A wireless precoding technique for millimetre-wave MIMO system based on SIC-MMSE

TELKOMNIKA, Vol.17, No.6, December 2019, pp.2782~2789
ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018
DOI: 10.12928/TELKOMNIKA.v17i6.12802 ◼ 2782
Received December 20, 2018; Revised May 25, 2019; Accepted July 2, 2019
A wireless precoding technique for millimetre-wave
MIMO system based on SIC-MMSE
Rounakul Islam Boby*1
, Khaizuran Abdullah2
, A. Z. Jusoh3
,
Nagma Parveen4
, A. L. Asnawi5
Electrical and Computer Engineering,
Kulliyyah of Engineering and International Islamic University Malaysia,
Gombak, Selangor, Malaysia, telp: (+603) 6196 4000.
*Corresponding author, e-mail: rounaqul2020@gmail.com1
, khaizuran@iium.edu.my2
,
azamani@iium.edu.my3
Abstract
A communication method is proposed using Minimum Mean Square Error (MMSE) precoding
and Successive Interference Cancellation (SIC) technique for millimetre-wave multiple-input
multiple-output (mm-Wave MIMO) based wireless communication system. The mm-Wave MIMO
technology for wireless communication system is the base potential technology for its high data transfer
rate followed by data instruction and low power consumption compared to Long-Term Evolution (LTE).
The mm-Wave system is already available in indoor hotspot and Wi-Fi backhaul for its high bandwidth
availability and potential lead to rate of numerous Gbps/user. But, in mobile wireless communication
system this technique is lagging because the channel faces relative orthogonal coordination and multiple
node detection problems while rapid movement of nodes (transmitter and receiver) occur. To improve
the conventional mm-wave MIMO nodal detection and coordination performance, the system processes
data using symbolized error vector technique for linearization. Then the MMSE precoding detection
technique improves the link strength by constantly fitting the channel coefficients based on number of
independent service antennas (M), Signal to Noise Ratio (SNR), Channel Matrix (CM) and mean square
errors (MSE). To maintain sequentially encoded user data connectivity and to overcome data loss, SIC
method is used in combination with MMSE. MATLAB was used to validate the proposed
system performance.
Keywords: channel matrix, millimetre-wave, minimum mean square error, quantized system, successive
interference-cancellation
Copyright © 2019 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
The communications in the millimetre wave band suffers from increased path loss
exponents, higher shadow fading, blockage and penetration losses, etc., where sub-6 GHz
systems leading to a poorer link margin than legacy systems [1-3]. Spatial sparsity of
the channel along with the use of large antenna arrays motivates a subset of physical layer
beamforming schemes based on directional transmissions for signalling. In this context, there
have been a few studies on the design and performance analysis of directional beamforming/
precoding structures for single-user multi-input multi-output (MIMO) systems [4-7]. However, by
restricting attention to small cell coverage and by reaping the increased array gains from
the use of large antenna arrays at both the base-station and user ends, significant rate
improvements can be realized in practice. These works show that directional schemes are not
only good from an implementation standpoint but are also robust to phase changes across
clusters and allow a smooth trade-off between peak beamforming gain and initial user discovery
latency. There has also been progress in generalizing such directional constructions for
multi-user MIMO transmissions [8-11]. Several recent works have addressed hybrid
beamforming for millimetre wave systems. The problem of finding the optimal precoder and
combiner with a hybrid architecture is posed as a sparse reconstruction problem in [12], leading
to algorithms and solutions based on basis pursuit methods. While the solutions achieve good
performance in certain cases, to address the performance gap between the solution proposed
in [12] and the unconstrained beamformer structure, an iterative scheme is proposed in [13, 14]
relying on a hierarchical training codebook for adaptive estimation of millimetre wave channels.

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A wireless precoding technique for millimetre-wave... (Rounakul Islam Boby)
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The authors in [13, 14] show that a few iterations of the scheme are enough to achieve
near-optimal performance. In [15], it is established that a hybrid architecture can approach
the performance of a digital architecture if the number of RF chains is twice that of
the data-streams. A heuristic algorithm with good performance is developed when this condition
is not satisfied. Several other works such as [16, 17] have also explored iterative/algorithmic
solutions for hybrid beamforming.
