### Highlights

- MIMO uses multiple transmit and receive antennas to increase capacity
- Different principles apply when MIMO is used in microwave systems
- MIMO makes sense in microwave systems with high frequencies, short hops

With the right deployment strategy, Multiple Input Multiple Output (MIMO) technology can increase capacity in LTE, WiMAX and microwave networks. But MIMO works differently in line-of-sight networks such as LTE and WiMAX than it does in line-of-sight microwave networks. To take full advantage of MIMO’s benefits, service providers need to understand MIMO, how it works, and why it works differently in different networks.

### The MIMO advantage

MIMO uses at least 2 — sometimes several — antennas on the transmit (Tx) side and on the receive (Rx) side to transmit a single channel. This approach increases data rates and spectral efficiency. For example, adding 6 antennas on each side delivers the same capacity increase as adding 100 times more power to a Singe Input Single Output (SISO) channel. The techniques used in MIMO increase capacity linearly with the number of antennas. In contrast, the approaches used in SISO, Single Input Multiple Output (SIMO) and Multiple Input Single Output (MISO) systems increase capacity logarithmically. Linear capacity increases provide a much more efficient path to higher capacities than logarithmic increases. The transmitter and receiver used in MIMO are more complex than in SISO, SIMO and MISO transmissions, but they don’t use more power. The MIMO advantage is so clear that many standards have already incorporated the technology. They include the:

- International Telecommunications Union (ITU) High Speed Downlink Packet Access (HSPDA) standard, which is part of the Universal Mobile Telecommunications System (UMTS) standard.
- Institute of Electrical and Electronics Engineers (IEEE) 802.11n standard used in wireless routers for the home.
- IEEE 802.16 standard for the mobile WiMAX technology used in cell phones.
- ITU LTE standard.

### MIMO meets Shannon

When MIMO systems were first described in the mid-to-late 1990s by Gerard Foschini and others, the dramatic bandwidth efficiency enabled seemed to violate Shannon’s law. In reality, the diversity and signal processing used in MIMO transform a single point-to-point channel into multiple parallel channels. Shannon’s law is based on a noisy channel with channel capacity C and information transmitted at a rate R. It then states that if R is less than C, there must be codes that allow the probability of error at the receiver to be made arbitrarily small. This means that, theoretically, it is possible to transmit information nearly without error at any rate below a limiting rate, C. This capacity is usually expressed in the form: C = W log2(1 + S/N) Where:

- C is the channel capacity in bits per second
- W is the bandwidth in Hertz
- S/N is the signal-to-noise ratio (SNR)

To determine the capacity of a channel with an SNR of 50 dB and bandwidth of 20 MHz, the math looks like this: C=20*log2(1+50)=20*5.6=112 Mb/s The capacity increases as a log function of the SNR, which is a slow increase. This example uses a 20 MHz channel, the channel spacing that is typically used in LTE and LTE-Advanced. But LTE-Advanced capacity at 20 MHz is 500 Mb/s or higher — clearly well beyond Shannon’s limit. One way to go beyond Shannon’s limit is to boost the SNR and the power transmitted by the base station. But even with an SNR of 100, throughput with 20 MHz channel spacing is only 133 Mb/s, far short of the 500 Mb/s that is possible with LTE-Advanced. That’s where MIMO comes in. It’s the not-so-secret ingredient in this high-capacity recipe.

### MIMO in LTE and WiMAX networks

The formula below is used to calculate the Shannon limit for MIMO. The maximum capacity that a MIMO system can achieve depends how the channel is created, not just the SNR as is the case in SISO systems. In mathematical terms, MIMO system performance depends on the condition of the channel matrix H and its properties. Think of the H channel matrix as a set of simultaneous equations. Each equation represents a received signal composed of a unique set of channel coefficients that are applied to the transmitted signal. The system performs best when the H matrix is full rank, with each row and column meeting conditions of independence. In other words, a matrix is full rank if the linear system defined by the matrix can be solved. This means that optimal system performance is only possible when each channel is fully independent of all others. And channels can only be fully independent of one another in an environment with extensive scattering, fading, reflections and other effects. Although this seems like a counter-intuitive statement, the only way to extract the transmitted information is when the H matrix is invertible. The H matrix can only be invertible if all of its rows and columns are uncorrelated, a concept taught in linear algebra. And rows and columns can only be uncorrelated when scattering, fading, reflections and other effects are present. This is the typical scenario for LTE and WiMAX networks, especially in dense urban areas.

### MIMO in point-to-point microwave networks

In a point-to-point microwave system, a matrix might consist of 2 transmit antennas and 2 receive antennas, as shown in Figure 1. This is referred to as a 2x2 MIMO system.

**If H12 represents the traffic traveling from transmit antenna 1 to receive antenna 2, the matrix becomes:**

- r1 = h11 t1 + h12 t2
- r2 = h21 t1 + h22 t2

Where:

- r1 = signal received at antenna 1
- r2 = signal received at antenna 2

In a line-of-sight system: r1 = t1 + t2 r2 = t1+ t2 So that, H = 1 1 1 1 Even with limited knowledge of math, it is clear that the equation has no solution and cannot be solved. With these results, it seems that MIMO does not apply to point-to-point microwave systems. The reality is that MIMO does apply to point-to-point microwave systems, but with different principles.

### Line-of-sight MIMO for microwave

In point-to-point microwave systems, MIMO does not rely on the fact that the received signals are uncorrelated due to scatter, reflections and fading to increase capacity. Instead, it relies on geometric spacing among receive and transmit antennas. With the right spacing among antennas, the interfering signal can be cancelled to double capacity between endpoints. To cancel the interfering signal, the propagation difference between the 2 paths must allow the 2 received signals to be orthogonal to each other at the receiver modems. In conventional MIMO systems, the differences in path propagation can be created using physical objects in the environment. This approach is not possible with microwave links because they are typically line-of-sight connections and use highly directional antennas. However, microwave links use high carrier frequencies. This makes it possible to use antenna spacing to design a 2×2 MIMO channel with the required orthogonal phase difference between short and long paths at the receiver end. This is commonly referred to as a Line-of-Sight (LoS) MIMO system In a 2x2 MIMO system, the required phase difference between paths at the receiver end is 90°. Figure 2 illustrates this principle.

**When the ideal phase difference of 90° is in place, the interfering signal can be completely cancelled. This creates two independent channels, effectively doubling the available channel capacity. The high frequencies used in microwave have very short wavelengths. However, the geometric characteristics of the propagation path mean that relatively large spaces are required between antennas to achieve the ideal phase shift. The graph in Figure 3 shows the optimal antenna spacing for different hop lengths and microwave frequencies.**

**The antenna spacing requirements for shorter hop lengths and higher frequencies are achievable. However, for systems with low frequencies and long links, the antenna spacing requirements become quite high, making them impractical or impossible to meet.**

### MIMO makes sense

MIMO is a powerful technique to increase capacity in non-LoS LTE and WiMAX networks. And LoS MIMO can play an important role in increasing capacity in certain point-to-point microwave scenarios. Service providers that understand when and where MIMO makes sense will be in the best position to make the most of MIMO. To contact the authors or request additional information, please send an e-mail to techzine.editor@alcatel-lucent.com.

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