Signal Processing - March 2017 - 55

due to quantization distortion causes resid8 bits/sample. The performance of the
Multicasting plays an
quantization scheme is gauged in terms
important role in vehicular ual multiuser interference, degrading the
achievable throughput. We observe a signifof the signal distortion introduced by
communications, since it
icantly better performance of RBD at low
the quantization process. We employ the
enables efficient sharing
signal-to-noise ratio (SNR), since this methchordal distance on the corresponding
of common information,
od implicitly reduces the number of served
manifold as distortion metric; see [18]
users with decreasing SNR via power allofor details. In Figure 7(a), we compare
such as traffic
cation; BD precoding, on the other hand,
the quantization distortion of predictive
management advices and
always serves three users in parallel each
quantization to memoryless and differenvehicle status updates,
with two spatial streams. At high SNR, BD
tial quantization. Memoryless quantizaamong vehicles.
performs slightly better due to the lower
tion refers to a quantization scheme that
quantization distortion of its Grassmannian
considers each sample m [k] individually
quantizer, causing less residual multiuser interference as comwithout accounting for the past of the process {m [k]}. Difpared to RBD with Stiefel manifold quantization. Notice that, in
ferential quantization refers to the case m p [k] = m q [k - 1] .
this simulation, we assume CSI feedback every millisecond
Both differential and predictive quantization achieve an
and negligible feedback delay between the users and the base staimprovement over memoryless quantization for x s # 0.1;
tion. In the considered low-mobility scenario with fd = 10 Hz,
x
at large s , the distortion of differential/predictive quantizathis is, however, not a significant restriction, because a reation saturates at the performance of memoryless quantization.
sonable feedback delay can be compensated via channel
Hence, the considered differential/predictive quantization
prediction at the receiver; see [12] for a breakdown of the conschemes achieve a significant gain only at low mobility; e.g.,
tributions of quantization and delay compensation onto the
assuming t s = 1 ms, fc = 800 MHz, the point x s = 0.01 coroverall distortion.
responds to v = 13.5 km/h. Since CSI feedback in LTE is
At high mobility, the presented CSI feedback method fails
currently at most foreseen once every subframe (once every
to achieve significant multiuser MIMO gains due to insuffimillisecond), this implies that currently available differential/
cient accuracy of CSIT. To support high-mobility scenarios,
predictive manifold quantization schemes are only advanit would be necessary to reduce the sampling and feedback
tageous at low mobility and not in vehicular scenarios. Perinterval x s at least by a factor of ten. Additional gains might
formance can be improved by extending the codebook size;
however, complexity issues will ultimately put limits on the
also be possible by improving the prediction function in (7); in
supported size.
our simulations, we employed linear prediction in combination
In Figure 7(b), we show the throughput of BD and RBD
with LMS to optimize filter coefficients. Alternatively, preprecoding when applying predictive Grassmannian and Stiefel
coding schemes that are robust with respect to outdated CSIT,
manifold quantization to obtain CSIT. We show the perforsuch as retrospective interference alignment, can be utilized.
mance relative to RBD with perfect CSIT. Imperfect CSIT
In general, though, such schemes require coding over many

10-1

95% Confidence Interval
Memoryless
Quantization
Differential
Quantization

10-2
10-3

Predictive
Quantization

10-4
10-5
10-3

Stiefel Manifold
Grassmann Manifold

Perfect CSI

95% Confidence Interval

100
Relative Sum Rate (%)

Quantization Distortion

100

Pred
Quanictive
tizatio
n

80
70

Di
Qu ffere
an ntia
tiza l
tion

60
50

Stiefel Manifold, RBD
Grassmann Manifold, BD

40
30

10-2
Normalized Sampling Interval

10-1

(a)

15
SNR (dB)

(b)

Figure 7. The quantization error of (a) manifold quantizers and (b) throughput comparison of RBD and BD with limited feedback at normalized sampling
interval x s = 0.01 and 8-b quantization codebook. We consider antenna arrays of size N t # N r = 6 # 2 .
IEEE SIgnal ProcESSIng MagazInE

March 2017

Table of Contents for the Digital Edition of Signal Processing - March 2017