A common theme that underlies most of these works is the assumption of phase-only
control in the RF/analog domain for the hybrid beamforming architecture. This assumption
makes sense at the user end with a smaller number of antennas (relative to the base-station
end), where operating the PAs below their peak rating across RF chains can lead to
a substantially poor uplink performance. On the other hand, amplitude control (denoted as
amplitude tapering in the antenna theory literature) is necessary at the base-station end with
many antennas for side-lobe management and mitigating out-of-band emissions. Further, given
that the base-station is a network resource, simultaneous amplitude and phase control of
the individual antennas across RF chains is feasible at millimetre wave base-stations at
a low-complexity and cost [18]. The millimetre wave experimental prototype demonstrated in
allows simultaneous amplitude and phase control. Table 1 shows the summary of the related
review papers.
Table 1. Summarization of notable review papers.
Methods Years Advantages Disadvantages
Conventional
mmWave
2016-17 1. High frequency 6GHz. 1. High path loss exponents,
2. higher shadow fading,
3. blockage and penetration losses, etc.
Single user MIMO 2013-16 1. Robust to phase changes across
clusters and allow a smooth trade-off
between peak beamforming gains.
Initial user discovery latency.
1. Large antenna arrays motivate a
subset of physical layer beamforming.
Multi-user MIMO 2014-17 1. Generalizing such directional
constructions for multi-user.
1. Switching mode decrease efficiency.
2. Certain data loss.
Pursuit methods-
based Hybrid
architecture.
2014 1. Increased performance by
addressing the performance gap
between the channel switching.
1. Assumed phase control in the
RF/analog domain, only possible in
small number of antennae.
Digital hybrid
architecture.
2016-17 1. Hybrid beamforming.
2. A heuristic algorithm used for
better performance.
1. Number of RF chains is twice that of
the data-streams.
2. Substantially poor uplink performance.
SAPC mmWave 2017 1. Simultaneous amplitude and
phase control of the individual
antennas across RF chains.
2. Low-complexity and cost.
1. Standard capacity of maximum 127
points.
Hybrid precoding
single-user
mmWave
2017 1. Hybrid precoding/combining is
capable.
2. Same performance of the fully
digital.
1. Failure of dedicated computer or
connection problem can fail the system.
2. Required maintenance.
Hybrid precoding for
multi-user mmWave
2015 1. Combination of RF combiner and
RF beamformer to maximize the
channel gain.
2. Derived as a zero-forcing (ZF)
precoder.
1. For a small plant.
2. Extension not possible.
Mean-squared error
(MSE) hybrid
precoder
2011 1. Maximum likelihood (ML) decoder
and a minimum mean square error
(MMSE) decoder.
2. Window coefficients used to
generate the quantized values.
1. The performance depends on
detection engine.
2. Research Method
The proposed system is a combination of successive interference cancellation (SIC)
and Minimum Mean Square Error (MMSE) or can be written as SIC-MMSE. In this process,
initially, the raw data is sampled and prepared for sub-band packaging according to users’ data
symbol. The coder is joined along with MMSE detection system, which will depend upon user or
operator. The MMSE detection process will continue to do channel pilot sensing, testing signal
quality, estimate the Signal to Noise Ratio (SNR), arrange Channel Matrix (CM) formation,
Channel selection & estimation. The MMSE processed data will be filtered for maximum

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TELKOMNIKA Vol. 17, No. 6, December 2019: 2782-2789
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correlation detection, which is the part of SIC method. This method is used to detect
the sequentially processed data according to the users’ symbols and regenerate the data to
transfer it through the new channel. While MMSE will constantly monitor the signal quality to
realter the channel coefficient, the SIC will help MMSE to improve its performance by fastly
processing sequential data so that MMSE can reselect any parameters at any moment to
reduce interruption and data loss. At the end of transmission process, the RF modulation will
modulate the data then filter with Spectrum Shaping Filter (SSF) and transmit through
the channel. A synchronizer is used in transmission process to synchronize any disrupted
operation. On the receiver side the signal will be demodulated and reshaped with SSF. After
demodulation the same concept of proposed MMSE will be used to decode the data.
The synchronizer on the receiver side and transmitter side will be synchronized together
through MMSE. Finally, the decoded data will be reframed using same SIC method. This
combination (SIC-MMSE) can reduce the channel shortage and performance losses. The total
process of proposed system for transmission unit and process of receiver unit are shown
in Figure 1.
