Increased data throughput is critical to the success of future mobile wireless services that promise reliable voice, data and video access. Although the data throughput of a communications channel can be increased by increasing the channel’s bandwidth, bandwidth is generally licensed and limited. A more practical approach lies in the adoption of advanced modulation formats, such as orthogonal frequency-division multiplexing (OFDM) and novel communications system architectures, such as multiple-input, multiple-output (MIMO) configurations. A MIMO system uses multiple antennas and the spatial diversity between them to increase data throughput without increasing bandwidth. The added system complexity, however, poses new requirements for test equipment and measurement strategies, which can best be satisfied through the use of modular measurement systems and specialized test software.

High data throughput has been a guiding requirement for many recent wireless communications standards, with provisions for the use of MIMO in a number of these newer standards, including IEEE 802.11n WLAN, IEEE 802.16e mobile WiMAX Wave 2 and 3GPP Long Term Evolution (LTE). These systems couple MIMO with the use of OFDM or orthogonal frequency division multiple access (OFDMA) modulation to achieve significant increases in data throughput without increasing the channel bandwidth.


Figure 1 Traditional radio link based on SISO configuration (a) and MIMO configuration (b).

In a conventional single-input, single-output (SISO) communications system (see Figure 1a), such as a standard IEEE 802.11a/b/g wireless local area network (WLAN) system, a radio link uses a single transmitter and receiver. It may have multiple antennas at each end of the communications link, but only one set of antennas is used at one time and a single channel carries a single stream of data. In an ideal communications channel, radio signals would travel a single path from transmit antenna to receive antenna. But obstructions (such as buildings and terrain) and propagation effects in the radio channel create multipath effects. As a result, multiple signals arrive at the receive antenna. The reflected signals suffer losses due to fading and delays due to longer path lengths than the direct-path signals. Due to differences in path lengths, the phases of these reflected signals are also different than those of direct-path signals. Because of this, signals at the receiver can combine constructively or destructively, causing fluctuations in received signal strength at the receiver. Excessive multipath effects can diminish the data throughput or cause lost data.

Because OFDM is often teamed with MIMO approaches to increase data throughput in a given communications channel, it is important first to understand OFDM before exploring MIMO concepts. For example, OFDM is used in IEEE 802.11g (WiFi) and IEEE 802.16e WiMAX systems. As with MIMO, OFDM can yield an increase in data throughput without an increase in channel bandwidth or an increase in the order of the modulation scheme, such as from a 16-state quadrature-amplitude-modulation (16QAM) approach to a 64-state QAM (64QAM) system.

OFDM essentially employs wireless signals comprised of a series of orthogonal subcarriers. The subcarriers are spaced for optimum isolation from each other, so that the maximum power of a given modulated subcarrier corresponds with the zero crossing point or minimum power of the adjacent modulated subcarrier. The data to be communicated is multiplexed across the multiple subcarriers, with some subcarriers serving as guard bands for isolation and to prevent adjacent-channel interference. For added robustness, many communications standards using OFDM include a small fading interval to allow time for multipath signal components to fade so that they do not interfere with the reception of the next transmitted symbol.

By processing OFDM subcarriers with digital signal processing based on the use of an inverse Fourier transform, they can be combined into a single stream and the data is recovered. Because multiple streams can be transmitted in parallel over a single channel while preserving their relative phase and frequency relationships, high data throughput is possible without extending bandwidth.

In contrast with a SISO communications system, a MIMO system (see Figure 1b) uses multiple radios and antennas simultaneously, with multiple data streams carried over a single communications channel. The multiplexing of these data streams is coordinated by the medium access control (MAC) layer at both ends of the communications link. MIMO systems do not require a symmetrical arrangement of antennas, such as two transmit and two receive antennas (2 x 2) or four transmit and four receive antennas (4 x 4); they can also operate in “unbalanced” configurations, such as with four transmit antennas and three receive antennas in a 4 x 3 configuration.

