Additionally, beamforming can be used to further optimize the wireless connection between transmitters and receivers. With beamforming, a MIMO receiver first tries to estimate the channel matrix (the channel between the transmitter and the receiver), and tells the transmitter how to pre-compensate on a tone-by-tone basis to optimize SNR of the received signal. If done dynamically, the MIMO receiver and transmitter can work together on beam re-direction, estimating, mitigating and/or pre-empting the adverse effects of any objects blocking or deflecting the beam. Ideally, the forward and backward channels must both be accurately estimated separately, which requires explicit (rather than implicit) beamforming to avoid issues related to potentially inaccurate nonlinearity associated with power amplifiers in the downstream and upstream directions of the link, and any possible mis-calibration typically associated with implicit beamforming.
Beyond The Raw Numbers: Outage Probability
In analyzing data rates it is not sufficient to look at simulated rate reach curves, where the results are upper-bounded due to fixed assumptions about the channel. It is very important to consider the MIMO system's outage probability, or the percentage of channels unable to support a specific data rate. With ideal code, outage probability is equal to PER. With non-ideal code, outage probability is at the lower bound of PER. The analysis in Table 1 shows the outage probability for two cases using different MIMO systems with IEEE channel model B. The first supports 150Mbps using one spatial stream with 64QAM. The second supports 300Mbps using two spatial streams with 64QAM modulation index.
In a 3x3 MIMO system supporting two streams of 64 QAM , 31.9 percent of the channels would not provide "reliable" transmission for two streams of 64QAM at the specific received SNR per chain-20 dB in this case. This is compared to a 4x4 system with an outage probability of 1 percent.
The probability of achieving full channel (or ergodic) capacity is fairly low without the help of transmit beamforming. It is relatively difficult to achieve full capacity unless channel state information (CSI) is known to the transmitter. This is because the transmitted symbol (codeword) should be spanned over all possible channel conditions (matrices) over all possible locations, and the packet duration should be longer than coherence time. Consequently, transmit beamforming also must be adaptive. If the channel changes and the system does not adapt quickly and dynamically through adaptive beamforming, there would be capacity (data rate) loss and no chance of achieving maximum channel capacity and full data rate.
Adequate beamforming update rate is also required in order to deal with the dynamics associated with activities in a home environment that impact channel conditions - from people walking around the home to a fan running in the living room. One parameter that could influence the beamforming update rate is the memory depth of the H.264 (or equivalent) decoder and its ability to conceal some of the error conditions. High compression ratios require very deep memory (on the order of 100msec). So, a good beamforming update rate should be designed to be between 20msec and 100mesc, which also can be adaptive in this range, depending on channel conditions.
Comparing MIMO Systems
Generally, correlated MIMO channels possess fewer degrees of freedom relative to ideal, fully scattered channels. As the SNR decreases, the number of spatial streams also decreases, which reduces the multiplexing gain of the MIMO system. Fig. 3 compares various MIMO systems and their associated rate/reach curves for the same channel conditions. This analysis focuses on a channel model consisting of three 10 dB walls spaced very close to the transmitter.
FIGURE 3 • Typical simulation graph used to show over-the-air bitrate. PER is set to about 1%, and packet retransmission is needed to achieve desired reliability at the expense of delay. In this model, at a distance of 50 feet, the 4x4 system's throughput outperforms that of a 3x3 system by about 180%.
Note that as distance increases and SNR decreases, the number of spatial streams also decreases. For a given a 4x4 system at sufficiently long distance and with enough attenuation, all versions of 4x4 MIMO systems will operate in one or two spatial streams.
While 2x2 MIMO is completely unsuitable, 3x3 MIMO technology offers insufficient performance for a long-term home-networking solution. 3x3 MIMO technology also is losing its cost advantage over emerging 4X4 solutions, whose cost of goods (COG) delta is expected to shrink to below $1 over time as it benefits from economies of scale. The new generation of 4x4 MIMO technology (with 4 spatial streams capable of unequal modulation, plus LDPC and dynamic beamforming) will provide significantly better coverage than alternative solutions, and we would expect it to exceed 120-150 Mbps over 95% homes and, as a result, reduce the overall cost of deployment for both carriers and consumers. Even with the remaining very large homes (i.e. 7000 sq. ft.or more), one can easily use a single mesh node with frequency re-use capability to achieve near 100% coverage in all homes across the globe.
Consumers expect the same quality in their wireless connections as they do from wired Ethernet. 4x4 MIMO solutions deliver up to four HD video streams at more than 100 Mbps data rates, over 100 feet, with near-zero PER data transfers, regardless of signal impairments and dead zones that are typical in the home. Ongoing advances will deliver further improvements in throughput, reach and reliability.
About the Author
Behrooz Rezvani, Ph.D., is founder, president and chairman of Quantenna Communications Inc.