MIMO

MIMO can be sub-divided into three main categories: precoding, spatial multiplexing (SM), and diversity coding.

Precoding is multi-stream beamforming, in the narrowest definition. In more general terms, it is considered to be all spatial processing that occurs at the transmitter. In (single-stream) beamforming, the same signal is emitted from each of the transmit antennas with appropriate phase and gain weighting such that the signal power is maximized at the receiver input. The benefits of beamforming are to increase the received signal gain – by making signals emitted from different antennas add up constructively – and to reduce the multipath fading effect. In line-of-sight propagation, beamforming results in a well-defined directional pattern. However, conventional beams are not a good analogy in cellular networks, which are mainly characterized by multipath propagation. When the receiver has multiple antennas, the transmit beamforming cannot simultaneously maximize the signal level at all of the receive antennas, and precoding with multiple streams is often beneficial. Note that precoding requires knowledge of channel state information (CSI) at the transmitter and the receiver.

Spatial multiplexing requires MIMO antenna configuration. In spatial multiplexing,[33] a high-rate signal is split into multiple lower-rate streams and each stream is transmitted from a different transmit antenna in the same frequency channel. If these signals arrive at the receiver antenna array with sufficiently different spatial signatures and the receiver has accurate CSI, it can separate these streams into (almost) parallel channels. Spatial multiplexing is a very powerful technique for increasing channel capacity at higher signal-to-noise ratios (SNR). The maximum number of spatial streams is limited by the lesser of the number of antennas at the transmitter or receiver. Spatial multiplexing can be used without CSI at the transmitter, but can be combined with precoding if CSI is available. Spatial multiplexing can also be used for simultaneous transmission to multiple receivers, known as space-division multiple access or multi-user MIMO, in which case CSI is required at the transmitter.[34] The scheduling of receivers with different spatial signatures allows good separability.

Diversity coding techniques are used when there is no channel knowledge at the transmitter. In diversity methods, a single stream (unlike multiple streams in spatial multiplexing) is transmitted, but the signal is coded using techniques called space-time coding. The signal is emitted from each of the transmit antennas with full or near orthogonal coding. Diversity coding exploits the independent fading in the multiple antenna links to enhance signal diversity. Because there is no channel knowledge, there is no beamforming or array gain from diversity coding. Diversity coding can be combined with spatial multiplexing when some channel knowledge is available at the receiver.

Third Generation (3G) (CDMA and UMTS) allows for implementing space-time transmit diversity schemes, in combination with transmit beamforming at base stations. Fourth Generation (4G) LTE And LTE Advanced define very advanced air interfaces extensively relying on MIMO techniques. LTE primarily focuses on single-link MIMO relying on SpatialMultiplexing and space-time coding while LTE-Advanced further extends the design to multi-user MIMO. In wireless local area networks (WLAN), the IEEE 802.11n (Wi-Fi), MIMO technology is implemented in the standard using three different techniques: antenna selection, space-time coding and possibly beamforming.[47]

Spatial multiplexing techniques make the receivers very complex, and therefore they are typically combined with orthogonal frequency-division multiplexing (OFDM) or with orthogonal frequency-division multiple access (OFDMA) modulation, where the problems created by a multi-path channel are handled efficiently. The IEEE 802.16e standard incorporates MIMO-OFDMA. The IEEE 802.11n standard, released in October 2009, recommends MIMO-OFDM.

MIMO is also planned to be used in mobile radio telephone standards such as recent 3GPP and 3GPP2. In 3GPP, High-Speed Packet Access plus (HSPA+) and Long Term Evolution (LTE) standards take MIMO into account. Moreover, to fully support cellular environments, MIMO research consortia including IST-MASCOT propose to develop advanced MIMO techniques, e.g., multi-user MIMO (MU-MIMO).

MIMO wireless communications architectures and processing techniques can be applied to sensing problems. This is studied in a sub-discipline called MIMO radar.

MIMO technology can be used in non-wireless communications systems. One example is the home networking standard ITU-T G.9963, which defines a powerline communications system that uses MIMO techniques to transmit multiple signals over multiple AC wires (phase, neutral and ground).[2]

MIMO channel model

In MIMO systems, a transmitter sends multiple streams by multiple transmit antennas. The transmit streams go through a matrix channel which consists of all ${\displaystyle N_{t}N_{r}}$ paths between the ${\displaystyle N_{t}}$ transmit antennas at the transmitter and ${\displaystyle N_{r}}$ receive antennas at the receiver. Then, the receiver gets the received signal vectors by the multiple receive antennas and decodes the received signal vectors into the original information. A narrowband flat fading MIMO system is modelled as:

${\displaystyle \mathbf {y} =\mathbf {H} \mathbf {x} +\mathbf {n} }$

where ${\displaystyle \mathbf {y} }$ and ${\displaystyle \mathbf {x} }$ are the receive and transmit vectors, respectively, and ${\displaystyle \mathbf {H} }$ and ${\displaystyle \mathbf {n} }$ are the channel matrix and the noise vector, respectively.

