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Multiple MIMO with Joint Block Antenna Number Modulation and Adaptive Antenna Selection for Future Wireless Systems

Multiple MIMO with joint block Antenna Number Modulation (M-MIMO-ANM) is proposed as a novel transmission method that exploits the features of both Massive Multiple Input Multiple Output (M-MIMO) and Antenna Number Modulation (ANM) concepts to improve the system performance more

Published onDec 25, 2020
Multiple MIMO with Joint Block Antenna Number Modulation and Adaptive Antenna Selection for Future Wireless Systems
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Abstract

Multiple MIMO with joint block Antenna Number Modulation (M-MIMO-ANM) is proposed in this paper as a novel transmission method that exploits the features of both Massive Multiple Input Multiple Output (M-MIMO) and Antenna Number Modulation (ANM) concepts. In this scheme, the main purpose is to increase the number of additionally transmitted data bits, which are sent without any consumption in the bandwidth. To achieve this, the antenna elements of a large array are divided into blocks, whose numbers are utilized to convey additional data bits along with those bits sent by the number of antenna elements within each block as well as those sent by conventional modulation schemes (e.g., BPSK). The implementation of M-MIMO-ANM scheme relies on the idea of dividing the whole antenna array into blocks, where each block corresponds to a group of bits depending on the total number of available blocks, thus ANM concept is applied not only to the antennas within each block but also to the blocks forming the entire antenna array. This creates an opportunity to convey even more additional data bits, compared with the conventional ANM scheme, while there is a noticeable improvement in the reliability of data transmission. With all these dynamics, M-MIMO-ANM concept is a candidate to create a new perspective to the Internet of Things (IoT) applications, with its energy efficient, spectrum efficient, robust, and both data and channel dependent data transmission nature that comes from the properties of Massive MIMO and ANM. The introduced system is investigated, and its validity is proven, where analytical and simulation results in terms of the bit error rate (BER) and throughput of the system are given. The numerical computer simulations furthermore compare the performances of M-MIMO-ANM with MIMO-ANM to show its superiority, and the advantages of the concept are discussed. M-MIMO-ANM is promising a highly reliable and resilient system thanks to its cascaded simultaneous bit transmission by the different number of both antenna blocks and antenna elements within each block.

Index Terms

M-MIMO with ANM and AAS, M-MIMO with ANM and AAS, MIMO, M-MIMO-ANM, block number modulation, antenna number modulation, adaptive antenna selection, spatial modulation, Rayleigh Channel, BER, Wireless Communication, 6G.

Introduction

The increasing demand for high speed, high spectral efficiency, high reliability, and low power consumption in online Internet devices, which have emerged due to the recent developments and unprecedented advances in communication and computation technologies, is pushing researchers to develop advanced and more effective transmission methods and techniques such as Massive MIMO that includes all the benefits of conventional MIMO, but doing this by using a large number of antennas at the base stations (BSs) to harvest more performance advantages [1][2][3][4].

As a promising technique in the applications of 5G, Massive MIMO obtains a solid place with its simultaneous multi-user servicing nature in wireless standards like 5G, and LTE [5][6]. In addition to multi-user service, Massive MIMO also exhibits superior performance in spectral efficiency over the standards established on a small number of antennas [7][8]. Aside from spectral efficiency, Massive MIMO is also capable of providing better channel reliability due to its diversity gain along with having low propagation loss [9]. In spite of all these advantages [10], which promote Massive MIMO to be an adopted technology in 5G wireless systems in a centralized or decentralized setup [11][12], there are still some certain issues that Massive MIMO suffers from, such as the hardware and signal processing costs that increase as the number of antenna elements in BSs increases [13]. The second issue is the RF chain complexity that inevitably comes with the dedication of RF chains for each antenna element [14], especially for Massive MIMO systems that contain roughly 50-400 antennas in each BS to serve multiple antenna users at the same time [15]. Another issue is the inter-channel interference (ICI) that occurs because of the overlapping of the signals that are emitted from the vast number of antennas [16].

To overcome these issues, an effective antenna selection algorithm could be a wise solution to reduce the number of RF chains by choosing the antennas that offer the highest signal rate [17][18], which enables the system to convey the data bits with much less channel effect, and consequently much less cost, complexity, and ICI, while the system performance is not sacrificed. In this regard, several antenna selection methods have been offered throughout the years. One of these methods mentioned in [18] relies on the idea that suggests choosing the antennas that have the maximum channel capacity under a perfect channel state information (CSI) assumption as a selection criteria. One other worthy to mention idea is based on solving the maximum volume offering submatrix in the whole antenna matrix instead of solving it directly as an antenna selection method, which is deeply investigated in [19][20][21]. In addition to these aforementioned antenna selection techniques, several variations of MIMO schemes have been adapted to Massive MIMO literature, such as [3][22], to offer a remedy for the cost, channel complexity and ICI issues of Massive MIMO. However, all these offered antenna selection methods created for the usage of Massive MIMO systems within the adaptation of MIMO schemes that are inherited from spatial modulation (SM), both have the same sufferings, that is the inability to make the antenna selections both channel and data dependent at the same time [23][24][25].

