Capacity is critical for the profitability of larger wireless networks, and multiple-input-multiple-output (MIMO) systems provide potentially high capacity.¹ These systems use multiple antenna elements in both the transmitter and receiver to improve the capacity over single antenna topologies when operated in multipath environment. The properties of these antennas play key roles in determining the overall system performance. And, in spite of the number of studies on MIMO systems, little has been reported on successful implementation and optimization of multiple antennas in a mobile telephone. What follows is a review of methods by which an antenna designer can evaluate the MIMO performance of mobile-telephone antennas in terms of channel capacity, capacity versus signal-to-noise-ratio (SNR). This study will also consider the capacity for MIMO systems with an unequal numbers of antennas in the link ends, and the impact of the antenna element properties on the MIMO system performance.

Early work in MIMO antenna elements includes the pioneering studies of Winters², Forschini³, and Telatar.⁴ The basic concept in a receive diversity system is to overcome multipath effects by arming the receiver with multiple versions of the transmitted signal, using distinct channels for each. Since the fading characteristics of each channel tend to be different, a simultaneous deep fade in all of the channels would be rare,¹ providing the receiver with at least one channel with good signal strength. By using spatial, polarization, or pattern diversity, the performance of a wireless system can thus be improved. This means that the signals on the two antennas (with different position, polarization, or radiation patterns) are combined such that fading is avoided in the combined signal. This corresponds to an increase in the SNR in the fading dips, and hence the fading margins in the system link budget can be reduced. Alternatively, the increased SNR can be used to increase the capacity of the communication channel. If two or more antennas are used on both the transmitter and the receiver side, and if the improved SNR is used to increase the capacity of the communication system, a MIMO system is obtained.^5-8

The idea behind MIMO is that the signals on the transmit antennas at one end and the receive antennas at the other end are "combined" in such a way that the quality in terms of the bit-error rate (BER) or the data rate (in terms of b/s) for each of the MIMO user can be improved.⁵ A MIMO system transmits data over a matrix channel rather than just over a single radio channel. This requires signal processing over both time and space (Fig. 1).⁹ The signal to be transmitted is fed to a simplified transmitting block in which proper error correction coding is added, and filtering and amplification is performed. Hereafter, the three different signals are transmitted simultaneously from antenna elements A1, A2, and A3. At the receiver, each of the antenna elements B1, B2, and B3 receives a signal from each of the transmitting antennas.

If the received signals at each of antenna elements B1, B2, and B3 are sufficiently independent, as is typically the case in the presence of a rich multipath environment, it is possible to reconstruct the original transmitted signal. The relationship between A_i(t), i = 1,2,3 and B_i(t), i = 1,2,3 is B(t) = H(t) A(t). Each matrix H represents the transmission at a certain time (t) and spatial location of the antennas in the multipath environment. Hence, a (3, 3) MIMO system, with three receive and three transmit antenna elements, has a potential capacity increase of three as compared to a single-element system. In an ideal multipath channel, this yields an upper theoretical MIMO capacity that is linear with the number of antenna elements N in a (N, N) MIMO system.¹ Compared to a traditional single-input-single-output (SISO) system, there is a linear increase in capacity by the amount m, where m is the smallest of the number of transmit or receive antenna elements.³

In theory this gives an upper speed limit that is limited only by the hardware cost and the requirement of a rich multipath environment. Therefore, MIMO systems are very attractive in order to boost the capacity of a wireless-communication system that operates in a rich multipath environment.

However, in a more practical MIMO system the capacity is reduced due to correlation between the signals in the receiver,¹⁰ this effect has been investigated both theoretically^{11, 12} and experimentally.¹³ Therefore, the correlation between the signals that are received from the different antenna elements is an important parameter in a MIMO system, due to the increased capacity for decreased correlation.⁶ As long as the envelope correlation is less than ρ_e < 0.5 diversity gain could be obtained in a mobile phone.¹ Even though, this motivates for low correlation, it is not a guarantee for high capacity, since in some special propagation scenarios, the MIMO channel capacity can be low (i.e., comparable to the SISO capacity) even though the signals at the antenna elements are uncorrelated.¹⁴ This effect that has been denoted "keyhole" leading to a drop in the capacity.¹⁵ It is related to scenarios where rich scattering around the transmitter and receiver leads to low correlation of the signals, while other propagation effects, like diffraction or wave guiding, lead to a rank reduction of the transfer function matrix. This gives rise to significant local scattering around both the transmitter and the receiver unit causing uncorrelated fading at each end of the MIMO link. However, the channels still have poor rank properties and hence low capacity. The rank of the MIMO channel is defined as the number of independent equations offered by the MIMO system (the algebraic rank).³ The rank is always less than both the number of transmit antennas and the number of receive antennas.

Recently, Oestges et al.¹⁶ found that high correlation does not necessarily result in low capacity. In Schumacher et al.,¹⁷ the physical channel is related to the observed correlations. In both cases, it is the cross correlation that is investigated; in the current work, the correlation between elements will be examined. The results obtained in refs. 16 and 17 are therefore not directly comparable to the results discussed by Thaysen et al.⁶

Moreover, in a lean scattering environment with mostly line-of-sight properties, a simple receiver diversity system will yield full transmission. However, for a MIMO system, mainly line-of-sight properties cause increased correlation at the receiver, and hence the principle behind the MIMO system collapses since three unknowns must be resolved from a linear system of one equation. By proper handshaking between the receiver and the transmitter, the potential collapse of the MIMO principle can be avoided.³

An expected linear enhancement in capacity with an increase in the number of antenna elements would imply a desire for an increased number of antenna elements. However, mutual coupling between the antenna elements affects the correlation.^18-23 For a finite-sized mobile telephone, the proximity of antenna elements causes inevitably higher mutual coupling.^{24, 25} Therefore, it is necessary to know more about how these antennas should be oriented to minimize the coupling²⁵ and improve the correlation.²⁶ Increased mutual coupling results in higher spatial correlation²⁶ which in many case leads to a lower MIMO gain compared to fully uncorrelated antenna signals.⁹

There are two kinds of antenna correlation: Signal correlation and envelope correlation. Signal correlation refers to the correlation between the complex signals received from two different antennas, while envelope correlation refers to the correlation between signal amplitudes received from two different antennas. Envelope correlation is often the parameter measured in antenna experiments (phase less) and is in most cases approximately equal to the square of the complex magnitude of the signal correlation.²⁷ In Vaughan et al.,²⁷ the maximum relative error is computed to being less than 10 percent. In the present work, unless otherwise mentioned, reference is to the correlation that is calculated using the complex value of the signals.