Code of the Mobile maker
The CDMA service used in 3G mobile phones will end this year in both Japan and the US. The method called W-CDMA will also end in 2026 (Docomo) and 2024 (Softbank). The CDMA system (called IS-95), which was first introduced in 2G, was mainly used in the United States. CDMA technology was researched in the 1950s, but it was used as a military technology, so until the 1980s, it was rarely used by civilians. Part of this is the evolution of digital technology and semiconductors, but CDMA technology is also used in GPS, and the fact that GPS has become available for private use has triggered the use of CDMA technology in the private sector.
The method of sharing a certain bandwidth with multiple communications is called "Multiple Access". Multiple access in wireless communication includes "Time" (Time Division Multiple Access, TDMA), "Frequency" (Frequency, FDMA), "Code" (Code, CDMA), and "Space" (Space, CDMA). .SDMA). TDMA and FDMA are relatively easy to understand because they are used by dividing them by time and frequency. On the other hand, it is difficult to grasp the image of CDMA in the first place.
Simply put, in CDMA, 1 bit of data to be transmitted is transmitted as a bit pattern consisting of multiple bits. At this time, since a radio signal that spreads over the entire band is used, it is also called "spread modulation" or "spread spectrum." This bit pattern satisfies a special condition, and even if it is mixed with other patterns having the same bit length, it can be separated later by calculation. The CDMA communication system uses this principle to enable multiple communications in a fixed frequency band. At this time, the receiving side uses the same bit pattern as the transmitting side. However, reception is not possible without knowing the bit pattern. This kind of secrecy is why it was used in military technology.
CDMA seems difficult, but it's surprisingly simple when you actually calculate it. I have tried to figure this out in Excel. The only formulas used were multiplication and addition. All the diagrams this time were created with Excel (God Excel?).
First, the bit pattern has to satisfy some special properties. This bit pattern is called "spreading code" or "pseudo-random noise" in CDMA, but mathematically it uses what is called "orthogonal code" (there are several methods). This orthogonal code can produce long bit patterns with simple calculations (Fig. 01). In the case of 8 bits, there are only 8 of the 256 possible combinations (7 to be exact, since no pattern of all 1s is available). In W-CDMA, this is called an OSVF code, and by repeating the same pattern and repeating the reversed pattern, a pattern with double the bit length can be created. For this reason, no matter how long the pattern is, it can be obtained easily by calculation without the need to record it in a table or the like. In the case of hardware, it can be created with relatively simple electronic circuits.
In the CDMA system, 1 and 0 in a digital signal are represented by 1 and -1 (or vice versa). This is because the digital signal is likened to a "wave". The diffusion code created in this way has a mysterious property. In the sum-of-products calculation with itself (multiplication and sum), the maximum and minimum values are obtained only when the phases are the same or completely opposite (Fig. 02). In any case, the product sum does not become the maximum value or the minimum value with another pattern of the same bit length (Fig. 03). Other bit patterns that are not spread codes do not have minimum and maximum values. This is related to the feature of having the same number of 1s and -1s in the pattern.
By using this property, even if communication with different spreading codes coexist, it is possible to separate them later, and it is possible to restore even if there is noise.
Here, let's try sending 3-bit data using an 8-bit spreading code. Here we have two terminals, channel 1 and channel 2 respectively. On the transmitting side, channel 1 and channel 2 use different spreading codes (pattern 3 and pattern 6).
Multiply the transmitted bit by the spreading code to obtain the 24-bit spreading result from the 1-bit original data (Fig. 04). This is transmitted, but because it uses the same frequency band, the two signals will be mixed. Also, noise is mixed here.
The receiver knows the pattern of the channel and the spreading code in advance. The original transmission data can be obtained by performing sum-of-products calculation using an appropriate spreading code pattern for mixed radio signals and examining the code.
In actual CDMA, it is necessary to match the starting position of the received signal and the spreading code pattern. This is called synchronization. Synchronization is performed when the mobile phone terminal and the base station are first connected, and when the mobile phone terminal moves and the base station is switched (handover). For the sake of simplicity, it is assumed here that they are synchronized.
In this figure, we only use multiplication and addition, and the SIGN function to check the sign of a number. It looks complicated, but the operation is surprisingly simple. For example, the "spreading result" of the "sender" is the result of multiplying the above two cells. The "composite signal" of the "radio signal" is the sum of the diffusion results of channels 1 and 2. The "matching process with the spreading code" on the "receiving side" is the result of multiplying the same bits of the spreading code pattern (top table in the figure) and the "signal containing noise" of the "radio signal". The rightmost cell is just a horizontal sum (SUM function). "Integration processing" also has a great name, but it just totals the values in the upper cells.
The mechanism is simple, but with this principle, many terminals can be connected to one base station at the same time. It's as if we're watching some kind of magic trick to make it possible to separate multiple communications simply by multiplying and adding with the spreading code.
The story of this title is "Code of the Lifemaker", the original title of J.P. Hogan's "The Creator's Code". In this work, "life forms" that have "evolved" to civilization appear. CDMA became popular in GPS, 2G, and 3G, but was replaced by other technologies such as OFDM in 4G. Although TDMA and FDMA are digital communication, they were analog technologies, but the concept of performing modulation processing as it is in digital data can be said to have "evolved" into succeeding technologies such as OFDM.
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