On the other hand, a recent study called Antenna Number Modulation (ANM) [26], which is applied to MIMO systems opens the door to create a possibility to make the antenna selection to be both data and channel dependent at the same time thanks to its nature that allows the additional data bits to be sent by the number (not indices) of active antennas in the system. Within this scheme [26], a portion of the incoming data stream is separated to determine the active antenna numbers in the system to convey the rest of the data stream by using conventional PSK/QAM modulation.

In an effort to further improve the data rate and reliability performance of the recently proposed MIMO-ANM scheme, in this paper, a novel method called Multiple Multiple Input Multiple Output with joint block Antenna Number Modulation (M-MIMO-ANM) is proposed for combining the benefits of both of the above mentioned schemes Massive MIMO and ANM. In this method, the antenna elements of a relatively large scale antenna array are grouped at the Base Station (BS) into blocks, whose number is used as an additional feature that can convey extra information bits. This is done by assigning a portion of the data stream for the number of antenna blocks and assigning another portion of data stream for the transmit antennas within each active block, whereas the remaining part of the data stream is sent by using conventional PSK/QAM modulation. The aim of the second part of this research is to improve the performance of the aforementioned scheme by proposing and designing a novel transmission M-MIMO-ANM scheme that can make the selection of the antenna blocks and transmit antennas in each antenna block to be both channel and data dependent simultaneously in a large scale of antenna system. To sum up, the proposed Multiple MIMO-ANM scheme is a promising technique, in terms of spectral efficiency, enhanced reliability, low complexity, and secrecy that comes from the inherits of Massive MIMO and ANM.

The following parts of this paper are organized as follows. In section II, system model of the Multiple MIMO-ANM is explained, details of the concept are analyzed with mathematical equations, and comprehensive illustrations; and a sample scenario is exemplified. In section III, the adaptive antenna selection ability of Multiple MIMO-ANM system is interrogated, the applicability of the system is analyzed by mathematical equations, and the understanding of the process is strengthened by an example. In section IV, performance analysis of the scheme is discussed. In section V, simulation results of regarding scheme and its comparisons with other schemes are shown. Lastly, section VI concludes the paper.

System Model

In this paper, a single user MIMO scheme under Rayleigh channel is considered. The number of blocks and number of transmit antennas are notated as BB and TT respectively while the number of receive antennas is notated as RR. For simplicity, number of receiver antennas is kept singular, i.e.i.e. R=1R=1.

This introduced novel transmission method, called M-MIMO-ANM, manipulates both the number of antenna blocks and the number of antennas that are situated in these blocks to send even more data bits per antenna than conventional MIMO-ANM scheme [26]. This creates a new dimension, called number of blocks in addition to dimensions that come from PSK/QAM and the number of antennas in space domain.

This results in a 4D modulated scheme that exploits the number of antenna array blocks, in addition to in-phase, quadrature components of the signal constellation diagram, and number of antennas that is already proposed in conventional MIMO-ANM.

The Transmission Structure of M-MIMO-ANM

Figure 1

Transmitter structure of M-MIMO-ANM.

The general structure of the proposed M-MIMO-ANM transmitter is shown in Fig. [1].

In the given data stream, symbols are separated into three sub-streams. The first sub-stream is named as the "Main Bits", and the symbols in this sub-stream are the actual symbols intended to be sent. The second sub-stream is named as the "BNM Bits", and the symbols in this sub-stream define how many antenna blocks will be used in the antenna system. The third sub-stream is named as the "ANM Bits", and the symbols in this data stream define how many antennas in each block will be deployed. By doing this separation, each individual element of the Main Bits sub-stream can be sent according to the BNM Bits and the ANM Bits sub-streams.

After this stage that is achieved by separating the total number of bits N=N1+N2+N3N=N_1+N_2+N_3 into the "Main Bits" (N1N_1), which is determined by the signal constellation modulation order (BPSK, QPSK, QAM, etc.) MM calculated by the formula of N1=log2(M)N_{1}=\log_2(M), "BNM Bits" (N2N_2), which is determined by the number of active antenna blocks at the transmission side BB calculated by the formula of N2=log2(B)N_{2}=\log_2(B), and the "ANM Bits" (N3N_3), which is determined by the number of available transmit antennas in each active block TT calculated by the formula of N3=log2(T)N_{3}=\log_2(T), the Main Bits are modulated by one of those conventional BPSK, QPSK, or different variations of QAM, while the BNM Bits are utilized to modulate the number of blocks by creating a look-up table that maps BNM Bits’ groups into a specific number of active blocks to make the decision to define how many antenna blocks will be activated. In a similar way, the ANM Bits are utilized to modulate the number of antennas by creating a look-up table that maps ANM Bits’ groups into a specific number of active antennas to make the decision to define how many antenna elements in each block will be activated.

