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Signals and Systems, Uppsala University

Researchers: A Ahlén, E Lindskog, M Sternad C Tidestav and M Wennström

In wireless mobile radio communication, there is an endless quest for increased capacity and improved quality. Within this area, we have during the last years studied ways to utilize antennas with multiple elements in an intelligent way.

Multiple Input Multiple Output (MIMO) Systems for Wireless Communications

In communication theory, MIMO refers to radio links with multiple antennas at the transmitter and the receiver side. Given multiple antennas, the spatial dimension can be exploited to improve the performance of the wireless link. The performance is often measured as the average bit rate (bit/s) the wireless link can provide or as the average bit error rate (BER). Which one has most importance depends on the application.

Given a MIMO channel, duplex method and a transmission bandwidth, the system can be categorized as

·         Flat or frequency selective fading

·        With full, limited or without transmitter channel state information (CSI)

Where full CSI means the knowledge of the complete MIMO channel transfer function. In a TDD system with a duplex time less than the coherence time of the channel, full CSI is available at the transmitter, since then, the channel is reciprocal. In FDD systems, there commonly exists a feedback channel from the receiver to the transmitter that provides the transmitter with some partial CSI. This could be information of which subgroup of antennas to be used or which eigenmode of the channel that is strongest. It is also possible to achieve a highly robust wireless link without any CSI at the transmitter, by using transmit diversity. Diversity can be achieved through so called space-time codes, like the Alamouti code for two transmit antennas and high bit rates is achieved by spatial multiplexing systems, such as the pioneer system from Bell Labs abbreviated as BLAST.

If a broadband wireless connection is desired, the symbol rate must be increased further which at some point will lead to a frequency selective channel. Then, there are two ways to go, either we employ pre- or post-equalization of the channel or we divide the channel into many narrowband flat fading sub-channels, a technique utilized by OFDM, and transmit our data on these sub streams, without the need for channel equalization. Hence, it is always possible to convert a frequency selective channel to many flat fading channels using OFDM and apply the developed flat fading MIMO signalling techniques to each of these sub-channels.

Our research on MIMO systems has so far considered flat fading MIMO channels, with or without CSI at the transmitter. Some results from our research is shown below

MIMO with full CSI at the transmitter

When full CSI is available at the transmitter, it is possible to transmit data on the MIMO channel eigenmodes. A MIMO system with N transmit antennas and M receive antennas has min(N,M) eigenmodes. The gain of these eigenmodes is proportional to the singular values of the MIMO channel, so they have disparate power. We propose to use adaptive modulation techniques to transmit over these eigenmodes, to maximize the bit rate or minimize the BER of the transmission.

The figure above shows the data throughput (bit/(sHz)) as a function of total transmit power for a 4 times 4 MIMO system in a Rayleigh fading channel. The blue curve is the Shannon limit and the dashed curve the throughput of the BER is fixed at the target 10^(-5). In practice, the data rates chosen for the sub-channels can not be arbitrarily chosen, they must belong to the discrete set of modulation types (BPSK,QPSK,16QAM,…) so the dotted curve shows the throughput when adopting the discrete rates. The figure below show the rate per subchannel corresponding to the figure above. We see that the subchannel with the lowest gain is only used when the total power (SNR) is larger than 26 dB.

MIMO performance in correlated channels with no CSI at the transmitter

When CSI is not available at the transmitter, transmit diversity at a low implementation complexity can be achieved with orthogonal space-time block codes (STBC). Multiple antennas at a portable device imply that the antenna spacing has to be small. This implies that the signals that enter the different antennas will be correlated and the performance will degrade. An important parameter in the model for the scattering channel is the angle spread D of the received signals. With small antenna element spacing, the mutual coupling can be significant, and in our model the electromagnetic coupling has been taken into account.

The figure above shows the outage capacity at 10% probability, which roughly is the bit rate per Hz of bandwidth that can be transmitted over the 2 times 2 MIMO Rayleigh fading channel 90% of the time when varying the antenna element separation  (assuming dipoles). The i.i.d. Rayleigh fading channel is also shown as a reference, and we see clearly how the correlation (introduced by the angle spread D) reduce the capacity of the channel. When mutual coupling is taken into account, the curves oscillate, due to the oscillating behaviour of the mutual impedance between two adjacent dipoles. It is interesting to note that when the signals are highly correlated (D=6 degrees), the mutual coupling actually improves the outage capacity for small antenna element spacing, by decorrelation of the signals.

Algorithms for Combined Spatial and Temporal Equalization in TDMA

The received baseband signal in a TDMA cellular system is corrupted by noise, by intersymbol interference due to multipath propagation and by co-channel interference from other users.

If only one antenna element is available at the receiver one can use filtering of the received time series in order to estimate the transmitted sequence, i.e. temporal equalization. If several antenna elements are available, it becomes possible to perform spatial filtering by forming beams in the direction of a desired signal. Noise and interference and also delayed signals which would result in intersymbol interference, can then be suppressed if they arrive from other directions.

The beamforming concept can be combined with temporal equalization, resulting in spatio-temporal equalization. It then becomes possible to make effective use of the energy in delayed signals arriving from several directions, while suppressing the signals from co-channel interferers.

Spatio-temporal equalization can be performed by generalizing the single-input-single-output (SISO) DFE to a multiple-input-single-output (MISO) DFE. One can also use a MLSE Viterbi detector.

A MISO DFE will, by necessity, contain a larger number of adjustable parameters than a SISO DFE. This leads to two potential problems.

