When there are frequency boundaries between different carriers or sub-networks, a CDMA phone behaves in the same way as TDMA or analog and performs a hard handoff in which it breaks the existing connection and tries to pick up on the new frequency where it left off.

[edit] CDMA features

  • Narrowband message signal multiplied by wideband spreading signal or pseudonoise code
  • Each user has his own pseudonoise (PN) code
  • Soft capacity limit: system performance degrades for all users as number of users increases
  • Cell frequency reuse: no frequency planning needed
  • Soft handoff increases capacity
  • Near-far problem
  • Interference limited: power control is required
  • Wide bandwidth induces diversity: rake receiver is used
  • Extended battery life because of effective power control.

[edit] Optical CDMA

  • Recently, CDMA has been also investigated to be employed in optical communication networks, especially in local access network (LAN). Current optical CDMA (O-CDMA) technques fall into two categories, coherent and inchoerent O-CDMA. In incoherent O-CDMA, unipolar codes (0, 1) are used to modulate the power of optical signals. In coherent O-CDMA, bipolar (-1, 1) or multilevel codes are used to modulate the field of optical signals.

[edit] See also

[edit] External links

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