IEEE Consumer Electronics Magazine - November/December 2020 - 18

5G in Consumer Electronics
DFT Implementation
Relying on a "divide and conquer" principle,
classical fast Fourier transform (FFT) algorithms
factorize the size of DFT into a set of prime numbers. FFT can be quickly and efficiently implemented on each of these small prime numbers of
FFT points, by exploiting the property that the
Fourier transform multipliers are periodic and
conjugate symmetric. The complexity of FFT
decreases significantly as the size of the FFT
reduces. For this reason, the smaller the prime
numbers are, the smaller the divided subproblems are, and the simpler the FFT implementation is. For instance, 3GPP has specified that the
DFT sizes must be the radix of f2; 3; 5g to balance
the implementation complexity and the coverage of the DFT size. As a result, the number of
subcarriers per user needs to be NkRB ¼ 2b1 Â
3b2 Â 5b3 , with b1 , b2 , and b3 being nonnegative
integers [10, subclause 5.2.3].
Intermodulation Distortion (IMD)
IMD is the amplitude modulation of signals
containing multiple different frequencies,
caused by nonlinearities of power amplifiers.
IMD can increase OOB emissions in clustered
DFT-s-OFDM. An effective way to suppress the
IMD is to limit the maximum allowable transmit
powers in clustered DFT-s-OFDM. The reduced
power is known as "maximum power reduction
(MPR)." The simplest way is to predefine MPR in
the worst case scenario of IMD, i.e., two clusters
are allocated at the two edges of the band; such
deterministic MPR is adopted in the LTE-A standard.11 Define the ratio A ¼ Nalloc =NRB , where
Nalloc is the number of RBs allocated to a user
and NRB is the total number of RBs. Within a carrier component, the predefined MPR is determined by the radio A.
Backward Compatibility
It is important to have a unified signaling
structure to accommodate flexible OFDM waveforms, including localized and clustered DFT-sOFDM. A physical downlink control channel has
been specified for localized DFT-s-OFDM in 3GPP
standard,10 where a "resource allocation field"
contains a resource indication value (RIV) per
user. A piecewise polynomial is designed to generate RIV based on the index for the first RB and

the number of RBs allocated to a user. Accommodating multiple nonconsecutive clusters of
RBs without violating RIVs and the resource allocation field, a coarser allocation granularity,
referred to as a resource allocation group (RBG),
has been defined to group a certain number of
consecutive RBs into an RBG.10 The number of
bits per user is limited by indicating the first and
the last RBGs of each cluster.
However, this signaling compatibility poses
critical challenges to resource allocations, since
every bit of resources is potentially allocated
at two different resolutions. The resolutions
depend on the numbers of RB clusters allocated
to a user. This leads to the coupling among the
allocations of different parts of resources.

MAC COMPLIANT RESOURCE
ALLOCATION OF FLEXIBLE OFDM

With its nature of integer programming,
resource allocation for localized DFT-s-OFDM, is
NP-hard.12 As the generalization of that for localized DFT-s-OFDM, resource allocation for clustered DFT-s-OFDM also renders a complexity of
NP-hard, and cannot be efficiently solved with
affordable (polynomial-time) complexity. The
practical constraints, such as prime-factor
requirement for DFT implementation, MPR for
OOB suppression, and multiresolution allocation
for backward compatibility increase further the
complexity of resource allocation task. In what
follows, we generalize some feasible algorithms
for the challenging resource allocation problem
of DFT-s-OFDM that can leverage between the
flexibility and compliance requirements.

Branch and Bound (B&B)
B&B is a classical optimal solver for integer
programs. Both localized and clustered DFT-sOFDM can be supported by the B&B method
with the global optimal solutions guaranteed. To
comply with the B&B method, we formulate the
resource allocation for DFT-s-OFDM into a set
partitioning problem as follows:
maxx wT x
s.t. Ax 1

(1)

where w is the vector collecting the weighted
rate corresponding to the allocation decision

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IEEE Consumer Electronics Magazine - November/December 2020

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