Digital Signal Processing Reference
In-Depth Information
Transceiveroptimization:
summaryandtables
Thisappendixprovidesasummaryofeachofthemainoptimizationresults
presentedinPart2ofthisbook.Eachmainresultissummarizedinonepage.
Forfurtherdetailsseetheappropriatesectionsofthechapterswhicharecited
below.ThegeneralformofthememorylessMIMOtransceiverisshowninFig.
I.1.Set
B
=
0
foralineartransceiver.Fornonzero
B
(strictlyuppertriangular)
wehaveaDFEsystem.NotethatZF-MMSEstandsfortheMMSEsystemwith
zeroforcingandpureMMSEstandsfortheMMSEsystemwithoutzeroforcing.
Generalnotationsandassumptions
1.Thetransmittedpowerisdenotedas
p
0
.
Theterm“powerconstraint”
meansthatthetotalpowerattheoutputoftheprecoderisconstrainedto
be
p
0
.
2.Themeansquareerrorisdefinedas
E
[
2
]
,
andthemeansquare
errorpersymbolisthisquantitydividedby
M,
where
M
isthenumberof
elementsin
s
(
n
)
.
s
(
n
)
−
s
(
n
)
3.Thenotation[
A
]
M
denotesthe
M
M
leadingprincipalsubmatrixof
A
(i.e.,thematrixobtainedbyretainingthefirst
M
rowsandcolumnsofthe
matrix
A
).
×
4.Weassume
q
(
n
)and
s
(
n
)arezero-mean,jointlyWSSprocesseswith
R
qq
=
σ
2
q
I
.
Furthermore,
R
ss
=
σ
2
s
I
,
exceptinthebitallocationprob-
lem.
5.Thechannel
H
hassingularvaluedecomposition(SVD)oftheform
H
=
U
h
Σ
h
V
†
h
,
812
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