TDMA
– Bitrate and Bandwidth
– Gaussian Minimum Shift Keying
GSM Bands for Europe
Time Slots
Intersymbol Interference and Channel Equalization
Special Time Slots
Access Call
Control Channels
Frequency Hopping

GSM was a completely digital system. Speech must therefore be digitized and transmitted in digital channels.

Description of the GSM Air Interface

TDMA

In all previous mobile radio systems, a subscriber was assigned a frequency channel. This channel was exclusively used by this subscriber. Other subscribers had to be assigned to different frequencies. This principle referred to as FDMA, i.e. Frequency Division Multiple Access.

With PCM, the sampling of the speech signal, it was possible to set multiple participants on the same channel „one behind the other“. Every participant gets a „time slot“. If a channel is shared by assigning time slots it is called TDMA, Time Division Multiple Access.

If speech is transferred digitally it makes sense to do this using a TDMA scheme.

Bitrate and Bandwidth

As we have discussed, bits can be transmitted using phase modulation. One of the key questions is therefore: how many bits should and can be transmitted per second. Of course, it is advantageous to choose the bit rate as high as possible, this would mean to transfer more information. But this comes with a price since there is a fundamental law:

The higher the bitrate, the higher the bandwidth

As discussed previously, for FM modulation a signal of a bandwidth up to 4.5 kHz results in a bandwidth of 10 kHz. For digital signals, the bandwidth depends on the sampling rate, i.e. how many bits are transmitted per second. It turns out that the bandwidth of a digital transmission is slightly lower than the sampling rate. For example, to transmit PCM modulated speech directly at 64 kbit/s it would require about 50 kHz bandwidth.

With GSM, there has been a long discussion about how high the bandwidth should be. Broadband TDMA or Narrowband TDMA? A high bandwidth, i.e. high sampling rates, leads to problems during transmission due to multipath propagation, which will be discussed later. So even if you accept broader bandwidth you can’t transmit as many bits as you like. On the other side, you also don’t want to use too small bandwidth, because it will allow less TDMA channels. For GSM it was finally agreed that a channel bandwidth of 200 kHz and a digital transmission bit rate of around 271 kbit/s should be used.

GAUSSIAN MINIMUM SHIFT KEYING (GMSK)

Typical ways for digital modulation of signals are found here: Digital Modulation. A special type of QPSK (Quadrature Phase Shift Keying) was chosen to modulate the bits. Only phase shifts of 90° are permitted. This is called minimum shift keying (MSK). It has the advantage that the amplitudes of the transmitted signal do not change significantly. Further enhancement comes by the fact that the input signals from I and Q are filtered with a so-called Gaussian filter. This smoothes the transitions which gas a positive influence on the spectrum of the transmitted channel. It creates less interference in the neighboring channels.

GSM Bands for Europe

As early as 1979, new bands around 900 MHz were reserved for GSM. Similar to previous cellular systems, there are two bands for duplex operation. Both bands have a width of 25 MHz.

890 MHz – 915 MHz lower band uplink (from mobile station to base station)

935 MHz – 970 MHz upper band downlink (from base station to mobile station)

With a channel width of 200 kHz, there were 124 radio channels available.

Time Slots

The GSM channels are divided into so-called frames. The length of a frame is 120/26 ms, i.e. 4.615 ms long. A frame is divided into 8 time slots. Each time slot therefore has a length of 577 μs.

148 bits are transmitted within the time slot, also called a burst. Only 114 bits are information. There are 3 so-called tail bits at the beginning and end of the slot. In the center is a fixed 26-bit training sequence. This training sequence is known to the base station (BS) and the mobile station (MS).

Intersymbol Interference and Channel Equalization

Ideally, an Mobile Station receives the signal from a Base Station directly. However, this only happens if there are no obstacles between the antennas. Normally, especially in the city, this is not the case. The received signals are from reflections. These are usually reflections from nearby buildings etc.

It is very likely to happen that there are reflections from several obstacles, that arrive at the receiving antenna. This is called multipath propagation. This isn’t too bad at first, as long as the different paths have similar lengths. However, it becomes critical when the transit times of the various paths become so different that the symbols that are transmitted over these paths overlap each other.

At 270 kbits/s, one bit corresponds to a length of 1.1 km. This means if a bit is transmitted it travels 1.1 km before the next bit is transmitted. If now a receiver has a direct path and a path that comes from, a building 550 meters away, the received bit from the direct path is superimposed on the previous bit coming from the reflected path. Let’s assume we receive the value y(k) at time k and assume that the values sent are x, this means:

y(k) = a0*x(k) + a1*x(k-1)

The coefficients a1 and a2 indicate the strength of the different paths. Due to multipath propagation, a symbol can disturb its neighboring symbols. In English it is called Inter Symbol Interference (ISI). This can be a serious problem with relatively high bit rates.