  • The adjustment of many filter parameters, based on short training sequences, is sensitive to noise. Misadjustment may lead to poor performance.
  • The computational complexity of the algorithm will increase.
These two key issues have been investigated, for different filter structures and different adjustment schemes. The structure of one promising algorithm, the Multiple Independent Beam Decision Feedback Equalizer (MIB-DFE), is illustrated below.


When multiple antenna elements are present, we may investigate the still harder task of detecting several users simultaneously, on the same frequency band. Our research in this direction is described on our page on multiuser detection.

The use of arrays of antenna elements is practical at the base station, but much less practical at the mobile. The investigated techniques are therefore primarily applicable in the transmission from the mobiles to the base stations.

Channel reuse within cell

In a TDMA system, the combination of a certain time slot and a certain frequency is called a channel. In a cellular system, every channel is used by multiple base stations. However, due to interference from one base station to another, not all channels are used in all cells. Instead, channels are reused at a certain interval. The interval with which the channels are reused is called the reuse distance. In a GSM system, the reuse distance is between 9 and 30.

In the future, the spatial dimension must be exploited more thoroughly. The first step is of course to decrease the reuse distance. This is the primary objective for the algorithms described above. If every channel could be used in each cell, the system capacity would rise by a factor equal to the reuse distance in the current system. But if an even larger increase in capacity is desired, we have to lower the reuse distance below one or, in other words, perform channel reuse within cell.

The algorithms previously described could actually be used as tools for such a scheme. For such an application, one of the users in the cell is considered as "desired", whereas the remaining users are considered as "interference". The signals from the other users will in this case be considered as nothing but colored noise, which can be significantly suppressed by using combined temporal and spatial equalization.

[TITO channel model] Another option would be to consider the signals as signals rather than as colored noise. We could in this case use the property that all signals are digital, i.e., they can only assume a finite number of values. The model would in this case be a multiple input-multiple output (MIMO) channel model. As input we would use the transmitted symbols from all users, and as output the sampled output from the antenna. The situation is depicted to the right for a case with two users and two antennas.

The problem of interference suppression has then become a problem of multiuser detection. We can then use a multiuser detector to detect both signals simultaneously. The problem is very similar to the multiuser detection problem encountered in a DS-CDMA system.

To solve this multiuser detection problem, it is possible to use generalisations of any equalizer used to mitigate intersymbol interference, i.e. a linear equalizer, a decision feedback equalizer or the Viterbi algorithm. The generalisation is relatively straightforward. The derivation is based on a multivariable channel model of the form

[MIMO channel model]

Here, d is a vector of input symbol and y is a vector of channel outputs. The matrix coefficients B constitute the channel and are the basis for the equalizer design.

[Performance of channel reuse within cell]

We have derived a multivariable DFE to solve the multiuser detection problem. This multivariable DFE is described in greater detail in the section Research on multiuser detectors for CDMA based cellular systems. To address the performance of this multiuser detector, we have performed simulations in a scenario which resembles a GSM system with two users and two antennas in each cell. As were the case for the CDMA system, it is of interest to investigate the performance when the received powers of the users are very different. In this case, the transmit powers of the users are either equal or differ by 20 dB.

The structure of the transmission is similar to the structure in GSM: the data is transmitted in bursts of length 148 with a training sequence of length 26 in the middle. Parameter estimation was performed using ordinary LS. We simulated the system for signal to noise ratios between 5 and 20 dB. We compared the performance to the performance of a corresponding system where one user and one antenna were removed.

As can be seen, the system performs better with two users and two antennas than with one antenna and one user. This algorithm will also be applied to measurements from an antenna array. These measurements are supplied by Ericsson.

PhD Thesis by Mattias Wennström, 2002. on MIMO systems and antennas
PhD Thesis by Claes Tidestav, 1999, on MIMO DFE's
PhD Thesis by Erik Lindskog, 1999, on space-time methods.
Licentiate Thesis by Erik Lindskog, 1995.
Licentiate Thesis by Stefano Bigi, 1995, which considers the design of SISO IIR DFE's based on short data records.

Paper (IEEE SP 2001), on multivariable DFE's for multiuser detection.
Paper (IEEE Com'99), on enabling channel reuse within a TDMA cell.

Conference paper (ICC'02), on reduced rank channel estimation in CDMA systems.
Workshop paper on the optimality and performance of transmit and receive space diversity in MIMO channels.
Conference paper (VTC'99), on enabling channel reuse within a TDMA cell.
Conference paper (VTC'99), on reduced rank channel estimation.
Conference paper (ICASSP'99), on the structure and design of MIMO Decision Feedback equalizers.
Conference paper (EUSIPCO'98), on exploiting pulse shaping informantion.
Conference paper (IEEE ICUPC'98), on "Bootstrap equalization"
Conference paper (IEEE VTC'97), on the implementation of Viterbi detectors in antenna array receivers.
Conference paper (IEEE ICUPC'96), on using direction-of-arrival parametrization.
Beamforming with the sample matrix inversion method for a GSM signal with sampling offset (IEEE PIMRC'95)
Combined spatial and temporal equalization using an adaptive antenna array and a decision feedback equalization scheme (IEEE ICASSP'95).
Spatio-temporal equalization for multipath environments in mobile radio applications (IEEE VTC'95).
Indirect spatio-temporal equalization and adaptive interference cancellation for multipath environments in mobile radio applications.
Conference paper (IEEE PIMRC'95), on the MIMO DFE as a multiuser detector.
Conference paper (Asilomar'95), on utilizing adjacent TDMA frames.
Master's Thesis by Claes Tidestav, 1993, addressing the impact of antenna correlation.

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Updated Oct. 8, 2002 (MS,MW) |