Signals and Systems Group, Uppsala University

Researchers: A Ahlén, M Sternad C Tidestav


One important property of the air interface of a cellullar telephone system is the multiple access method. Each user of the cellular system is given a channel, and all users get different channels. The way in which these channels are different is determined by the multiple access method. Traditionally in a radio communication system, each channel occupies its own frequency. This is for instance the case in FM radio broadcasting: different stations have different frequencies. By tuning the radio receiver to a specific frequency, the listener can choose which station he or she wants to listen to. This multiple access scheme is called Frequency Division Multiple Access or FDMA. The analog cellular systems, e.g. NMT, use FDMA.

The pan-european cellular system GSM uses Time Division Multiple Access or TDMA as its main multiple access method. In TDMA, the channels are separated by use of time slots. Many users occupy the same frequency, but not at the same time. The mobile telephones take turn to transmit. Typically, each time slot is a few microseconds long. TDMA is also used in the Northamerican cellular standard IS-54 and in the japanese system PDC.

[Transmission in a DS-CDMA system]

In a cellular system employing Direct Sequence Code Division Multiple Access (DS-CDMA), all users use the same frequency at the same time. Before transmission, the signal from each user is multiplied by a distinct signature waveform. The signature waveform is a signal which has a much larger bandwidth than the information bearing signal from the user. The CDMA system is thus a spread spectrum technique. All users use different signatures waveforms to expand their signal bandwidth. The procedure is depicted below for a two-user case. Notice the phase shifts in the transmitted signal due to the negative pulses in the data stream.

The conventional receiver

At the base station, the sum of all the broadband signals is received. To demodulate a signals from a specific user, the received signal is correlated with the signature waveform of that user. The procedure is illustrated by correlating the sum of the two signals above with the respective signature waveforms:

[Received signal in the DS-CDMA system]

Under ideal conditions, the correlation between different signature waveforms is zero. In that case, the output of the correlator will be the transmitted signal of the desired user, as depicted above.

This correlation receiver is known as the conventional receiver.

Disadvantages with the conventional receiver

The conventional receiver has some serious drawbacks. The underlying assumption is that the signals from different users are uncorrelated. In this case the conventional receiver is optimum. In practise the signals from different users will be correlated, which means the conventional receiver will be suboptimum. Still the conventional receiver will still work rather well under these two conditions:
  • The correlation between the signature sequences is small
  • The signals from different users are received with approximately the same power.
The first condition can be fulfilled by careful design of the code sequences that determine the signature waveforms. The second condition can be fulfilled by accurate power control. The base station measures the received power of all the transmitting mobiles. By sending power control commands to all the mobiles, telling them to increase or decrease their transmit power, the received power levels of all the users can be kept at approximately the same level. Without power control, the received power levels may differ by 60 dB or more! If the power of the received signals differ significantly, we say we suffer from the near-far problem.

Code sequence design also has problems. It turns out that the correlation between the signals from different users is critically dependent on the relative delays of the signals from different users. It is possible to design codes that are orthogonal, i.e. have zero cross correlation if the signals arrive at the base station synchronously. It is however impossible to design code sequences (with finite length) that have very low cross correlation for all relative delays.

A multiuser detection problem

Due to the problems with the conventional receiver mentioned above, a different type of detector has been derived. These detectors, which do not treat other users as noise, but as digital signals are called multiuser detectors.

Different types of multiuser detectors

Most multiuser detctors are used in conjunction with the conventional receiver. This means that the received signal is first correlated with each of the signature waveforms. The output from this bank of correlators is treated as a vector. The multiuser receiver then performs some linear or non-linear transformation on this vector.

Several multiuser detectors of this kind has been proposed. Usually, some parameters need not be known, whereas others must be estimated. Unfortunately, some of the necessary parameter estimation may be difficult in a situation where there is a near-far problem. This is true in particular for estimation of the propagation delay, which is necessary for most of the multiuser detectors in this category.

Other multiuser detectors do not operate on the output from the bank of correlators. Instead the demodulated wideband signal is sampled at a high rate and fed into an adaptive discrete time filter. The coefficients of the filter are adjusted so that the output of the filter resembles some known training sequence, which is transmitted before transmission of the actual message. These coefficients are then used during the remainder of the transmission.

Amazingly enough, these detectors need no side information except the training sequence! Still, they have some problems. The use of these detectors place severe restrictions on the choice of spreading codes. Also the detectors may not be able to adapt to changing transmission conditions due to fading. Fading and ways to combat it is discussed in detail in the section Research on parameter tracking and adaptive filtering.

A multivariable decision feedback equalizer operating on the correlator outputs

As an example of a multiuser detector that operates on the output from the bank of correlators, we have studied a multivariable decision feedback equalizer (DFE). Decision feedback equalizers were first derived in the 1960's. They were then used to mitigate intersymbol interference, which was a major problem for construction of high speed telephone line modems.

