A robust game for MmWave MIMO
under Channel Distribution Uncertainty
Massa Ndong, Hamidou Tembine
Learning & Game Theory Laboratory, New York University Abu Dhabi
Abstract
Wireless communications consist of transmission and reception of data (infor-
mation) which is piggybacked by a spectrum of frequencies. Such spectrum has
become insufficient to satisfy the current demand in wireless communications
because of the high number of devices vying to access and use the wireless net-
work. By increasing the spectrum, the capacity of wireless networks increases.
Mm-wave piggyback frequencies (F=28GHz , 73GHz ,... ) have been recently
considered for additional spectrum to address the issue along with Multiple
Input Multiple Output (MIMO). A MIMO channel is formed when Nt anten-
nas transmit and Nr antennas receive for Nt ≥2 and N r ≥2. The capacity
(maximum rate) of a MIMO channel is proportional to min(Nt, N r). However,
mm-wave with MIMO requires channel state information(CSI) at both trans-
mitter and receiver antennas to yield an optimal capacity. Since the current
state-of-the-art relies on channel estimation, an inherent error is computed in
the evaluation of the capacity because of the channel error estimation. Wireless
communications use digital communications. The data are encoded into sym-
bols in the baseband (low frequencies) before being sent in the wireless channel
in the passband (high frequencies+). A symbol is transmitted every 1
Wseconds
where Wis the bandwidth occupied by the baseband signal. The transmitted
signal arrived at the receiver via several paths. Thus, the received signal is a
sum of weighted versions of the transmitted signal. The weights are called fad-
ing gains or complex taps. Each path is characterized by its delay and complex
tap. The delay which differs from one path to another, is the travel time from
transmitter to receiver. The multipath propagation occur in a continuous time.
At the reception of the delayed version on the lth path, only the paths which
fall in the delay bin [ l
W−1
2W,l
W+1
2W] are considered in the computation of
the complex tap hlexpressed as hl=∑iaie2jπF τi, where j2=−1, Fis the
piggyback frequency and τiis the delay of the lth path. Thus, all paths out
of the delay bin cannot be considered in the reception of the signal. If such
paths carry the symbols which can be decoded at the reception, then hlhas to
be estimated with the paths which fall in the bin. Moreover, the delay on each
path may cause signals in different paths adding up at the reception to cancel
each other. The received signal is expressed as y[m] = ∑lhlx[m−l], where m
is the discrete arrival time and x[m−l] is the received symbol at previous time
Preprint submitted to NYUAD Poster Session November 1, 2017
