Article written by John Scourias, with comments in maroon by Tom Farley

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Supplement: R.C. Levine's comments on GMSK modulation 

A reader asks:

 

In GSM technology, I just need an explanation on how we are able to fit a gross bit rate of 270 Kbps in the 200 KHz channel on the air interface in the GSM system. GSM uses Gaussian-filtered Minimum Shift Keying or GMSK. That technology has a spectral efficiency of 1 bit/symbol/Hz. Does that mean we use 1 bit per symbol and not more?

 

Professor Levine responds:

 

I am writing this quickly and may not remember all the numbers exactly, so if you find other numbers in other source documents, I may have the numbers wrong.

 

GMSK modulation has a "spectral efficiency" of APPROXIMATELY 1 bit per symbol or 1 bit per hertz of bandwidth. The word "approximately" is used because there are several different ways to measure the bandwidth of a signal.

 

The method used for GMSK signals in GSM is to find the bandwidth that contains about 99% of the radio signal power. GMSK was developed specifically for GSM by the COST (Council on Science and Technology, a scientific advisory group funded by CCITT and later ETSI). GMSK is a type of minimum frequency shift (MFS) modulation that achieves an approximately optimum compromise between the amount of power out of the desired bandwidth of the modulated carrier signal (only about 1% for the type used in GSM) and still allows the binary data to be accurately demodulated from the received radio signal in the presence of noise. GMSK uses a special waveform to achieve a gradual change in frequency when the two consecutive binary bits to be transmitted are 01 or 10. This waveform (frequency vs. time) is the so-called "Gaussian integral curve." It is the same curve that you can find in some statistics textbooks for the "cumulative distribution function of the 'normal' or 'Gaussian' distribution." A normal or Gaussian distribution is also called a "bell-shaped curve" in some statistics books. (I include all this reference to other statistics books because it is inconvenient to include a figure or diagram with this e-mail.)

 

The time duration of the Gaussian integral frequency transition can be elongated or shortened by the system designer. If we shorten it, the signal will have a larger bandwidth, but it will stay at the upper or lower frequency for a larger part of each symbol interval (bit time interval), and thus it can be accurately demodulated in the presence of noise (it will work OK if the signal to noise ratio is worse). If we lengthen the transition time the frequency will only stay at the high or low shifted frequency for a short part of the total bit or symbol time. (In GSM the high and low shifted frequencies are approximately 67 kHz above and 67 kHz below the nominal carrier frequency, respectively.) Due to the slow frequency transition, the bandwidth will be narrower, but the signal must be used with less noise present. It requires a higher signal to noise ratio to yield error free demodulation. The relationship of the transition time is usually expressed in an indirect way, by stating the product of the 99% bandwidth (called B), and the total bit or symbol duration (called T). This product is called BT. In GSM, a transition time giving a BT product of about 0.3 was chosen by the designers. It puts 99% of the signal power into a 200 kHz bandwidth centered at the carrier frequency. It also allows an almost error-free (about 1% bit error rate -- BER, as I recall) demodulation of the binary data in the presence of noise at the ratio of 8 to 1 (signal power to noise power). Power ratio of 8/1 corresponds to 9 dB signal to noise ratio in logarithmic decibel units. This 1% BER can be handled adequately by the forward error correcting codes and other error protection methods used in the GSM system design.

In the GSM system, with BT=0.3, the spectral efficiency is therefore about 1.35 bits/second/Hz (270/200). GMSK designs with different BT values have a different spectral efficiency value as well.

 

If you are used to other methods to measure the bandwidth, you easily become confused. One widely used method (but NOT used in GSM documents) to measure bandwidth is to find the two points on a figure showing power versus frequency, where the power is half of the peak power (usually the peak power occurs at the center of the signal bandwidth). These two points are also called "3 dB points" because the logarithmic measure of power there is 3 dB lower than the peak or center frequency power. The half power bandwidth is the difference in frequency between the two half power points. The 'half power" method is simpler to do experimentally that the 99% power method. If the type of modulation chosen produces a spectrum of the signal that is very "flat" and uniform throughout the signal bandwidth, and then falls off suddenly to a very low value at the "edges" of the bandwidth, the two different methods for measuring bandwidth will give the same result. If the spectrum of the signal is very gradually sloping away from peak power on either side of the center of the spectrum, the half power bandwidth will be much smaller than the 99% bandwidth.

 

The important thing about use of GMSK for GSM is that the power produced in an adjacent modulated carrier bandwidth (the 200 kHz section of spectrum next to the desired channel) is less than 1/2 percent of the desired signal power. Therefore, two equally strong radio transmissions (the desired modulated carrier, and the adjacent undesired modulated carrier) can be received in the same cell at a receiver without causing unacceptable interference to the desired signal. In previous analog cellular systems, the adjacent "channel" interference was very bad because the bandwidth of the analog signal (and particularly the spectrum bandwidth of the FSK control bursts that were used occasionally to control transmitter power, control handovers, etc.) was much bigger than the nominal 30 kHz signal bandwidth of AMPS (or 25 kHz for TACS, NMT, NETZ, etc.). Consequently many frequencies were excluded from the frequency plan in each cell of an analog cellular radio frequency plan to avoid mutual interference when two mobiles were near the common boundary between two neighboring cells and transmitted at the same power. This reduced use of carrier frequencies was a serious capacity problem. In GSM it is allowed to use a frequency plan that places spectrally adjacent carrier frequencies in geographically neighboring cells.

 

GMSK is also used in some other systems too, such as DECT. However, a different BT product value is used there (I think it is larger, perhaps 0.5, but I don't remember the exact value).

I hope that this answers your question. If not, write to me again with a follow up message for further clarification.

 

Regards,

Richard Levine

Levine's page is here

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