IEEE Consumer Electronics Magazine - November/December 2020 - 19

vector x (of binary entries), and 1 is an all-one
vector. A is designed to ensure that a user can
only be allocated with one of the predefined allocation specified in A and the allocations to different UEs do not conflict. A collects all possible
allocations of RBs, which comply with the prime
factorization and multiresolution requirement.
The B&B method has a worst case complexity
of Oð2jxj Þ. Here, jxj denotes the size (i.e., the number of entries) of x, which can be as large as K 4 M
with K being the number of RBs and M being the
number of UEs. In other words, an exponential
time-complexity can be required, which is unaffordable even for medium K and M. Nevertheless, the method provides a useful benchmark to
evaluate the gain of utilizing DFT-s-OFDM.

Riding Peaks (RP)
RP is an efficient heuristic algorithm, originally developed for localized DFT-s-OFDM. It
allows each user to be allocated only a single
cluster of RBs.12 Specifically, the technique
recursively pairs up the UEs and unallocated
RBs in such a way that the pair, contributing the
most to the growth of the overall utility, is
selected during each iteration. The adjacency
requirement of RBs allocated to a user can be
readily guaranteed by ... With no consideration
on the prime factorization, the complexity of RP
is OðKMÞ12.
Extended RP for Clustered DFT-s-OFDM
We now extend RP to clustered DFT-s-OFDM.
Consider that each user can be allocated up to
two nonconsecutive clusters of RBs, as discussed in the "MAC Compliance of Flexible
OFDM Waveforms" section. A UE already allocated with two nonconsecutive clusters of RBs
cannot be a candidate for an RB nonadjacent to
either of the two clusters during each iteration.
This extension of RP to clustered DFT-s-OFDM
can be referred to as "RB-based clustered RP."
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The complexity of RP is O MðK þ MÞ in the
case of clustered DFT-s-OFDM with up to two
clusters per user. Another possible extension of
RP to clustered DFT-s-OFDM is to pair up the
UEs and unallocated RBGs (rather than RBs),
thereby accommodating the resolution of RBG.12
Accordingly, the extension is referred to as
"RBG-based clustered RP."

November/December 2020

These extensions of RP to clustered DFT-sOFDM can lead to substantial losses of utility, as
compared to the B&B method. This is due to the
fact that the extension, still operating on either
an RB or RBG basis, fails to take into account the
multiple resolutions, during the recursive oneto-one mapping process. Postadjustments are
necessary for the compliance with multiple different resolutions in each of the two extensions.
Postadjustment for MAC Compliance
Although not captured in the article by Lee
et al.,12 the compliance with DFT implementation
needs to be considered in both localized and
clustered DFT-s-OFDM. This can be done after
the RP algorithm. Specifically, we can check all
the RBs from the smallest to the largest indexes.
For a user, if the allocated clusters of RBs do not
comply with the prime factorization requirement, we can allocate more RBs adjacent to the
high end of the allocated cluster, or remove
some of the allocated RBs at the high end of the
cluster to satisfy the compliance requirement.
Adjustments are critical to comply with the multiresolution allocation for backward compatibility, as well as the IMD suppression.

Multiresolution Clustered RP
We now extend RP for clustered DFTs-OFDM
that accommodates multiresolution allocation in
two separate stages. The new multiresolution
clustered RP is able to balance the data rate of
clustered DFT-s-OFDM and computational complexity. It can allocate RBGs at the first stage. To
fulfill the flexibility of multiple resolutions, multicluster allocations are preserved while the onecluster allocations are removed and reallocate
RB after finishing the coarser granularity allocation. At the second stage of allocation, an
enhanced greedy method can be carried out,
where the multiresolution clustered RP first
divides the rest of the RBs into coherent subband. The multiresolution clustered RP can identify the "best" subband for each unallocated
user, and allocate the "best" RB in the subband
to the user as its "base," until either all the subbands or unallocated UEs are processed. After
that, the RP-like procedure can be carried out
while the adjacency constraint is considered.
Furthermore, the postadjustment can be carried

IEEE Consumer Electronics Magazine - November/December 2020

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