Understanding MIMO Antennas: Part I

The use of multiple transmit and receive antennas is defined as MIMO, or multiple-input-multiple-output. This technology has garnered a fair amount of attention of late. As wireless systems become more popular, the need to ensure radio signal reception, quality and consistency become a top priority, MIMO has become a way to ensure optimal wireless performance. Furthermore, as wireless technologies evolve to their limits in terms of performance using DSP-based platforms with single antennas, multiple antennas can be a key technology to provide the necessary performance.

MIMO comes in many flavors of MIMO. One of the key design challenges is to determine which approach is most suited for the products being developed. Wireless systems impairments generally center on performance and capacity limitations due primarily to spectrum availability, multi-path, delay spread, and co-channel interference (Fig. 1 below).

Spectrum availability
There''''''''s a limited amount of spectrum available to transmit signals. This limited spectrum leads to various problems for wireless systems, including theoretical limits on data rate for a given transmit/receive power with one transmit/receive antenna. Ultimately, for wireless to reach its promise, limitations of the available spectrum must be overcome.

Consider the Rayleigh fading of a multi-path environment. Going from the transmitter to the receiver, signals in a wireless environment flow through various paths reflecting off many objects—buildings, desks, walls, cabinets, etc. —before reaching the intended receiver. Because these different paths arrive at the receiver with different phases, the signals may be in and out of phase. Many different paths gives rise to a complex Gaussian channel which generates the Rayleigh fading.

Plotting amplitude versus time as users move around or as the environment changes, the receive signal power varies (Fig. 2). Therefore, the amplitude isn''''''''t constant and at some points, the signal will fade out or have a low level. Assuming that the difference in time delays between different paths is smaller than the symbol period (i.e., the time delay is less than 10% of the symbol period), then there''''''''s negligible inter-symbol interference due to the multiple paths. This is called flat fading, where the channel has a flat response across the signal''''''''s bandwidth.

Fig. 1: Wireless system impairments.

Fig. 2: Multi-path fading.

Polarization also plays a part here—fading is independent between different orthogonal polarizations. As fading leads to an amplitude that varies with time and position, the signal-to-noise ratio (SNR) varies with time and position, resulting in a distribution of the bit error rate in a digital communications system. This distribution can help examine the outage probability, defined as the probability that the bit error rate is less than a given value. To provide protection against multi-path fading, a fading margin must be added to the received signal power, which depends on the required outage probability.

Delay spread
Delay Spread becomes a problem when the difference in time delays between various paths arriving at a receiver exceeds 10% of the symbol period (referred to as T). Delay spread in this case can be looked at in different domains: time, frequency, and delay spectrum.

Because the signal paths have different delays associated with the signal, even though just one pulse is transmitted, the receiver will see different pulses separated in time based on the paths taken by the pulses. This leads to intersymbol interference at the receiver which can cause bit errors.

The amount of power received can be seen as a function of time when an impulse is transmitted over a channel. Different environments provide many different types of delay spectrum, including a double spike (Fig. 3). This would be the main ray coming in, followed by a second ray. In general, the longer the delay in a given path, the weaker the signal is due to the longer paths created by reflections off objects that are farther away. This translates into a decrease in receive signal power as a function of time delay.

Fig. 3: Delay spectrum for the double spike and exponential delay spread.

Frequency Domain Response
Converting from the time domain to the frequency domain results in the channel frequency domain response, i.e., the amplitude and phase as a function of frequency. If the fading isn''''''''t constant with frequency, it''''''''s seen as frequency-selective fading. In other words, the channel itself has an amplitude that varies with frequency. Regardless of whether this is viewed in the frequency or time domain, the result is intersymbol interference, which can cause bit errors. For a given channel with delay spread, if the symbol duration is short enough (the data rate is high enough) the intersymbol interference will cause bit errors.

With limited spectrum available, frequency reuse in cellular systems is critical for capacity optimization. In a graphical representation, a given area is divided into various cells (Fig. 4). A frequency channel is assigned to each cell. Because there''''''''s limited spectrum/channels available, the channel must be reused in different cells.

Fig. 4: Cellular layout.

Reusing the channels allows for substantial increases in the overall system capacity. However, cells using the same frequency channels must be spaced as far apart as possible to reduce the co-channel interference to an acceptable level. This decreases the level of frequency reuse, limiting system capacity. Two operations can further increase capacity: decrease cell size and increase the level of frequency reuse that''''''''s tolerable with co-channel interference.

Decreasing cell size
Decreasing the cell size would create more cells and thereby increase overall system capacity. However, there''''''''s a limit in doing this. To use frequencies properly, one needs adequate co-channel interference propagation loss relative to the propagation loss of the desired signal. Although this can be reasonably predictable in large cells, if the cell size is too small, then the amount of interference from other cells isn''''''''t always predictable, resulting in potentially high co-channel interference levels. This is even more pronounced indoors, where the propagation loss isn''''''''t always well defined based on distance alone.

Another way to increase capacity is to increase the level of frequency reuse. For instance, take a reuse factor of 3 and reduce that it to 1. That will increase capacity by a factor of 3. However, any reduction in frequency reuse results in increased co-channel interference as well, so this produces limitations.

