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# Create wireless base station MIMO antennae (Part 2)

Posted: 14 Nov 2014     Print Version

Keywords:Multiple Input Multiple Output  MIMO  antenna design  maximum likelihood  ML

Read Part 1 of this series here.

In MIMO antenna design, the maximum likelihood (ML) receiver has consider advantages, however their implementation can be quite complex.

The maximum likelihood (ML) receiver estimator solves the following equation:

For the sake of simplicity, let's use a SISO single transmit and receive antenna configuration as an example. In this case, y is the signal sampled at the receiver, s is the transmitted symbol, and H is the channel impulse response describing the channel between the transmit antenna and receive antenna.

The receiver looks for the transmitted symbol s, which minimises this absolute value:

in which s belongs to a group of finite values that are defined by the symbol modulation. For 64QAM modulation, for example, s can have 64 different values.

Basically, this boils down to an exhaustive search. The receiver must scan all possible values of s to find the one that when multiplied by the estimated channel H will be closest to the received signal.

For a SISO system this is quite simple, but when moving to a MIMO system the complexity grows exponentially. For example, in a 2X2 MIMO configuration with 64QAM modulation, s is a vector of two values. The first antenna can transmit 64 different symbols and the second antenna can also independently transmit one of 64 possible symbols. There are a total of 642 or 4096 values of s that must be evaluated.

For 2X2 MIMO, a number of algorithms are used to reduce complexity of the ML receiver. Worth noting is the LORD algorithm, which is capable of reducing the search complexity from 642 options to 64*2 or 128 evaluations reaching ML precision.

For 4X4 MIMO 64QAM this number now grows to 644, or 16,777,216 different values of s that must be evaluated. Solving this magnitude of complexity requires a new approach; this is where the suboptimal ML receivers come in to play.

 Figure 7: MIMO symbol tree.

Suboptimal ML receivers try to scan the possible transmitted signals in a more efficient way, thereby reducing the overall complexity and reaching near-ML precision results. The reduced complexity contributes to a more practical hardware implementation in terms of area and power. This also enables the hardware to keep up with the high throughputs defined by advanced communications standards.

Solving a suboptimal ML equation may be defined as a tree search (figure 7) in which each level of the tree corresponds to a transmitted symbol. The number of the branches protruding from each node matches the QAM or modulation of the transmitted symbol. A 4X4 MIMO configuration is represented by a four-level tree. If the modulation is BPSK, each node will contain two branches.

Once the tree symbol is defined, tree traversal algorithms may be deployed, borrowing from other fields such as computer science.

In this context, suboptimal ML receivers can be partitioned into two main types: breadth first search, and depth first search

Breadth first search. An example of breadth first is the K-best algorithm. This decoder is a fixed-complexity solution that starts from the tree root and ascends until it reaches the last level of the tree.

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