Signal Processing for Wireless Transceivers - Signal Processing Systems - page 177

generalized for the LSD version. The breadth-first tree search based K -best LSD
algorithm [ 49 , 107 , 135 ] is a variant of the well known M algorithm [ 5 , 64 ] . It keeps
the K nodes which have the smallest accumulated Euclidean distances at each level.
If the PED is larger than the squared sphere radius C 0 , the corresponding node will
not be expanded. We assume no sphere constraint or C 0 = ∞

, but set the value for K
instead, as is common with the K -best algorithms. The depth-first [ 111 ] and metric-
first [ 89 ] sphere detectors have a closer to optimal search strategy and achieve a
lower bit error rate than the breadth-first detector. However, the K -best LSD has
received significant attention, because it can be easily pipelined and parallelized
and provides a fixed detection rate. The breadth-first K -best LSD can also be more
easily implemented and provide the high and constant detection rates required in
the LTE.
In the discussion above, we have assumed mostly one-pass type receiver process-
ing. In other words, equalization/detection and channel estimation are performed
first. The detector soft output is then forwarded to the FEC decoder where the final
data decisions are made. However, the performance can be enhanced by iterative
information processing based on so called turbo principle [ 1 , 2 , 51 ] , originating from
the concept of parallel (or serial) concatenated convolutional codes often known as
turbo codes [ 15 , 16 , 107 ] . This means that the feedback from FEC decoder to the
equalizer as shown in Fig. 2 is applied. Therein, the decoder output extrinsic LLR
value is used as a priori LLR value in the second equalization iteration [ 138 ] . This
typically improves the performance at the cost of increased latency and complexity
[ 73 ] . Because the decoder is also usually iterative, the arrangement results in
multiple iterations, i.e., local iterations within the (turbo type) decoder and global
iterations between the equalizer and decoder. The useful number of iterations is
usually determined by computer simulations or semianalytical study of the iteration
performance.

2.4 Channel Estimation

The discussion above assumes that the channel realization or the matrix H is
perfectly known, which is the basic assumption in coherent receivers. Therefore,
channel estimation needs to be performed. This is usually based on transmitting
reference or pilot symbols known by the receiver [ 20 ] . By removing their impact, the
received signal reduces to the unknown channel realization and additive Gaussian
noise. Classical or Bayesian estimation framework [ 69 , 106 ] can be then applied
to estimate the channel realization. The channel time and frequency selectivity
and other propagation phenomena need to be appropriately modeled to create a
realistic channel model and corresponding estimation framework [ 93 ] . If orthogonal
frequency-division multiplexing (OFDM) [ 52 ] is assumed, the frequency-selectivity
of the channel can be handled very efficiently. This is a benefit from the equalizer
complexity perspective.