To increase the data throughput of a SISO system, a more complex modulation format, or additional bandwidth, or a combination of the two is required. Quite simply, to double the data throughput of a SISO system channel, the channel bandwidth must also be doubled. To increase the data throughput of a MIMO system, the number of transmitters, receivers and their antennas is increased. Through the use of multiple antennas and spatial multiplexing among the signal propagation paths, a MIMO system can increase capacity by a factor of about 3.5 without increasing channel bandwidth.

A MIMO system takes advantage of variations in the received signals to increase data throughput. Received signals are treated as simultaneous equations with unknowns (the transmitted symbols). Greater variations in the multiple signal paths simplify the solution of these simultaneous equations, resulting in increased data throughput.

How does the channel capacity of a SISO communications channel compare to that of a MIMO communications channel? Shannon’s equation for the theoretical throughput of a communications channel can be applied in the SISO case:

C=Blog2(1+S/N) (1)


C = the channel capacity (in bits per second),
B = the bandwidth (in Hertz),
S = the total signal power over the bandwidth [in Watts or Volts squared (V2)], and
N = the total noise power over the bandwidth [in Watts or Volts squared (V2)].

When this equation is modified for MIMO applications,

C=ABlog2(1+S/N) (2)


A = the number of transmit antennas

The equation points out the direct correlation between the number of transmit antennas in a MIMO system and the resulting channel capacity. A MIMO system transmits multiple bit streams across the same physical channel using multiple transmit antennas by using a technique known as spatial multiplexing. The bit stream is multiplexed to multiple transmitters without changing the symbol rate of each independent transmitter. By adding more transmitters and transmit antennas, the system throughput increases without changing the channel bandwidth.

Figure 2 A radio channel in a MIMO system can be modeled as a number of different vector quantities.

Modeling the communications channel of a MIMO system must take into account the multiple data streams, including the direct and reflected signals arriving at each receiver. By using a convention in which the multiple transmitters are identified as Tx1, Tx2...Txn for n number of transmitters, and the similar convention of Rx1, Rx2...Rxn for n number of receivers, a MIMO communication can be represented in the form of a matrix of signal vectors (hxy) where x designates the number of the transmitter and y is the number of the receiver. For example, h21 is the signal from transmitter 2 to receiver 1, while h22 is the signal from transmitter 2 to receiver 2 (see Figure 2). With these conventions, a MIMO channel can be modeled as

y=H*x+n (3)


y = the receive signal vector,
H = the channel matrix (of hxy signal elements),
x = the transmit signal vector, and
n = the noise vector.

Different channel effects on received signals, such as fading and multipath, can be corrected through this same matrix algebra approach, using the relationship

Rx=H*Tx+n (4)

where Rx represents the matrix of Rx1, Rx2...Rxn receive antennas and Tx represents the matrix of Tx1, Tx2...Txn transmit antennas. For a 2 x 2 MIMO system, this relationship would appear in matrix form, as shown in Figure 2.

The signals in these relationships consist of amplitude, frequency and phase components, making it practical to represent them as vectors. Similarly, it is also practical to represent these signals in a measurement system as vector signals.

Measurement Challenges

The increases in data throughput from MIMO techniques come with added system complexity that results in challenges when designing test equipment and measurement systems for evaluating the performance of MIMO systems and the components in those systems. Before deciding on the type of test equipment best suited for MIMO measurements, it might make sense to determine the type of measurements needed for characterizing the performance of a MIMO communications channel. MIMO measurements can generally be categorized as system-level measurements and channel-response measurements, as well as functional measurements for the components used in a MIMO system.

It has already been noted that MIMO signals are defined by their frequency, amplitude and relative phase, and measurements of MIMO signals must determine the accuracy and fidelity of those three signal characteristics. In addition, MIMO systems are often based on downconversion of received signals to a zero intermediate frequency (zero-IF) with baseband in-phase (I) and quadrature (Q) signal components. For high modulation accuracy, the fidelity of the I and Q signal components must be preserved, requiring high performance and minimal distortion from all components in the signal path, including amplifiers, filters, mixers, and I/Q modulators and demodulators.

