Digital Signal Processing Reference
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antennas at the receiver is achievable at a reasonable price. In the resulting multiple
antennas with a single RF chain receiver scenario, only traditional selection or switched
combining schemes can be employed to explore the diversity benefit. In this chapter, we
complement the previous work on joint adaptive transmission and diversity combining
by extending the design and analysis in [18, 19] to the lower-complexity selection and
switched combining schemes. The proposed joint design can also apply to a transmit
diversity system to achieve high efficiency with low feedback load and no power spread-
ing loss.
The selection combining (SC) scheme [4, section 6.2] has much lower complexity than
MRC. The receiver with SC uses only the best diversity paths of all available ones. This
nevertheless requires the estimation and comparison of the quality indicators, such as
the signal-to-noise ratio (SNR), of all diversity paths. With switched combining, where
switch-and-stay combining (SSC) is the popular example [20-27], the complexity is fur-
ther reduced by eliminating the need for simultaneously checking the path quality of all
diversity paths. In fact, SSC, where the combiner switches to the other branch only when
the output SNR of the current branch is below a certain threshold, can be viewed as the
origin of aforementioned adaptive combining schemes such as MS-GSC and OT-MRC.
Recent applications (such as transmit diversity, for example) have also motivated studies
of multibranch switch-and-examine combining (SEC) [28, 29]. In particular, with SEC,
if the current path is not of acceptable quality, then the combiner switches and examines
the quality of the next available path. This switching-and-examining process is repeated
until either an acceptable path is found or all available diversity paths have been exam-
ined. In the latter case, the combiner either settles on the last examined path [28] or
connects to the receiver the path with the best quality among all examined paths, and
this SEC variant is known as SEC with post-examine selection (SECps) [29].
In this chapter, we study joint adaptive transmission and diversity combining with
SC, SEC, and SECps schemes. We first examine the spectral efficiency benefit provided
by the SC scheme for adaptive transmission systems. Then, capitalizing on the adap-
tive nature of switched combining, we develop more integrated joint designs based on
the SEC and SECps schemes. In particular, the resulting system jointly selects the most
appropriate transmission mode and diversity paths based on the current channel con-
ditions and the desired bit error rate (BER) requirement. Depending on the primary
objective of the joint design, we arrive at a scheme that requires a minimum number of
path estimations (termed as minimum estimation scheme) and a scheme with a high
bandwidth efficiency (termed as bandwidth-efficient scheme), both of which satisfy the
desired BER requirement. For both schemes under consideration, we quantify through
accurate analysis their processing complexity (quantified in terms of average number
of paths estimated), spectral efficiency (quantified in terms of average number of trans-
mitted bits/s/Hz), and performance (quantified in terms of average BER). Finally, some
selected numerical examples are presented to illustrate the mathematical formalism.
The rest of this chapter is organized as follows. Section 6.2 contains the general
description of the system and channel model under consideration. While section 6.3
addresses the design and analysis of SC-based joint adaptive modulation and diver-
sity combining schemes, section 6.4 is dedicated to the operation and performance
of switched combining-based schemes. Finally, section 6.5 provides some concluding
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