In another example, current TDMA/GSM systems typically employ a frequency reuse of 7. Reducing that to 3 more than doubles capacity, but again increases the co-channel interference. Looking at the typical mobile radio system shows that because the cells are hexagonal, any given cell has a first tier of interferers (6 interferers) who''''''''s received interference power is set primarily by frequency reuse. Although there are six equidistant cells, because the environment causes multi-path fading and shadow fading and the fact that the cells aren''''''''t 100% loaded (typically 60% loading at the peak), there''''''''s generally one dominant interferer.

Most studies assume that co-channel interference is a Gaussian noise. That simplifies the analysis, but that''''''''s not what is really happening. This interference is actually other signals, not just background noise.

These factors result in lower quality of service from a wireless system. End-users can be too far away from a base station or access point, behind a wall, in a dead spot, or suffering from too much interference from other users.

Antenna diversity
The use of antenna diversity to overcome the above impairments is an important step. Antenna diversity is defined as the use of multiple antennas with the receive signals weighted and combined to produce an output signal (Fig. 5). The reverse is used on transmit.

Fig. 5: Antenna diversity.

Showing the user transmitting from one antenna and being received by M antennas, each signal from the M antennas is weighted (adjusted in phase and amplitude). These signals are combined to produce an output signal. The key principle behind antenna diversity is the desire to have the fading at each antenna be independent of the other antennas to minimize the likelihood of all signals fading identically. There are three ways to get this independent fading.

The first is to space the antennas far enough apart. This approach works particularly well when the signals are coming from different angles. Generally, a quarter-wavelength spacing between antennas is adequate to reach independent fading if the scattering environment produces signals arriving from all directions (wider spacing is needed if the signals arrive from a limited range of angles).

The second method is to point the antennas in different directions or use antennas with different patterns. This helps achieve independent fading by receiving different signal paths in each antenna.

The third method is to employ antennas with different polarizations. Signals with different orthogonal polarizations (such as horizontal and vertical) generally have independent fading.

The number of antennas on a device generally isn''''''''t limited by the device''''''''s size/form factor. A mixture of spatial, pattern, and polarization diversity can be used to have as many antennas as needed on a given device. The only limitation on the number of antennas is the cost/complexity/power of the RF circuitry needed for each antenna.

Antenna gains
There are two basic types of gains achieved with smart antennas—antenna gain and diversity gain. The antenna gain is the increased average output SNR with these multiple antennas. Hence, if M antennas are employed, the combined signals are added in phase, while the noise is added incoherently, producing a gain of M with M antennas. To visualize this, consider a narrower beam with half-wavelength-spaced antenna elements, i.e., an equally spaced linear array forming a narrow beam in a given direction. Because the signal energy is focused on a smaller area, the SNR increases in that area. Note that this isn''''''''t the antenna-array approach typically used in wireless systems with multi-path.

Diversity gain is the decreased required receive SNR for a given bit error rate (BER) averaged over the fading. Specifically, this is the reduction in fading margin that''''''''s obtained by reducing the fading with the smart antenna. This gain depends on the BER and has a maximum limit of the fading margin, regardless of how many antennas are used. For example, for a binary phase-shift-keyed system at a 1% BER, the fading margin needed is 9.5 dB with one antenna. This margin is reduced to 4.3 dB (a diversity gain of 5.2 dB) with two antennas, and 1.9 dB (7.6 dB diversity gain) with four antennas. Thus, the diversity gain can be larger than the array gain for a small number of antennas, but the array gain dominates for a larger number of antennas as the array gain grows linearly with the number of antennas. But the diversity gain saturates at the fading margin.

Consider the case of transmit diversity to obtain the same gains for transmit or receive. The two main types of transmit diversity techniques are space-time coding and transmit beam forming. With space-time coding, the same data is sent on multiple transmit antennas, but is coded differently on each antenna. Because the coding is different on each transmit antenna, the receiver can distinguish the fading of each antenna and through appropriate signal processing, obtain a diversity gain against the multipath fading.

However, because the signals have been transmitted without knowledge of the receiver''''''''s location, it''''''''s not possible to obtain an array gain. With transmit beam forming, the same data is sent from each antenna, but with a phase/amplitude adjustment for each antenna, such that the signal energy is maximized at the receiver. Thus, both a diversity and array gain can be achieved. This implies that transmit beam forming is preferable to space-time coding. However, determining the required phase/amplitude adjustment with transmit beam forming can be more problematic and have larger impairment degradation than space-time coding. Hence, space-time coding may be preferable, particularly with a small number of antennas.

On to Part 2 of this article takes a closer look at the MIMO techniques that are the focus of this discussion. In particular, it examines the various types of MIMO design.

About the author
Dr. Winters is Motia''''''''s Chief Scientist, and is responsible for the creation and development of the company''''''''s smart antenna technology. He is an IEEE Fellow, holds more than 20 patents, and received his Ph.D. in electrical engineering from The Ohio State University. Based in Pasadena, Calif., the company can be reached at (866) 426-6842