One of the least-understood aspects of the real-world RF environment is the effect of real-time motion on radio receivers. This becomes especially interesting in modern radio technologies, which are quickly converging on Multiple-In Multiple-Out (MIMO) antenna techniques as a means of increasing data rates without sacrificing temporal or spectral resources.
While much has been written regarding MIMO performance in static conditions, this article addresses time-varying channel conditions, such as those caused by movement of a mobile device, on MIMO performance.
Toward that end, some discrete topics are discussed: the relationship between channel correlation and the capacity of a system; the effect of motion on correlation; and the sensitivity of correlation to orientation and design.
Finally, measured data shows some unanticipated effects on throughput as the result of varying correlation caused by motion, emphasizing the need to test mobile device designs under dynamically varying correlation conditions.
Correlation in MIMO Systems
Consider two transmit antennas sending distinct data signals to two receive antennas at the same time and in the same frequency band. These signals undergo multiple reflections that traverse diverse paths between the transmitter and the receiver. As a result, multiple copies of the transmitted signal combine to produce multipath fading at each antenna. The multipath components from various angles of arrival combine to form a composite signal.
The composite signals seen by the two receive antennas are different as a result of their phase relationships due to the physical environment surrounding the device. The quantitative measure of this similarity in received signals is called spatial correlation.
The focus of this article will be 2 × 2 MIMO systems, since this configuration will be commonly deployed in initial LTE systems.
Figure 1 MIMO path gains represented as an H matrix.
The MIMO channel is represented by H, a matrix of complex path gains (see Figure 1).
The correlation observed in a MIMO channel depends on a variety of factors such as device geometry (orientation, antenna pattern, antenna spacing) and scattering environment. In the real world, many of these factors constantly vary due to motion, resulting in varying correlations as well.
Impact of Correlation on MIMO performance
MIMO systems take advantage of the spatial domain to realize increased spectral efficiency. In order to understand MIMO performance, it is important to understand how MIMO systems realize throughput gains by exploiting RF channel conditions.
One important metric in understanding MIMO system performance is the rank (R) of the MIMO channel. For a MIMO system with M transmit and N receive antennas, the rank is R <= min (M, N). As an example, for a 2 × 2 MIMO system rank can be either 1 or 2. In a full rank channel realized in rich scattering (low correlation) environments, R = 2. Other environments (high correlation) will result in R = 1.
MIMO systems realize capacity gains by decomposing the spatial channel into independent orthogonal streams. The number of useful streams with sufficient signal-to-noise is always less than or equal to the rank, R. Independent data is then multiplexed onto these orthogonal streams to achieve data rates that are up to R times that of comparable single-stream systems.3
Under full rank conditions, a 2 × 2 MIMO system can essentially be decomposed into two streams, thereby offering twice the throughput of a SISO system. When R = 1, the MIMO system offers much lower capacity gain. The best MIMO performance will be realized when R = 2.
The theoretical bound on the capacity of a MIMO system with full channel knowledge at transmitter and receiver is given by
where Φ is the signal-to-noise ratio seen at the receiver, m is the number of transmit antennas, I is the 2 × 2 identity matrix and H is the MIMO channel matrix.1
Figure 2 Capacity curves showing the effect of correlation on capacity.
Based on this information, Figure 2 illustrates the dependence of the theoretical maximum capacity on correlation between receive antennas for a constant signal-to-noise ratio (SNR) = 10 dB. Here, ρrx refers to the correlation between transmit antennas, set to 0 in these plots. ρrx refers to the correlation between receive antennas and is varied from one plot to another. Hence, any change in capacity from curve to curve is as a result of the variation of ρrx.
The red curve shows the cumulative distribution function (CDF) of capacity for a fully-correlated MIMO channel, while the blue curve shows the CDF for an independent identically distributed (i.i.d.) MIMO channel (essentially a MIMO channel with correlation equal to zero). It is clear that the higher the correlation in the MIMO channel, the lower the capacity.
Figure 3 Correlation responses to SCME Urban Micro (a) and Single Cluster (b) channel models.
Variability In Correlation
In order to investigate the variation of correlation under real conditions, two illustrative examples are provided. The first demonstrates variation resulting from slight changes in the mobile device's orientation. The second uses data logged from an LTE device prototype during live drive testing to show a real-world example of variations in correlation.
Correlation Variation as a Function of Mobile Device Orientation
Antenna patterns of realized mobile devices are quite varied. Typically they are functions of frequency and external factors (e.g. the user's hands and head). In Figure 3, spatial correlation is calculated for an actual handset device in response to the SCME Urban Micro and Single Cluster models. The SCME Urban Micro model is considered to be a typical urban micro-cell scenario, while the Single Cluster model is encountered less often, typically 10 to 20 percent of the time in the real world. Three polarizations are shown in the plots: vertical, horizontal, and an equal combination of the two.
It is clear from these examples that there is significant variation in spatial correlation as the device observes different orientations with respect to the incoming signal. From the plots below, a 70 to 80 percent correlated signal can easily drop to 20 percent with a minimal change in orientation, such as a user turning his head. This clearly indicates that a MIMO system must be able to react to rapid changes in spatial correlation in normal situations with typical user behaviors.
