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Fig. 5. Data transmission throughput versus SNR ina2 × 2 H-BLAST system
and correlated TU channel.
Fig. 6. Data transmission throughput versus SNR ina2 × 2 H-BLAST system
and uncorrelated channel.
A. 2 × 2 MIMO System
The throughput performances of the LMMSE, SIC and
А-best detectors with 4-QAM, 16-QAM, and 64-QAM and
two transmit and receive antennas is illustrated in Figs. 5-7.
The highly correlated TU channel is applied in 5 and a spatially
uncorrelated channel in 6; both figures assume horizontal en-
coding denoted as H-BLAST. A moderately correlated channel
and vertical coding (denoted as V-BLAST) was assumed in
Fig. 7. A real valued signal model was assumed in the .A-best
LSD and QRD of the channel matrix H with no sorting of the
layers was used.
The results in Fig. 5 show that the A-best LSD outperforms
the SIC receiver with all modulations under high correlation.
Only the 8-best LSD with 64-QAM performs worse than the
SIC in low SNRs. Using the turbo decoder outputs to update
the LLRs in the LSD receiver improves the performance by
roughly 1 dB compared to the LSD without any iterations. With
64-QAM, approximately the same performance is achieved with
8-best and two iterations as with 16-best without iterations. Per-
forming interference cancellation improves the performance up
IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 58, NO. 6, JUNE 2010
to 4 dB compared to the LMMSE receiver. Turbo decoding for
the bit LLRs is performed once both in the SIC receiver and the
A-best receiver with no iterations. The iterative A-best LSD in-
cludes turbo decoding the bit LLRs twice.
The SIC receiver also outperforms the А-best LSD when the
channel has no correlation as presented in Fig. 6. With highly
correlated channels, the initial decisions in the SIC receiver are
more likely to be incorrect which is found to lead to error prop-
agation.
The SIC receiver improves the performance of the LMMSE
receiver only very marginally in the vertically encoded system,
as illustrated in Fig. 7. This is understandable and not surprising
at all, because both layers have to be decoded before soft inter-
ference cancellation can be performed. Thus, the SIC receiver
provides no benefit compared to the plain LMMSE receiver in
the vertically encoded case, and it will be considered for the hor-
izontally encoded case only in the sequel. The А-best LSD, on
the other hand, performs similarly to the horizontally encoded
case.
B. 4× 4 MIMO System
The data transmission throughput versus SNR with four
transmit and receive antennas is presented in Fig. 8. Two
streams are encoded separately and the first stream is multi-
plexed onto the first two antennas and the second stream onto
the third and fourth antenna [21]. Two iterations are performed
with the SIC receiver. The symbols from the strongest layers
are detected and decoded first and then cancelled from the
remaining layers. The streams from the spatially multiplexed
layers are separated only with the LMMSE equalizer in the SIC
receiver. Interference cancellation is performed only between
the two horizontally encoded streams. The correlation of the
channels used in the simulations depends on the BS azimuth
spreads of 2 degrees and 5 degrees, and it varied from 0.7 in
Fig. 8(a) to 0.4 in Fig. 8(b). In the correlated TU channel, the
A-best LSD outperforms the SIC and the LMMSE receivers.
In the uncorrelated channel, the difference in performance is
smaller and the SIC receiver outperforms the А-best LSD.
With moderate correlation, the SIC performance is close to that
of the А-best LSD. The performance of the SIC receiver is
worse in the 4 × 4 antenna case than in the 2 × 2 case because
cancellation is performed between the two streams and only
LMMSE detection is used in the vertically encoded streams.
This is due to the LTE encoding structure, which was described
in the beginning of Section III.
C. Enhanced Tree Search and LLR Calculation
The impact of the enhanced tree search described in
Section II-B-1) on the performance in a 2 × 2 64-QAM case is
shown in Fig. 9. It can be seen that the performance degradation
is minimal but the detection rate will be doubled. The new
strategy is the most beneficial with high order modulations,
when the nodes have several branches. When a lower order
modulation is used, the performance degrades more with the
new strategy.
The LLR calculation in the А-best LSD is simplified from
(7) by leaving out the refinement part from (7). The impact of
using the simplified LLR calculation is presented in Fig. 10.