As a predefined case, where the total number of antenna blocks in the system is four and the total number of antenna elements in each block is four (i.e.,B=4,T=4i.e., B=4, T=4 ), the mapping tables are shown for BNM Bits and ANM Bits in Table I and Table II, respectively.

Table 1

BNM bits (N2N_2)

Active Antenna Blocks Pattern (v\mathbf{v})

[0 0]

[1; 0; 0; 0]

[0 1]

[1; 1; 0; 0]

[1 0]

[1; 1; 1; 0]

[1 1]

[1; 1; 1; 1]

TABLE 1: BNM mapper with with N2=2{N_{2}}=2 bits & B=4B=4

Table 2

ANM bits (N3N_3)

Active Antennas Pattern (ζ\mathbf{\zeta})

[0 0]

[1; 0; 0; 0]

[0 1]

[1; 1; 0; 0]

[1 0]

[1; 1; 1; 0]

[1 1]

[1; 1; 1; 1]

TABLE 2: ANM mapper with N3=2{N_{3}}=2 bits & T=4T=4

To have a more clear aspect in Table I, if the BNM Bits group or couple is ”00” this means the number of active blocks is one, if it is ”01” this means the number of active blocks is two, if it is ”10” this means the number of active blocks is three, and if it is ”11” this means the number of active blocks is four. The mapping numbers of each block is defined by the number of antenna blocks in the system. A similar explanation to clarify the process in Table II can also be expressed for ANM Bits as follows. If the ANM Bits group or couple is ”00” this means the number of active antennas in a block is one, if it is ”01” this means the number of active antennas in a block is two, if it is ”10” this means the number of active antennas in a block is three, and if it is ”11” this means the number of active antennas in a block is four. The mapping numbers of each antenna is defined by the number of antennas in the system. If B=2N2B=2^{N_{2}} is assumed as the number of the transmit antenna blocks and T=2N3T=2^{N_{3}} is assumed as the number of the transmit antennas in each block in the system, where N2N_2 represents the number of data bits for each BNM Bits group and N3N_3 represents the number of data bits for each ANM Bits group. For example, for four antenna blocks and eight antenna elements in each block B=2N2=4B=2^{N_{2}}=4, N2=log2(B)=2N_{2}=\log_2(B)=2 and T=2,N3=8T=2, {N_{3}}=8, N3=log2(T)=3N_{3}=\log_2(T)=3, then the BNM Bits grouping possibilities are in two bits as 00,01,10,1100, 01, 10, 11, whereas the total possibilities for ANM Bits are grouped in three bits from 000000 till 111111. To acquire the most optimized results in this scheme and simplify its demonstration, the case is established on four transmit antenna blocks (B=4B = 4), four transmit antenna elements in each block (T=4T = 4), and one receive antenna (R=1R = 1).

As the next step of modulating "Main Bits" with respect to different varieties of signal modulation constellation types (i.e., BPSK, QPSK, 16QAM, 64QAM), "BNM Bits", and "ANM Bits", each individual formed data symbol (xx) is conveyed from the active antennas, which are specifically activated according to their positions in certain antenna block. This specific antenna activation is operated according to Table I and Table II. After that, the transmitted data symbol is multiplied by the flat fading coefficients of the blocks, which are obtained by the average value of each four antennas that are adjacent to each other, and also multiplied by the active antennas in each active antenna group. The acquired result is then summed by the noise (ww) with zero mean and N0N_0 variance at the receive antenna to acquire the signal that reaches the receiver. As a result, the formula of 1×161\times16 MISO system model for each symbol in this scheme is given as

y=PZ×V×g×ζ×h×ve×x+w,y=\sqrt{\frac{P}{Z\times V}} \times \mathbf{g} \times \mathbf{\zeta}\times \mathbf{h} \times \mathbf{v}_{e} \times x + w, (1)

where PP is the power required for the transmission of each data symbol xx, and Z=ζ2=i=1Bζi2Z=\|\mathbf{\zeta}\|_2= \sum_{i=1}^{B}\zeta_{i}^2 is the total number of activated blocks in the entire antenna array, whereas V=v2=i=1Tvi2V=\|\mathbf{v}\|_2= \sum_{i=1}^{T}v_{i}^2 is the total number of active antennas in each active block. ve=[v;v;v;v]B16×1\mathbf{v}_{e} =[\mathbf{v}; \mathbf{v}; \mathbf{v}; \mathbf{v}] \in \mathbb{B}^{16\times 1} is the activation vector of all the antenna array elements of the system, in which v=[v1;v2;v3;v4]B4×1\mathbf{v}=[v_1; v_2; v_3; v_4] \in \mathbb{B}^{4\times 1} is the activation pattern vector corresponding to a single block, whose elements are Boolean, i.e., zero or one. In addition to that,