In many wireless systems, error vector magnitude (EVM) is a standard parameter for evaluating performance and is highly useful for MIMO systems as well. EVM, which is also known as the received constellation error (RCE) because it is graphically shown on a constellation diagram, is essentially the vector difference between ideal signals and measured signals and can be used as a direct measure of the modulation accuracy and overall signal quality of a MIMO transmitter and the performance of a MIMO receiver. An EVM measurement captures a signal’s amplitude and phase errors and reduces the many parameters that characterize distortion of a transmitted RF signal into one parameter that allows comparison of different transmitters. Additional key MIMO transmitter tests include evaluation of group delay and variations in group delay, phase noise, amplifier compression and I/Q mismatches in signal-processing components. Signal distortion caused by these effects will generally be noticeable on an EVM constellation diagram.

In an EVM constellation diagram, an ideal signal would have all constellation points sharply defined at their ideal locations. But signal and component imperfections, such as phase noise and carrier leakage, cause these constellation points to shift from their ideal locations. EVM is a measure of these deviations from the ideal. In addition to overall EVM as a MIMO system test parameter, EVM as a function of frequency and EVM as a function of time can provide insights into transmitter performance when assessing MIMO channel behavior. In addition, EVM displayed versus subcarrier and symbol can offer further details on a MIMO transmitter’s performance.

Figure 3 An EVM constellation diagram provides a graphical indication of potential MIMO system problems.

Sharply defined points in an EVM constellation diagram indicate good MIMO system performance. In an example measurement of a 2 x 2 MIMO system with OFDM and 64QAM, color is used to differentiate the different transmitter signals as well as the pilot carriers. In the constellation diagram shown in Figure 3, red and blue dots represent the two transmit signals, Tx0 and Tx1, in the 2 x 2 MIMO system. They are overlaid on white dots, which represent the ideal locations for the subcarriers. Pilot carriers are shown by yellow dots, which are overlaid on white dots representing ideal pilot carrier locations.

Such a color-coded diagram makes it a simple matter to identify transmit signal problems. For example, red or blue subcarrier constellation points that were significantly offset from the ideal white points would indicate an I/Q imbalance, while a fuzzy appearance to the points would result from the effects of noise on the transmitted signals. A donut-shaped appearance to the constellation's points would be a sign of excessive phase noise.

Figure 4 Plotting condition number as a function of subcarrier shows the orthogonality of a MIMO channel's subcarrier.

In terms of more conventional X-Y type plots of performance, measurements of channel metrics basically show the health of the signal matrix in a MIMO system, plotting matrix condition versus subcarrier. The plot shown in Figure 4, that is a measure of the system’s capability to invert the channel and solve for the transmitted symbols, can be used to determine the orthogonality of each stream in the MIMO system. By transmitting inverted symbols, the coverage of the system can be analyzed. By transmitting parallel symbols, the system throughput can be evaluated.

Figure 5 The channel flatness and isolation can be evaluated by directly connecting MIMO transmitters to receivers.

Channel response measurements showing subcarrier flatness as a function of subcarrier number can shed light on the MIMO channel behavior. In example measurements made on an IEEE 802.16e OFDM channel as shown in Figure 5, the green trace shows the power of the signal from the first transmitter (Tx0) to the first receiver (Rx0); the upper red trace represents the signal from the second transmitter (Tx1) to the second receiver (Rx1) in a 2 x 2 MIMO system. The blue trace shows the signal from the first transmitter (Tx0) to the second receiver (Rx1) and the bottom red trace shows the signal from the second transmitter (Tx1) to the first receiver (Rx0). The power level versus subcarrier indicates channel flatness, while the difference between the first and indirect signals shows channel isolation (less than 40 dB in this example). These measurements were made by connecting transmitters directly to receivers with coaxial cables.