If a well known training sequence is received, it is possible to estimate the coefficients a0 and a1. If this is achieved, it becomes possible to eliminate the inter symbol interference and restore the original signal x from the received signal y. Such an algorithm is called a channel equalizer. The trainingsequence form each time slot can be used for the equalizer. An equalizer is typically realized by a signal processor.

Special Time Slots

The first two time slots of a TDMA frame are not used for voice data or payload data, but are used for control channels and special other channels. A so-called superframe is defined for this, which has a length of 51 TDMA frames for the first two time slots. These are numbered consecutively with FN (frame number).

Frequency Correction

Every ten time frames, FN0, FN10, FN20, FN30, FN40, a so-called frequency correction time slot (FCCH = Frequency Correction Channel) is transmitted. Only logical zeros are transmitted, which corresponds to a constant frequency. A mobile station can use this fixed frequency to adjust its own frequency reference frequency, which is generated by a very stable VCO (Voltage Controlled Oscillator), by setting a correcting voltage.

Time Synchronization

Another special time slot is transmitted every ten time frames FN1, FN11, FN21, FN31, FN41. This has a particularly long training sequence which is always the same and can be used by the mobile station to precisely synchronize the TDMA time frames. It is called a synchronization burst (SCH).

Broadcast

The time slots FN2…FN5 are channels in which general information about the cell is communicated to all mobile stations in the cell. Important information that is distributed via these channels are the frequencies of the immediate neighboring base stations so that the mobile station can measure and check them directly in order to prepare handovers if required.

Paging

Twelve time slots in a superframe are reserved to signal incoming calls. Those channels are called paging channels PCH. However, the subscriber’s phone number is not used here. Instead, each time the subscriber registers with the network, he receives a temporary number for the cell in which he is located, a TMSI, Temporary Mobile Subscriber Identity. This TMSI is to show an incoming call in the paging channel. An mobile station must therefore always check the paging channels to see whether a call is received for it. The TMSI is used to avoid, that a subscriber can´t be tracked down in the network.

Access Call

When a mobile station is on a network, it can and will synchronize to the frame and time slot structure. However, this synchronization is only in one direction. As we have already discussed, one bit is equal to 1.1 km. If a mobile station is 5.5 km away, a time slot is shifted 5 bits compared to the base station. If the mobile station were to simply respond in the same grid, the bursts would arrive at the base station shifted by 10 bits.

For this reason, the time slot that a mobile station uses to register is shorter than normal time slots. This prevents the time slot received by the base station from overlapping with the following time slot. Such a call request channel is called a random access channel (RACH) because it arrives at the base station “randomly”. If it is received, the base station determines the delay of the RACH compared to its own frame. In response to the RACH, the base station transmits a timing advance value. In further communication, the mobile station will send its time slots earlier by exactly this timing advance value so that it fits exactly into the grid of the associated base station.

Control Channels

In addition to the special time slots, there are control channels in the first two time slots of a GSM Frame. New to GSM are so-called “Dedicated Control Channels”. These are control channels (time slots) that are assigned to a mobile station for a certain time, for example to handle certain procedures such as registration and call setup. A total of 8 assigned channels are available. There is not an assigned dedicated control channel in every frame. This is why it is also referred to as a slow dedicated control channel (SDCCH = Slow Dedicated Control Channel).

If a traffic channel (TCH) is assigned to a mobile station, in one of the time slots 2-7 for a call, a slow associated control channel is also made available. (SACCH = Slow Associated Control Channel). In this channel, measurement values can be exchanged during the call.

However, the SACCH is not sufficient for exchanging information during a handover, for example. For this reason there is also a FACCH (Fast Associated Control Channel). For a FACCH a complete time slot of the traffic channel is „stolen“. This is indicated by the two bits to the right and the left of the training sequence, the so called stealing bits. All bits of the traffic slot is lost but with proper error correction (see Signal Processing) it is possible to reconstruct the lost frame.

Frequency Hopping

Interference between channels is disruptive and can lead to poor quality and transmission losses. This is especially true if two traffic channels are in the same time slot and in the direct neighboring channel. It can also happen that a particular channel has poor transmission conditions. Such a channel should be avoided if possible.

In order to reduce such cases, the GSM standard introduced frequency hopping. In this case, the mobile station is requested to change the channel frequency from time slot to time slot. A predetermined jump pattern is followed. This is different for other mobile stations in the cell, so that mobile stations do not jump “in parallel” in the same time slot.