Figure 4 Receive correlation reported by an LTE device during drive test.
Correlation in Live Drive Test Scenarios
Figure 4 illustrates the receive correlations reported by an LTE device from a live drive test scenario at typical urban driving speeds. This device reported correlation several times per second. It can be seen that the correlation varies rapidly. The plot reveals that correlation can vary from 0.9 to 0.1 in as little as 200 ms. This points to the fact that the correlation varies significantly in real-world conditions and MIMO systems need to be designed to adapt to the same.
The Effect of Correlation on LTE Systems
LTE is arguably the most widely anticipated wireless technology in many years. Feedback mechanisms have been refined and optimized for efficiency in LTE. In the connection between a base station and an LTE mobile device, there are three key feedback parameters, collectively called Channel State Information (CSI):
- Channel Quality Indicator (CQI) – this feedback is used by the adaptive modulation and coding (AMC, also called "link adaptation") process
- Precoding Matrix Indicator (PMI) – in closed-loop (feedback) systems, the mobile device must make frequent recommendations to the base station regarding each transmit antenna's optimal signal power and phase. LTE uses a pre-defined set of "codeword" matrices, and the PMI indexes whichever matrix is most appropriate at the moment
- Rank Indicator (RI) – This reports the rank value described earlier
While LTE is quite efficient in calculating and transmitting these parameters, they still require processing time and packaging/transmission time. If the MIMO scenario changes significantly in the time it takes the system to process feedback and adjust, performance can be impacted. A MIMO system that can quickly process and respond to feedback will offer better performance.
The Effect of Varying Channel Conditions on MIMO Performance
In order to understand the true impact of varying channel conditions on the performance of an actual MIMO system, some procedures were performed in the laboratory. A lab-based emulated LTE network was connected through an SR5500 Wireless Channel Emulator (to control the RF environment) and then to an LTE UE (User Equipment, or mobile device). The SR5500 was set up to toggle between two channel conditions: rank 1 (minimum rank) and rank 2 (full-rank) channels.
In a rank 2 channel, maximum MIMO throughput is expected, while minimum throughput (that of a single stream) is expected in a rank 1 channel. While the SR5500 can be used to create any dynamically varying correlation conditions, this investigation used two channel correlation conditions. This relatively simple case was chosen to examine the effects of correlation. Performance was measured as Physical Downlink Supplementary Channel (PDSCH) Layer 1 throughput.
Figure 5 Throughput while toggling correlation models at 5 s intervals.
Figure 5 shows the rank as reported by the device and the system throughput as a percentage of the nominal maximum. The dark blue and light blue curves represent the throughput contributions of two streams; the green curve represents overall system throughput. When channel conditions were toggled at five-second intervals, the system was able to adapt between the expected data rates, although it is clear from the graphical presentation of the data that the transition time was significant. By inspection, the UE takes roughly 900 ms to fully adapt to the variation in channel conditions. The average throughput (not shown in Figure 5) is a little above 70 percent of the maximum system throughput. Note that a calculation assuming insignificant transition time would produce an expected value of about 75 percent.
Figure 6 Throughput while toggling correlation modes at 1 s intervals.
When channel conditions are toggled more frequently, the throughput range and mean drop. When toggling occurs every second (see Figure 6), average throughput drops to roughly 60 percent of maximum.
When the channel conditions are toggled every 500 ms, the system essentially offers the throughput of a single stream system, as shown in Figure 7. Note that there is no effective MIMO throughput gain even though the system offers an ideal MIMO channel 50 percent of the time.
Figure 7 Throughput while toggling correlation modes at 500 ms intervals.
Conclusion
This article explores the relationship between variations in correlation in a cellular MIMO system and data throughput. Results show that:
- Slight changes in the orientation (movement) of a mobile device can cause significant variations in correlation
- Correlation measured in actual drive testing shows that correlation varies rapidly and significantly in live conditions
- Data throughput is affected not only by changes in channel conditions, but by the rapidity with which those changes take effect. In one case, it was shown that with frequent rapid movement, a MIMO system might offer no throughput gain over a single stream system, even though MIMO conditions are ideal half of the time. Accounting for all the aspects of adjustment (feedback, processing, etc.) can often point out that data capacity is being wasted
These factors point out the importance of designing MIMO system components (base stations and mobile devices) that can dynamically respond to varying correlation. The potential pitfalls can be uncovered and mitigated by using equipment to emulate controllable dynamic correlation conditions in the design laboratory. n
References
- D.S. Shiu, G.J. Foschini, M.J. Gans and J.M. Kahn, "Fading Correlation and Its Effect on the Capacity of Multi-element Antenna Systems," IEEE Transactions on Communications, Vol. 48, No. 3, March 2000, pp. 502-513.
- 3GPP TR 25.996, Spatial channel model for multiple input multiple output (MIMO) simulations, v8.0.0, December 2008.
- A. Goldsmith, Wireless Communications, Cambridge University Press, 2005.