Figure 1. Proposed system approximation for transmission and receiver
2.1. Symbolize Sampling
A multiple user with multiple nodes for base station (BS) was considered based on time
division duplex (TDD) method where upload and download channel data links consider within
coherence interval in a point to point MIMO system. Considering the system have N numbers of
nodes on a base station per cells having M number of total antennas per cells and K number of
single antennae known as user terminal (UT) in each cell. For K antenna user terminal to base
station J can be expressed as:
Hjk = Bjk Gjk
where, Hjk is the fading’s on J station for K number of single antennae. Bjk is the fading
coefficient of large scale and Gjk is the fading coefficient of small scale [7]. Here, Bjk represent
path loss and shadow fading of the channel. The matrix was denoted by upper case and bold
uppercase used for vector identifications. The Gjk is the total nodal fading effect induced in per
cell’s capacity can be represented by [7],
Gjk = CM (0, Im)
where, C and M are the capacity sum rate & number of BS antennas respectively and Im is
the indication function of M. So,
H = G√𝐵

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here, H is channel fading, B represents the large-scale diagonal matrix and G represents
the small-scale matrix each column represents a channel from UT to BS. When the number of
BS antennas increase the channel, the approximates orthogonal matrix will be lim
𝑛→∞
𝐻𝐻 𝐻
= B.
Each terminal is assigned with a pilot sensing for k number of single antennas, the sensing pilot
sk with power equal to, sk,t = [sk1; sk2….skt ]T and at each BS station, ‖𝑠 𝑘 𝑠𝑗
𝐻
‖2 = 0, if j ≠ k and
the transmitted power is equal for all pilots. For the conventional detection the receiver vector
matrix y can be denoted by
y ∈ CM×1 [8] or y = Hx + n (1)
where, C is channel matrix and complex additive white gaussian noise (AWGN) vector, H∈CM×K,
x is the symbol vector sent by K user can be denote by x ∈ Ck×1 and number of nodes n. If
the symbol error vector e then,
e = x - ẋ (2)
here, ẋ is the receiving signal. Assuming correlation parameter σ is known perfectly at the base
stations and h[n] be the channel vector between a UT and a BS at time t. Then [9],
h[t] = σ h [t - 1] + ev[t] (3)
here, t is time index and e[t] is white noise with zero mean and temporal correlation parameter
σ2 obtained through the Yule-Walker equation [7]. The channel model above is known as
the stationary ergodic Gauss-Markov block fading channel model [8].
2.2. MMSE Detection Process
For the MIMO model equation according to reference no [7], where receiving signal
vector ŷ from receiver signal y and the fibrinous norm ‖𝑦‖2 to limit sphere of validity of general
norm.
ŷ = y − H ẋ = H (e + x) (3)
where, x is transmitted symbol massages and ẋ is the received symbol massages. Error vector
e should be zero for ideal communication system. So, that the error detection should be
overcome from receiver signal vector. Some researcher expresses the compressing sensing
methods, where they proposed to naturally consider the symbol error vector e [7].
In compressing sensing methods M should be less then K, but if M becomes more then equal to
K, this system will be impractical. For MIMO multi-antenna mode, the M is generally greater
then equal K, the receiver signal vector later filter by matrix WMMSE is given by:
WMMSE = =
𝐻ℎ
𝐻 𝐻ℎ +𝐼 𝑚
(4)
where, W is a predefine filter matrix, WMMSE is the filter matrix for MMSE matrix for and AWGN
(Gaussian noise) vector n ∈ CM for CM (0, Im) [8]. By Maximum A Posterior (MAP) detection
known as detection system detection method the optimal detection é can be found from
the reference paper no [10].