h=[h11,h12,h13,h14,h15,h16,h17,h18;h19,h110,h111,h112,h113,h114,h115,h116]C1×16\mathbf{h} = [h_{11}, h_{12}, h_{13}, h_{14}, h_{15}, h_{16}, h_{17}, h_{18}; h_{19}, h_{110}, h_{111}, h_{112}, h_{113}, h_{114}, h_{115}, h_{116} ] \in \mathbb{C}^{1\times 16}is the flat fading channel vector of the whole antenna array, in which hRTh_{RT} represents a Gaussian channel coefficient with zero mean and unity variance that corresponds to the connection link between the TthT'th transmit antenna, which is situated in BthB'th antenna block, and RthR'th receive antenna. g=[g1,g2,g3,g4]C1×4\mathbf{g}= [g_1, g_2, g_3, g_4] \in \mathbb{C}^{1 \times 4} is the artificially1 introduced flat fading channel vector for the antenna blocks in the system, which is acquired by the average values of each four h\mathbf{h} values that are adjacent to each other as shown below:g1=h11+h12+h13+h144g_1=\frac{h_{11}+h_{12}+h_{13}+h_{14}}{4}, g2=h15+h16+h17+h184g_2= \frac{h_{15}+h_{16}+h_{17}+h_{18}}{4}, g3=h19+h110+h111+h1124g_3=\frac{h_{19}+h_{110}+h_{111}+h_{112}}{4}, g4=h113+h114+h115+h1164g_4=\frac{h_{113}+h_{114}+h_{115}+h_{116}}{4}. ζB4×1\mathbf{\zeta} \in \mathbb{B}^{4 \times 1} is the activation pattern vector that is created to determine the inactive antenna blocks by zeros and the active antenna blocks by ones according to N2N_2 bits and mapping process indicated in Table I, whereas v\mathbf{v} is the activation pattern vector that is created to determine the inactive antennas in each active antenna block by zeros and active antennas in each active antenna block by ones according to N3N_3 bits and mapping process indicated in Table II. 2

In addition to the antenna number feature of the MIMO system, the capability of M-MIMO-ANM is offering even more spectral and power efficiency with its block number feature. Moreover, by conserving the nature of MIMO-ANM’s independent mapping process of the indices or position of the antennas, the simultaneous channel and data dependency sustains the advantage that the spatial index modulation cannot offer [27][28], as shown in the following example.

Example: To clarify the process and improve the understanding of the concept a comprehensive example is submitted as follows. Assume a small sample of data bit sequence that is given as "101101101011011101101101011011", and this data stream is desired to be sent by a B×T×R=4×4×1B \times T \times R = 4 \times 4 \times 1 M-MIMO-ANM system using BPSK modulation, which also can be considered as TTotal×R=16×1T_{Total} \times R = 16 \times 1. Since there are four antenna blocks in the given system, determination of the number of different BNM group is operated by the previously given formula 2N2=B=42^{N_2}=B=4. With this formula, the number of bits in each BNM group can be found as N2=log2B=2N_2=\log_{2}{B}=2. To find N3N_3, the number of bits in each ANM subgroup, a similar formula 2N3=T=42^{N_3}=T=4, which is also previously given leads that N3=log2T=2N_3=\log_{2}{T}=2. These results, N2=2,N3=2N_2=2, N_3=2, imply that for the transmission of each element of the Main Bits group that is modulated by BPSK, there are two bits in the BNM Bits group that activate the antenna blocks, and there are two bits in the ANM Bits group that are assigned to activate the transmit antennas in each block according to their bit numbers. This separation of the incoming data bits as Main Bits (modulated by BPSK), BNM Bits (modulated by the number of antenna blocks), ANM bits (modulated by the number of antennas in each block) for this example is shown in Fig.2.

Figure 2

Main Bits, BNM Bits and ANM Bits Separation

from Incoming Data Stream for 4 Antenna Blocks, 4 Transmit

Antennas and 1 Receiver Antenna when BPSK is used.

After the bit separation, M-MIMO-ANM process proceeds as follows. To send the first element of the Main Bits group, first two bits of the BNM Bits group and first two bits of the ANM Bits group are taken under consideration. As it is seen in Fig.2, these correlated bits are indicated by blue color. According to these bits, it can be inferred that the transmission of 11 is operated by three blocks, since the 1010 in the BNM Bits group corresponds to three blocks, and two transmit antennas that are situated in these three blocks activated, since the 0101 refers to two antennas in each active block. The transmission of the second bit of the Main Bits group is executed by the second pairs of both BNM Bits and ANM Bits group, which are colored by red in Fig. 2. Within these bits, it can be stated that 00 is conveyed by three antennas that are located in each of the four antenna blocks in the system, since the 1111 in the BNM Bits group means the activation of four antenna blocks, and 1010 in the ANM Bits group means the activation of three antennas in each activated block. Lastly, the third element of the main bits group is conveyed by the third pairs of the BNM Bits group and ANM Bits group, which are specified by green color. According to these pairs, the transmission of 11 is achieved by two blocks, since the 0101 in the BNM Bits block regards to two antenna blocks, and each of these two antenna blocks contains four active transmit antennas, since the 1111 in the ANM Bits group means activation of two antennas in each active antenna block. The visualized scheme of this process is displayed in Fig. [3].