A number of measurements over time and over time and frequency can be used to show MIMO performance characteristics that may change under different conditions. For example, measurements of EVM versus OFDM symbol time help identify problems with interference or performance variations with time. Measurements of EVM versus subcarrier can be used to analyze in-channel effects of noise, such as spurious. Measurements of power versus OFDM symbol time can isolate in-band amplitude deviations. Measurements of frequency versus OFDM symbol time can be used to check frequency accuracy, isolating problems such as frequency drift over the duration of a packet.

Hardware Considerations

A test system for making MIMO measurements must accurately emulate the operation of the MIMO system, with the capabilities of generating signals with known frequency, amplitude and phase characteristics, and then capturing and analyzing those signals from a device under test (DUT). The test system must support the modulation formats of interest as well as the full modulation bandwidth of the system under test. For generating test signals, an arbitrary waveform generator or vector signal generator (VSG) provides the control needed to create practical test signals, while a vector signal analyzer (VSA) can serve as the test receiver. Any test system designed for MIMO testing should provide the required number of test signal sources and signal analyzers to match the transmitters and receivers in the system to be tested, and should be scalable to meet future requirements. For instance, the MIMO test system provided by Keithley Instruments is scalable from stand-alone VSGs and VSAs up to an 8 x 8 channel system and is flexible enough to handle any combination of sources and analyzers within that range.

Figure 6 Example of MIMO test system using multiple VSGs, VSAs and synchronization units (computer controlled).

Given that synchronization of multiple sources and analyzers is essential to achieving meaningful MIMO measurements, a common reference oscillator is needed for these instruments. For example, in the 2 x 2 MIMO measurement system shown in Figure 6, dedicated synchronization units are used for the multiple VSAs and VSGs. These units distribute common signals such as a local oscillator, common clock, and precise trigger, that provide for low sampler and RF carrier phase jitter, which is necessary for the most accurate and repeatable measurements required by OFDM MIMO signals. In particular, the synchronization unit provides for less than one degree of peak-to-peak jitter.

The effectiveness and ease of use of any MIMO test system also depends on the system’s test software. With the growing adoption of MIMO techniques in wireless communications systems, off-the-shelf test software solutions are commonly available for simplifying system and channel measurements. For example, Keithley’s SignalMeister™ RF Communications Test Toolkit software provides both complex signal generation and signal analysis capability for MIMO applications like WLAN 802.11n and WIMAX 802.16e Wave 2. In addition to extensive EVM and MIMO channel response measurements, this software can also be used to evaluate SISO systems.

The test equipment and measurements discussed so far apply to evaluating the performance of systems and their components for MIMO communications, typically under ideal conditions. But how well will a MIMO system perform under impaired signal conditions? In that case, a different type of test system is required, known as a channel emulator. It provides the means to exercise a MIMO system and its components with such channel impairments as signal fading, additive white Gaussian noise (AWGN), co-channel interference, and even Doppler effects, the type of problems that might be experienced by a mobile unit in a vehicle in motion relative to a base station.

A channel emulator must act as the transmitter and receiver in a MIMO system, but must also have the capabilities of attenuating signals and adding delays to model real-world conditions. A suitable channel emulator will also provide software-defined channel models, such as ITU M.1225 A and B profiles for WiMAX. A practical channel emulator should exceed the performance of the system that it is testing with full automation capabilities for manufacturing testing when needed. The emulator should also be bidirectional in function so that it can support channel models for both uplink and downlink testing. By also supporting calibrated reciprocal tests, the emulator will be useful in testing MIMO systems employing advanced beam-forming techniques. Finally, although the examples presented in this article have applied to 2 x 2 MIMO systems, an effective channel emulator should support testing of 4 x 4 MIMO systems in order to allow for hand-off testing between MIMO systems. As an example, the model ACE 400WB channel emulator from Azimuth Systems is a bidirectional unit capable of exercising 4 x 4 MIMO systems.