é ≅ arg max
𝑒∈ ˆA 𝐾
(1 √2𝜋𝜎2⁄ ) exp [
−0.707
𝜎2 ((||ŷ − He||)2
2
] Pr(e) (5)
According to the paper the approximation is because of e and n dependency and may
omit while SNR increases and can be precise at high SNRs [10]. Pr(e) is probability of priority
error symbol. When BPKS values are +1 & -1, ˆA is the finite alphabet having the values -2, 0 &
+2 and for the nonzero value of A´ detection error becomes -2 & 2. If transmitted symbols are
from -1 to 1, then the possibility of the e will be no zeroes from +2 to -2 and possible probability

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can be 0.5P. When λ is the degree of sparsity, ||e||= 0.25||e||2
. If, e is the element of Â 𝐾
and e
is the symbol error vector for initial iteration, by solving (5):
e=
HHˆy
HHH+0.5 λ
e= 𝑀ˆy; [if, Â 𝐾
is finite and initially é= e] (6)
here, M is MMSE detection method with tuneable degree of sparesλ, where, λ is
the replacement of noise. If, Qθ(*) is vector dividing function and θ optimal threshold then,
optimal detection, é=Qθ(e) for discrete function [10]. So, we can rewrite:
é = Qθ(e) = 2sin(e)I ; [||e||>θ] (7)
where, “I” is the indication function. If, the optimal threshold, θ = {θ1, θ2, θ3, …, θn} and for
the non-zero components, e = {0, ±2}; [i.e. ||e||<θ]. Similarly, QPSK detection the equivalent
transform with real (R) and imaginary (I), where I(e) and R(e) parts of x,
é = 2sin [ {R(e) + I(e)} T]; [Where, e Â ] (8)
here, y initial receiver signals, n is the Gaussian noise, e(l) is the lth symbol error vector. (8) is
the prior probability detection of e. If, e(l) is non-zero, for the nth entry, 𝑥 𝑛
𝑙−1
is of 𝑥 𝑙−1
, the 𝑦 for
nth entry of lth symbol,
𝑦 𝑛
𝑙
= W(l−1) 𝑒 𝑛
𝑙
+∑ 𝑤 𝑛𝑗
1−𝑙
𝑖≠𝑗 𝑒𝑗
𝑙
+ 𝑥 𝑛
𝑙−1
(9)
so, Gaussian approximates with following variance𝜎,
(𝜎 𝑛
𝑙−1
)2 = ∑ 4(𝜔𝑗𝑛
1−𝑙
)2
𝑝𝑙−1
+ {∑ (𝑙 − 1)𝑛
𝑛
𝑛≠𝑗 } (10)
2.3. SIC Algorithm
Considering the mm-wave MIMO system with Distributed Antenna System (DAS)
configuration, where, number of base antenna MB having k number of single antenna and N
number remote radio heads. If the Q user also equipped with MU antenna, the receiving
antennas, MR = MB + Nk ≥ QMU [19-26]. For Q user MU number flat fading channels, the MMSE
pilot sk was considered before now can be rewritten as vectoral form, sk ∈ CM
u
×1. From
the model as Gauss-Markov block fading channel shown above in (3), the data vector sk have
zero mean.
The SIC algorithm relies on sequential detection receiver signals, where it is required to
equalize the channel matrices WMMSE given in (4), then carrier channels can get the higher
Signal to Interference Noise Ratio (SINR). From the reference no [26] the SINR per symbol for
Ith iteration for the jth number of symbols is thus can be expressed as,
𝑆𝐼𝑁𝑅 𝑗
𝑖
= (𝜎 𝑖
)−2
(𝑎𝑖
)2
(|ski|)2 (13)
where, 𝑎𝑖
is the amplitude, Gaussian approximates variance𝜎, pilot sk for Ith iteration. The fading
matrix Hk for k user, having N+1 submatrix in each remote radio head, then, Hk = [Hk1, Hk2, …,
Hk(N+1)]T. When the symbol is decides according a decision will be made depends on MMSE
operator given in (11). Instead of executing don’t care sign decision, it is possible to use
operator Q as soft switch through the hyperbolic tangent non-linear detector whose argument is
weighted by an estimation of the SINR [26]. So, the expression for sk for Ith iteration can be
given in QPSK constellation as,
𝑠 𝑘𝑖 = 0.707 [tanh{𝑅(𝑦 𝑘𝑖)/(𝜎𝑘𝑖
2
)} + 𝑗 tanh{𝐼(𝑦 𝑘𝑖)/(𝜎𝑘𝑖
2
)}] (14)
finally, for the decoded case in receiver end, while all symbols are retrieved, the don’t care
decision will perform for the resulting output y = (y1, y2, …, yn)T.