Figure 3

Simple visualization of the antenna activation process and mapping in M-MIMO-ANM scheme.

Since there are different possibilities to convey the main signals from different blocks and antennas, the corresponding received main signal may vary according to those blocks and antennas in usage. These variations for received main signal expressions are listed in the following equations.

When active blocks’ number is one and active antennas’ number in each active block is one, the received signal is given as

y1=P1×1×(g1)×(h11)×xi+w.y_{1}=\sqrt{\frac{P}{1\times 1}} \times (g_1)\times(h_{11})\times x_i+w. (2)

When active blocks’ number is one and active antennas’ number in each active block is two, the received signal is given as

y2=P1×2×(g1)×(h11+h12)×xi+w.y_{2}=\sqrt{\frac{P}{1\times 2}} \times (g_1)\times(h_{11}+h_{12})\times x_i+w. (3)

When active blocks’ number is one and active antennas’ number in each active block is three, the received signal is given as

y3=P1×3×(g1)×(h11+h12+h13)xi+w.y_{3}=\sqrt{\frac{P}{1\times 3}} \times (g_1)\times(h_{11}+h_{12}+h_{13})x_i+w. (4)

When active blocks’ number is one and active antennas’ number in each active block is four, the received signal is given as

y4=P1×4×(g1)×(h11+h12+h13+h14)xi+w.y_{4}=\sqrt{\frac{P}{1\times 4}} \times (g_1)\times(h_{11}+h_{12}+h_{13}+h_{14})x_i+w. (5)

When active blocks’ number is two and active antennas’ number in each active block is one, the received signal is given as

y5=P2×1×[(g1)×(h11)+(g2)×(h15)]xi+w.y_{5}=\sqrt{\frac{P}{2\times 1}} \times [(g_1)\times(h_{11})+(g_2)\times(h_{15})]x_i+w. (6)

When active blocks’ number is two and active antennas’ number in each active block is two, the received signal is given as

y6=P2×2×[(g1)×(h11+h12)+(g2)×(h15+h16)]xi+w.y_{6}=\sqrt{\frac{P}{2\times 2}} \times [(g_1)\times(h_{11}+h_{12})+(g_2)\times(h_{15}+h_{16})]x_i+w. (7)

When active blocks’ number is two and active antennas’ number in each active block is three, the received signal is given as

y7=P2×3×[(g1)×(h11+h12+h13)+(g2)×(h15+h16+h17)]xi+w.\begin{gathered} y_{7}=\sqrt{\frac{P}{2\times 3}} \times [(g_1)\times(h_{11}+h_{12}+h_{13})+\\(g_2)\times(h_{15}+h_{16}+h_{17})]x_i+w.\end{gathered} (8)

When active blocks’ number is two and active antennas’ number in each active block is four, the received signal is given as

y8=P2×4×[(g1)×(h11+h12+h13+h14)+(g2)×(h15+h16+h17+h18)]xi+w.\begin{gathered} y_{8}=\sqrt{\frac{P}{2\times 4}} \times [(g_1)\times(h_{11}+h_{12}+h_{13}+h_{14})+\\(g_2)\times(h_{15}+h_{16}+h_{17}+h_{18})]x_i+w. \end{gathered} (9)

When active blocks’ number is three and active antennas’ number in each active block is one, the received signal is given as

y9=P3×1×[(g1)×(h11)+(g2)×(h15)+(g3)×(h19)]xi+wy_{9}=\sqrt{\frac{P}{3\times 1}} \times [(g_1)\times(h_{11})+(g_2)\times(h_{15})+(g_3)\times(h_{19})]x_i+w (10)

When active blocks’ number is three and active antennas’ number in each active block is two, the received signal is given as

y10=P3×2×[(g1)×(h11+h12)+(g2)×(h15+h16)+(g3)×(h19+h110)]xi+w\begin{gathered} y_{10}=\sqrt{\frac{P}{3\times 2}} \times [(g_1)\times(h_{11}+h_{12})+\\(g_2)\times(h_{15}+h_{16})+(g_3)\times(h_{19}+h_{110})]x_i+w \end{gathered} (11)

When active blocks’ number is three and active antennas’ number in each active block is three, the received signal is given as

y11=P3×3×[(g1)×(h11+h12+h13)+(g2)×(h15+h16+h17)+(g3)×(h19+h110+h111)]xi+w\begin{gathered} y_{11}=\sqrt{\frac{P}{3\times 3}} \times [(g_1)\times(h_{11}+h_{12}+h_{13})+\\(g_2)\times(h_{15}+h_{16}+h_{17})+(g_3)\times(h_{19}+h_{110}+h_{111})]x_i+w \end{gathered} (12)

