CDMA is a spread spectrum technology used in 2G and 3G communication systems. It is used in ultra-high frequency (UHF) cellular telephone systems in the 800 MHz and 1.9 GHz bands. It is a multiplexing technique that allows several signals to share a transmission channel – optimizes the use of available bandwidth. Transmissions from different stations occupy the entire frequency band at the same time.
Different codes are used to produce the transmitted signals and to distinguish them. The code used by one station is orthogonal to the codes used by other stations. Two vectors are orthogonal if their inner product is 0. Example: Let’s say we have two vectors: (1, 2, 3) and (2, 2, -2). The product of the two vectors is (1, 2, 3) * (2, 2, -2) = 2 + 4 + (-6) = 0. Therefore, they're orthogonal to each other.
A spread spectrum technique spreads the bandwidth needed to transmit data. Assume that user data is generated at R bps. Each station is assigned a unique binary pseudorandom sequence, also known as the chip values. Each bit of user data is transformed into G bits by multiplying the user bit value by G chip values. The result is a sequence that appears to be random.
The spreading factor G is selected so that the transmitted signal occupies the entire frequency band of the medium. A chip is one bit of a direct sequence spread spectrum code. A chip rate of a code is the number of bits per second (chips per second) at which the code is transmitted/received. The sequence G chip values are (c1, c2, c3,… cG), where ci takes a value of either +1 or -1. The -1 symbol represents bit 0 while +1 represents bit 1.
When a station wants to transmit -1, it multiplies the -1 value by the sequence of G chip values. The resulting value is the signal transmitted to the receiver. When the signal arrives at the receiver, it is multiplied by G again and the resulting products are added. If the signal is received correctly, the resulting output correlator is either +G or -G.
Let’s say station A and station B use spreading sequences that are orthogonal to each other. Assume that G = 4 and the spreading sequence of stations A and B are (+1, -1, -1, +1) and (+1, -1, +1, -1), respectively.
Let’s say station A wants to transmit -1 (bit 0). It multiplies the symbol it wants to transmit by its spreading sequence, -1 * (+1, -1, -1, +1) = (-1, +1, +1, -1). The resulting symbol is transmitted to the receiver.
When the receiver receives the signal, it calculates the product of the signal it receives with station A’s spreading sequence. (-1, +1, +1, -1) * (+1, -1, -1, +1) = (-1, -1, -1, -1) = -4 = -G. The result of the calculation, i.e. -G, tells the receiver that it has decoded the signal correctly and that the received symbol is -1 (bit 0).
If station A transmits +1, the result of the calculation should yield +4 = +G, which tells the receiver that the transmitted value is +1 (bit 1).
If station B receives the signal and tries the decode it using its spreading sequence, the result is (-1, +1, +1, -1) * (+1, -1, +1, -1) = -1 -1 +1 +1 = 0. Station B is unable to determine whether the received symbol is +1 or -1.
Only a transmitter and receivers with knowledge of the correct spreading sequence would be able to decode a received signal correctly.
Related links
No comments:
Post a Comment