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3. Measurement and Simulations
For MATLAB simulation we used Gaussian noise as reference with different SNR levels
to analyse the performance of the proposed SIC-MMSE system. In this simulation process we
have compared results with conventional mm-wave MIMO system and MMSE system. For
the simulation process we first considered the number of antennae per cells M=1000. For
the process, initially we detected symbol vector j using conventional MIMO system and
proposed MMSE. For the output SNRs priority probability for conventional and MMSE we
followed equations from the reference papers [7-10] shown in (15):
lim
𝑆𝑁𝑅→∞
log 𝑃𝑐 (𝑆𝑁𝑅)
log 𝑆𝑁𝑅
= −𝑑; lim
𝑆𝑁𝑅→∞
log 𝑃 𝑆𝐼𝐶−𝑀𝑀𝑆𝐸 (𝑆𝑁𝑅)
log 𝑆𝑁𝑅
= −𝑑 (15)
Then, the degree of sparsity λ, can be obtained from λ=ln[
2(1−𝑝)
𝑝
]; Considering
the MMSE linear detection, for the Ith iteration the error probability é for SIC-MMSE based MIMO
was obtained from (8), where optimal threshold 𝜃 𝑛
𝑙
was obtained by solving the (7). This
proposed research was conduct on Time Division Duplex (TDD) method. So, to determine
the Spectral Efficiency (SE) for SIC-MMSE is expressed [27]:
ηhMMSE =
(𝑇 𝑓− 𝑇 𝑝 − 𝑇𝑡)𝑁 𝑖
𝑇 𝑖 𝑁 𝑠
(16)
where Tp = preamble period, Tt = trailer time period, Tf = frame duration and Ns = number of
symbols in a t time slot, Ni = number of information bits. By resoliving the equations in MATLAB
finally we got SE for the SIC-MMSE.
Simulating the proposed system in MATLAB the performance of SIC-MMSE was
achieved. For the comparison and benchmarking we also simulated the conventional
mm-Wave, where the simulation was done by Spectral Efficiency (SE) [bit/s/Hz/cell] vs Number
of BS Antennas (M). Figure 2 shows the comparison of the Spectral Efficiency (SE) with
the increase number of BS antenna at base station for conventional or single millimetre-Wave
system, where it is depicted that spectral efficiency increases from 0 to maximum
136 bits/s/Hz/cell with the increase of base antennas from 0 to 1000. Where, the parameters are
optimized for the better performance, the maximum SE was recorded to 157 bits/s/Hz/cell for
the 1000 number of antennas.
Figure 2. Conventional mm-waves MIMO and optimized mm-waves MIMO spectral efficiency
performance with the increase number of Antennas.
The SIC-MMSE simulation in Figure 3 shows better performance than conventional
mm-Wave MIMO system after optimization. Before optimization the maximum SE was found to
133~132 bits/s/Hz/cell while number of antennas was maximum. Where, after optimization

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the value crossed 195 bits/s/Hz/cell. Every system requires optimization, where this proposed
system performed almost the equal to optimized conventional mm-wave MIMO system, but after
optimization it rapidly increased. Figure 4 shows the performance comparison simulation block
for the both methods having same parameters, spectral efficiency according to increase number
of antennas.
Figure 3. Proposed SIC-MMSE and optimized
SIC-MMSE spectral efficiency performance
according to increase number of antennas
Figure 4. The performance of both methods’
spectral efficiency according to increase
number of antennas
4. Conclusion and Future Work
This paper has presented a communication method which is the combined methodology
of MMSE and SIC technique for mm-Wave MIMO based wireless communication system.
The combined method was proposed to reduce the relative orthogonal coordination and multiple
node detection problem while transmitter or receiver moves. The development of the equations
was done by comparing, reading and reoptimizing the existed several concepts. From
the simulation it can found that, the proposed combined technique for wireless power
communication is better than conventional mm-wave MIMO. Though, the Proposed SIC-MMSE
require optimization for better performance more combined technique with better optimization
can lead a better performance then single one. In future we would like to improve this research
by adding more system together for optimal performance and compare with recent research.
5. Acknowledgements
This paper was part of works conducted under the IIUM Research Initiative Grant
Scheme (RIGS16-334-0498 & RIGS17-031-0606). The authors would also like to acknowledge
all supports given by the IIUM Research Management Centre through the grant and RAY R&D
for their research support.
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A wireless precoding technique for millimetre-wave MIMO system based on SIC-MMSE