When active blocks’ number is three and active antennas’ number in each active block is four, the received signal is given as

y12=P3×4×[(g1)×(h11+h12+h13+h14)+(g2)×(h15+h16+h17+h18)+(g3)×(h19+h110++h111+h112)]xi+w\begin{gathered} y_{12}=\sqrt{\frac{P}{3\times 4}} \times [(g_1)\times(h_{11}+h_{12}+h_{13}+h_{14})+\\(g_2)\times(h_{15}+h_{16}+h_{17}+h_{18})+\\(g_3)\times(h_{19}+h_{110}++h_{111}+h_{112})]x_i+w \end{gathered} (13)

When active blocks’ number is four and active antennas’ number in each active block is one, the received signal is given as

y13=P4×1×[(g1)×(h11)+(g2)×(h15)+(g3)×(h19)+(g4)×(h113)]xi+w\begin{gathered} y_{13}=\sqrt{\frac{P}{4\times 1}} \times [(g_1)\times(h_{11})+(g_2)\times(h_{15})+\\(g_3)\times(h_{19})+(g_4)\times(h_{113})]x_i+w \end{gathered} (14)

When active blocks’ number is four and active antennas’ number in each active block is two, the received signal is given as

y14=P4×2×[(g1)×(h11+h12)+(g2)×(h15+h16)+(g3)×(h19+h110)+(g4)×(h113+h114)]xi+w\begin{gathered} y_{14}=\sqrt{\frac{P}{4\times 2}} \times [(g_1)\times(h_{11}+h_{12})+(g_2)\times(h_{15}+h_{16})+\\(g_3)\times(h_{19}+h_{110})+(g_4)\times(h_{113}+h_{114})]x_i+w \end{gathered} (15)

When active blocks’ number is four and active antennas’ number in each active block is three, the received signal is given as

y15=P4×3×[(g1)×(h11+h12+h13)+(g2)×(h15+h16+h17)+(g3)×(h19+h110+h111)+(g4)×(h113+h114++h115)]xi+w\begin{gathered} y_{15}=\sqrt{\frac{P}{4\times 3}} \times [(g_1)\times(h_{11}+h_{12}+h_{13})+\\(g_2)\times(h_{15}+h_{16}+h_{17})+(g_3)\times(h_{19}+h_{110}+h_{111})+\\(g_4)\times(h_{113}+h_{114}++h_{115})]x_i+w \end{gathered} (16)

When active blocks’ number is four and active antennas’ number in each active block is four, the received signal is given as

y16=P4×4×[(g1)×(h11+h12+h13+h14)+(g2)×(h15+h16+h17+h18)+(g3)×(h19+h110+h111+h112)+(g4)×(h113+h114++h115+h116)]xi+w\begin{gathered} y_{16}=\sqrt{\frac{P}{4\times 4}} \times [(g_1)\times(h_{11}+h_{12}+h_{13}+h_{14})+\\(g_2)\times(h_{15}+h_{16}+h_{17}+h_{18})+(g_3)\times(h_{19}+h_{110}+h_{111}+h_{112})+\\(g_4)\times(h_{113}+h_{114}++h_{115}+h_{116})]x_i+w \end{gathered} (17)

The Reception Structure of M-MIMO-ANM

The corresponding reception side structure of M-MIMO-ANM is given in Fig. 4.

Figure 4

Receiver Structure of M-MIMO-ANM.

To detect the data bits that come from both conventional M-ary signal constellation symbols, the number of antenna blocks and the number of antennas in each block at the receiver side, different approaches of detection methods can be used. One of these approaches is joint detection of Main Bits, BNM Bits, ANM Bits, whereas the other approach is individual detections independently separate from each other in a successive manner. Further explanation about these two methods is provided below.

Demodulation of the data bits can be operated under a common detection process for both Main Bits, which is modulated by either one of those BPSK, QPSK, 16QAM, or 64QAM, BNM Bits, and ANM Bits, or a sequential detection can be applied individually by demodulating the BNM Bits first, then demodulating ANM Bits, then demodulating Main Bits with respect to demodulations of BNM Bits and ANM Bits. It should be stated that by applying a common detection procedure at the reception side, the complexity of the system is dramatically increased. The reason behind that is, by applying a joint detection, the number of operations becomes B×T×MB\times T\times M, while in the separated detection this number is B+T+MB+T+M.

