Application-Specific Accelerators for Communications - Signal Processing Systems - page 736

The spatial multiplexing MIMO system can be modeled similar to Eq. ( 1 ) with T = 1

since there is no coding across the time domain:

y = Hx + n , (2)

where H is the N M channel matrix, x is the M -element column vector where its

x i -th element corresponds to the complex symbol transmitted from the i -th antenna,
and y is the received N -th element column vector where y i is the perturbed received
element at the i -th receive antenna. The additive white Gaussian noise vector on the
receive antennas is denoted by n .
While spatial multiplexing can support very high data rates, the complexity
of the maximum-likelihood detector in the receiver increases exponentially with
the number of transmit antennas. Thus, unlike the case in Eq. ( 1 ) , the maximum-
likelihood detector for Eq. ( 2 ) requires a complex architecture and can be very
costly. In order to address this challenge, a range of detectors and solutions have
been studied and implemented. In this section, we discuss some of the main
algorithmic and architectural features of such detectors for spatial multiplexing
MIMO systems.

×

2.2.1 Maximum-Likelihood (ML) Detection

The Maximum Likelihood (ML) or optimal detection of MIMO signals is known to
be an NP-complete problem. The maximum-likelihood (ML) detector for Eq. ( 2 ) is
found by minimizing the

y

Hx

2
2

−

(3)

M . This brute-force search can be a
very complicated task, and as already discussed, incurs an exponential complexity
in the number of antennas, in fact for M transmit antennas and modulation order of
w

norm over all the possible choices of x ∈ Ω

, the number of possible x vectors is w M . Thus, unless for small dimension
problems, it would be infeasible to implement it within a reasonable area-time
constraint [ 11 , 25 ] .

= | Ω |

2.2.2 Sphere Detection

Sphere detection can be used to achieve ML (or close-to-ML) with reduced
complexity [ 19 , 31 ] compared to ML. In fact, while the norm minimization of Eq. ( 3 )
is exponential complexity, it has been shown that using the sphere detection method,
the ML solution can be obtained with much lower complexity [ 19 , 30 , 70 ] .
In order to avoid the significant overhead of the ML detection, the distance norm
can be simplified [ 16 ] as follows:

2

( )= −

D s y Hs

1
i = M | y i −

M
j = i R i , j s j |

Q H y

2 2

= − Rs = , (4)