For application as a multiuser detector in an asynchronous DS-CDMA system, the DFE has to be extended to have multiple inputs as well as multiple outputs. For this purpose, we use the vector of sampled correlator outputs as the output of a discrete time multivariable channel model. We also collect the transmitted symbols of all users at a certain time instant in a vector. The situation is depicted in the figure below:

[The multiuser channel model]

Note that both input and output of the filter are vectors.

By using the information about the transmission and reception in a DS-CDMA system, it is possible to relate the output to the input. This relation will be a discrete time multivariable FIR-filter with the number of inputs and the number of outputs equal to the number of users. The resulting FIR filter have three taps, where each tap is a matrix:

[The multiuser channel model difference equation]

Here, A is a matrix which contains phase shifts and gains of the transmission channel, whereas R(-1), R(0) and R(1) are functions of the mutual crosscorrelations of the signature sequences, as well as of the relative transmission delays among the users.

The vector y(t) is used as input to the multivariable DFE shown below:

[The multivariable decision feedback equalizer]

The vector of correlator outputs are used as input to the feedforward filter, which suppresses most of the intersymbol interference and cross-couplings in the channel. From the outputs of the feedforward filter, the outputs from the feedback filter remove the impact of symbols that have been previously detected.

[Performance of the multivariable DFE] We tried the multivariable DFE in a CDMA scenario with two users. The received powers of the two users differed by 20 dB, and the codes used were Gold codes, which is a common choice in CDMA systems. We varied the signal to noise ratio between 5 and 20 dB, and counted the number of errors in the symbol decisions. The performance of the multivariable DFE was compared to the performance of the coventional receiver, and also to the performance of the decorrelating detector, a linear multiuser detector.

The performance of the DFE is superior to the performance of the conventional detector. This is natural, since the performance of the conventional detector is limited by the interference from the other user. This is in contrast to both the DFE and the decorrelating detector, which strangely enough have the same performance. It should be noted however that the decorrelating detector can not be impelented without modifiction in a real system, since it is a block detector. In a block detector, an entire sequence is received and demodulated simultaneously. It is then implicitely assumed that the transmission begins and ends at specified instances, which are not separated too far apart. This will not be the situation in a real system: in a CDMA system, transmission takes place continuously. The performance of a practical implementation of the decorrelating detector is then overbounded by the performance indicated in the graph. Also, the decorrelating detector has been shown to perform very badly in a situation were the propagation delay has been estimated inaccurately. Thirdly, the complexity of the DFE is lower than the complexity of the decorrelating detector.

A multiuser detector operating directly on the wideband signal

As previously stated, multiuser detector operating on the output of the correlator bank rely on accurate estimation of among other things the propagation delay. To circumvent the problem of propagation delay estimation, we have also devised a multiuser detector operating directly on the wideband signal. But we do not want to have the disadvantages associated with such a detector: lack of flexibility in the code selection part and inability to cope with fast fading. A multiuser detector for application in mobile radio must be able to adapt to rapid changes in transmission conditions. A multiuser detector fulfilling these conditions would be an ideal candidate for practical implementation.

Such a detector can in fact be devised. By rewriting the system for transmission and reception in a CDMA system, it becomes clear that we are dealing with a simple equalization problem rather than a complex detection problem. There are only two differences from the equalization problems considered since the 1960's:

  • the channel has several inputs, one for each user and
  • the output of the channel must be sampled much more rapidly than once per symbol.
The situation we have to consider is depicted below.

[A multiple input-single output channel]
These equivalent channels are discrete time FIR filters. The coefficients of these filters will depend on two things

  • the codes that are used and
  • the physical channel.
The former is known at the receiver, whilst the latter must be estimated using a training sequence. This estimation problem is relatively simple and does not suffer from the near-far problem. Also, the parameter tracking can use the a priori information about the parameter variations mentioned in the section Research on parameter tracking and adaptive filtering.

Based on knowledge of the channels, a number of different detectors can be designed. All of them have counterparts among equalizers used to combat intersymbol interference. Examples of such detectors are

  • fractionally spaced linear equalizers,
  • fractionally spaced decision feedback equalizers (DFE:s) and
  • detectors based on the Viterbi algorithm.
[Performance of the fractionally spaced DFE] As an example of such a detector, we have studied a fractionally spaced decision feedback equalizer. We have performed simulations to investigate its performace in a realistic scenario. In this case, we have studied its performance for an asynchronous DS-CDMA system with five users. The received signal differ by 0, 10, 20 or 30 dB. The physical channels have four taps, and random codes are used. This means that over time, different codes are used to spread different symbols and that in a given symbol period the correlation between different signature waveforms may be high. We compare the performance of the DFE to the performance of a single-user under the same conditions.

The results in the graph indicate that the performance of the system is satisfactory, despite the heavy load and the severe near-far situation. The difference between the DFE and the single user case is rather large, but the system in which the DFE operates is very heavily loaded.

PhD Thesis by Claes Tidestav.
Conference paper (IEEE ICUPC'96), on equalizer design based on explicit channel models of DS-CDMA systems.
Conference paper at the Swedish Radio Conference on the same theme.
Report which includes a derivation of the fractionally spaced SIMO-DFE.
Conference paper (IEEE PIMRC'95), on multiuser detection using a multivariable DFE.