In the joint demodulation of Main Bits, BNM Bits, and ANM Bits, a Maximum Likelihood (ML) detector can be used to detect the active blocks, active antennas in these active blocks, and signal constellation points at once. The regarded formula for this detector can be derived as

Jζ,v,x=minx^,ζ^,v^(y(i=1ζ^gi)(i=1v^h1i)x^2),J_{\zeta,v,x}=\min_{\hat{x},\hat{\zeta},\hat{v}} \left(||y-\left(\sum_{i=1}^{\hat{\zeta}}g_{i}\right) \left(\sum_{i=1}^{\hat{v}}h_{1i}\right)\hat{x}||^2\right), (18)

where ζ1,2,3,4\zeta\in 1,2,3,4 is the possible number of active antenna blocks, v1,2,...,16v\in 1,2,...,16 is the possible number of active antennas in the system, yiy1,y2,...,y16y_{i}\in y_{1},y_{2},...,y_{16} is the received signals that is defined by certain combinations of active antenna blocks and antennas in these active blocks, and xix_{i} is the estimated constellation symbols.

On the other hand, the individual detection of the Main Bits, BNM Bits, and ANM Bits, that provides less complexity might be a wiser alternative in some certain cases that requires low delay, less processing, and less power consumption, like IoT devices. In such a case, the ML detector formulas for each individual group of bits as BNM Bits, ANM Bits, Main Bits are given as

Jζ=minζ^(y(i=1ζ^gi)x2),J_\zeta=\min_{\hat{\zeta}} \left(||y-\left(\sum_{i=1}^{\hat{\zeta}}g_{i}\right){x}||^2\right), (19)
Jv=minv^(y(i=1v^h1i)x2),J_v=\min_{\hat{v}} \left(||y-\left(\sum_{i=1}^{\hat{v}}h_{1i}\right){x}||^2\right), (20)
Jx=minx^(y(i=1vh1i)x^2).J_x=\min_{\hat{x}} \left(||y-\left(\sum_{i=1}^{{v}}h_{1i}\right)\hat{x}||^2\right). (21)

As it can be seen from (21), the gg values which were set as the average values of the channel coefficients in each corresponding block do not have an effect at the reception side of M-MIMO-ANM. The reason why behind that is, the gg is used only for creating an activation pattern for the antenna blocks. Since the deployment of the gg values in (21) would create an artificial performance increment and obstruct to reflect the true performance of the system, it is not considered as a parameter of the detection of Main Bits.

During the simulation process of this scheme, detection of the bits are achieved individually due to its aforementioned advantages.

Multiple MIMO with Joint Block Antenna Number Modulation and Adaptive Antenna Selection (M-MIMO-ANM-AAS)

In this section, the main advantage of the MIMO-ANM system over MIMO-SM, which is the ability to make antenna selection channel dependent as well as data dependent is offered as an improved version of Multiple Input Multiple Output System with Antenna Number Modulation and Adaptive Antenna Selection (MIMO-ANM-AAS). The source of this improvement relies on making the antenna selection not only based on channel coefficients of each individual antenna, but considering each antenna in each block as a member of a team and acquiring the total channel coefficients for each antenna blocks. This application leads the system to select the antenna blocks and antennas in each block, not only by the BNM Bits and ANM Bits, but also the channel amplitude responses of each block and antenna that blocks contain. Multiple Multiple Input Multiple Output System with Antenna Number Modulation and Adaptive Antenna Selection (M-MIMO-ANM-AAS) is designed to select the best antennas among the best antenna blocks.

The application procedure of M-MIMO-ANM-AAS is explained as follows:

  1. By sending an experimental signal from the receiver in a Time Division Duplex (TDD) system, the transmitter estimates the channel amplitude responses of each transmit antennas.

  2. As the next step, the average values of each adjacent TT antennas in one block are calculated to assign a channel amplitude value to each antenna block.

  3. Within this step, the transmitter can achieve the detection of the channel amplitude values of antenna blocks with respect to the receiver. For a singular receive antenna at the reception end and BB antenna blocks at the transmission end, the channel amplitude vector of antenna blocks becomes g=[g11,g12,g13,...,g1B]C1×B\mathbf{|g|} = [|g_{11}|, |g_{12}|, |g_{13}|, ..., |g_{1B}|] \in \mathbf{\mathbb C}^{1 \times B}.

  4. The channel response values of vector g\mathbf{|g|} is then sorted by the transmitter from its highest value to lowest value.

  5. After the ranking of the blocks is done, the channel amplitude values of transmit antennas, which are previously obtained for the detection of the channel amplitude values of antenna blocks, are specified for each block that contains TT transmit antennas. For a singular receive antenna at the reception and TT transmit antennas in each of BB blocks the channel amplitude vector of transmit antennas becomes h=[h11,h12,h13,...,h1TTotal]C1×TTotal\mathbf{|h|} = [|h_{11}|, |h_{12}|, |h_{13}|, ..., |h_{1T_{Total}}|] \in \mathbf{\mathbb C}^{1 \times T_{Total}}.

  6. For the next step, the transmitter maximizes the SNR of the receiver, which leads to an increase in the reliability performance of the receiver since it reduces the BER of the system. Even though, there are many strategies3 to select antennas according to their channel gains, in this study transmitter deploys the strategy that suggests using the antennas that provides the largest channel gain, thanks to block and antenna number selective nature of number modulation scheme rather than their indices or positions in the system.