Ergodic closed-loop (channel is known, perfect CSI) and ergodic open-loop (channel is unknown, no CSI) capacities. Number of transmit and receive antennas is 4 (${\displaystyle N_{r}=N_{t}=4}$).[48]

Referring to information theory, the ergodic channel capacity of MIMO systems where both the transmitter and the receiver have perfect instantaneous channel state information is[49]

${\displaystyle C_{\mathrm {perfect-CSI} }=E\left[\max _{\mathbf {Q}$ ;\,{\mbox{tr}}(\mathbf {Q} )\leq 1}\log _{2}\det \left(\mathbf {I} +\rho \mathbf {H} \mathbf {Q} \mathbf {H} ^{H}\right)\right]=E\left[\log _{2}\det \left(\mathbf {I} +\rho \mathbf {D} \mathbf {S} \mathbf {D} \right)\right]}

where ${\displaystyle ()^{H}}$ denotes Hermitian transpose and ${\displaystyle \rho }$ is the ratio between transmit power and noise power (i.e., transmit SNR). The optimal signal covariance ${\displaystyle \mathbf {Q} =\mathbf {VSV} ^{H}}$ is achieved through singular value decomposition of the channel matrix ${\displaystyle \mathbf {UDV} ^{H}\,=\,\mathbf {H} }$ and an optimal diagonal power allocation matrix ${\displaystyle \mathbf {S} ={\textrm {diag}}(s_{1},\ldots ,s_{\min(N_{t},N_{r})},0,\ldots ,0)}$. The optimal power allocation is achieved through waterfilling,[50] that is

${\displaystyle s_{i}=\left(\mu -{\frac {1}{\rho d_{i}^{2}}}\right)^{+},\quad {\textrm {for}}\,\,i=1,\ldots ,\min(N_{t},N_{r}),}$

where ${\displaystyle d_{1},\ldots ,d_{\min(N_{t},N_{r})}}$ are the diagonal elements of ${\displaystyle \mathbf {D} }$, ${\displaystyle (\cdot )^{+}}$ is zero if its argument is negative, and ${\displaystyle \mu }$ is selected such that ${\displaystyle s_{1}+\ldots +s_{\min(N_{t},N_{r})}=N_{t}}$.

If the transmitter has only statistical channel state information, then the ergodic channel capacity will decrease as the signal covariance ${\displaystyle \mathbf {Q} }$ can only be optimized in terms of the average mutual information as[49]

${\displaystyle C_{\mathrm {statistical-CSI} }=\max _{\mathbf {Q} }E\left[\log _{2}\det \left(\mathbf {I} +\rho \mathbf {H} \mathbf {Q} \mathbf {H} ^{H}\right)\right].}$

The spatial correlation of the channel has a strong impact on the ergodic channel capacity with statistical information.

If the transmitter has no channel state information it can select the signal covariance ${\displaystyle \mathbf {Q} }$ to maximize channel capacity under worst-case statistics, which means ${\displaystyle \mathbf {Q} =1/N_{t}\mathbf {I} }$ and accordingly

${\displaystyle C_{\mathrm {no-CSI} }=E\left[\log _{2}\det \left(\mathbf {I} +{\frac {\rho }{N_{t}}}\mathbf {H} \mathbf {H} ^{H}\right)\right].}$

Depending on the statistical properties of the channel, the ergodic capacity is no greater than ${\displaystyle \min(N_{t},N_{r})}$ times larger than that of a SISO system.

One of the main problems in MIMO is knowing the channel matrix ${\displaystyle \mathbf {H} }$ at the receiver. In practice, in communication systems, the transmitter sends a Pilot signal and the receiver learns the state of the channel (i.e., ${\displaystyle \mathbf {H} }$) from the received signal ${\displaystyle Y}$ and the Pilot signal ${\displaystyle X}$. There are several algorithms for estimating ${\displaystyle \mathbf {H} }$ from multiple received signals ${\displaystyle Y}$ and the Pilot signal ${\displaystyle X}$, such as zero-forcing,[51] successive interference cancellation a.k.a. V-blast, Maximum likelihood estimation (assuming the noise is Gaussian) and recently, Neural network MIMO Detection.[52][53] As the number of antennas at the transmitter and receiver grows, the MIMO detection problem becomes more difficult and the Neural network approach becomes superior, especially in the presence of impairments.[52]

MIMO signal testing focuses first on the transmitter/receiver system. The random phases of the sub-carrier signals can produce instantaneous power levels that cause the amplifier to compress, momentarily causing distortion and ultimately symbol errors. Signals with a high PAR (peak-to-average ratio) can cause amplifiers to compress unpredictably during transmission. OFDM signals are very dynamic and compression problems can be hard to detect because of their noise-like nature.[54]

Knowing the quality of the signal channel is also critical. A channel emulator can simulate how a device performs at the cell edge, can add noise or can simulate what the channel looks like at speed. To fully qualify the performance of a receiver, a calibrated transmitter, such as a vector signal generator (VSG), and channel emulator can be used to test the receiver under a variety of different conditions. Conversely, the transmitter's performance under a number of different conditions can be verified using a channel emulator and a calibrated receiver, such as a vector signal analyzer (VSA).

Understanding the channel allows for manipulation of the phase and amplitude of each transmitter in order to form a beam. To correctly form a beam, the transmitter needs to understand the characteristics of the channel. This process is called channel sounding or channel estimation. A known signal is sent to the mobile device that enables it to build a picture of the channel environment. The mobile device sends back the channel characteristics to the transmitter. The transmitter can then apply the correct phase and amplitude adjustments to form a beam directed at the mobile device. This is called a closed-loop MIMO system. For beamforming, it is required to adjust the phases and amplitude of each transmitter. In a beamformer optimized for spatial diversity or spatial multiplexing, each antenna element simultaneously transmits a weighted combination of two data symbols.[55]

• NIST UWB-MIMO Channel Propagation Measurements in the 2–8 GHz Spectrum
• Literature review of MIMO
• Antenna and Wireless Multipath Virtual Channel Interaction