  7. The selection process in M-MIMO-ANM-AAS, which comes after the decision that how many antenna blocks and transmit antennas in each block are activated by BNM Bits and ANM Bits respectively, relies on activating specific antenna blocks and specific transmit antennas in those certain amounts of antenna blocks and transmit antennas that are specified by BNM Bits and ANM Bits, according to their channel coefficient qualities.

    By the given equation below, the optimal antenna block selection positions of the antenna blocks can be calculated according to their SNR values

    {ζ1opt,,ζZopt}=argmax{ζ1,,ζZ}AZSNR[ζ1,,ζZ],\{\zeta^{opt}_{1},\cdots ,\zeta^{opt}_{Z}\} = \mathrm {arg}\max _{\{\zeta_{1},\cdots ,\zeta_{Z}\} \in \mathcal {A}_{Z}}SNR_{{\left [{ \zeta_{1},\cdots ,\zeta_{Z} }\right ]}}, (22)

    where AZ\mathcal {A}_{Z} is the possible combinations of antenna block activation patterns, SNR[ζ1,,ζZ]SNR_{{\left [{\zeta_{1},\cdots ,\zeta_{Z}}\right ]}} is the summation of the SNR values that is acquired from ZZ number of activated antenna blocks in the system.

    A similar equation is given below to calculate the optimal antenna selection positions of the transmit antennas in each active block according to their SNR values

    {v1opt,,vVopt}=argmax{v1,,vV}AVSNR[v1,,vV],\{v^{opt}_{1},\cdots ,v^{opt}_{V}\} = \mathrm {arg}\max _{\{v_{1},\cdots ,v_{V}\} \in \mathcal {A}_{V}}SNR_{{\left [{ v_{1},\cdots ,v_{V} }\right ]}}, (23)

    where AV\mathcal {A}_{V} is the possible combinations of transmit antenna activation patterns in each activated antenna block, SNR[v1,,vV]SNR_{{\left [{v_{1},\cdots ,v_{V}}\right ]}} is the summation of the SNR values of that is acquired from VV number of activated transmit antennas in each antenna block.

    In order to take these equations one step further, antenna block selection and transmit antenna selection in each block can be achieved by the channel coefficients, since a uniform power allocation is used in the system. The corresponding equations for antenna block selection and transmit antenna selection in each block are given below

    {ζ1opt,,ζZopt}=argmax{ζ1,,ζZ}AZg1Z[ζ1,,ζZ],\{\zeta^{opt}_{1},\cdots ,\zeta^{opt}_{Z}\} = \mathrm {arg}\max _{\{\zeta_{1},\cdots ,\zeta_{Z}\} \in \mathcal {A}_{Z}}|g_{1Z}|_{{\left [{ \zeta_{1},\cdots ,\zeta_{Z} }\right ]}}, (24)

    {v1opt,,vVopt}=argmax{v1,,vV}AVh1V[v1,,vV],\{v^{opt}_{1},\cdots ,v^{opt}_{V}\} = \mathrm {arg}\max _{\{v_{1},\cdots ,v_{V}\} \in \mathcal {A}_{V}}|h_{1V}|_{{\left [{ v_{1},\cdots ,v_{V} }\right ]}}, (25)

    Example: Another example that deeply explains the M-MIMO-ANM scheme is given as follows. However, in this example, the Adaptive Antenna Selection feature of the system is emphasized. Assume the same sample of data sequence that is used in the first example as given in Fig. 2, and this data sequence is desired to be sent by the same amount of antenna blocks, same amount of transmit antennas, and the same amount of receive antennas as the first example (ie., B×T×R=4×4×1B\times T\times R = 4\times 4\times 1 or TTotal×R=16×1T_{Total}\times R = 16\times1) in an M-MIMO-ANM-AAS system. Let the coefficients of the transmission part of the system is notified as in Fig. [5].

    Figure 5

    Variable Table of the Given Example.

    TABLE 3: The calculated statistics of the effective Rayleigh fading channel amplitude of MISO-ANM with B=4, T=4

    Table 3

    BNM Bits (ζ\mathbf{\zeta})

    ANM Bits (v\mathbf{v})

    Active Antennas Pattern

    heff|h_{eff}|

    Scale (β\beta)

    Mean Square (α2\overline{\alpha^{2}})

    [0 0]

    [0 0]

    [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

    g1×h1|g_{1} \times h_{1}|

    0.681

    1

    [0 0]

    [0 1]

    [1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

    g1×(h1+h2)|g_{1} \times (h_{1}+h_{2})|

    1.371

    2

    [0 0]

    [1 0]

    [1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]

    g1×(h1+h2+h3)|g_{1} \times (h_{1}+h_{2}+h_{3})|

    2.013

    3

    [0 0]

    [1 1]

    [1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0]

    g1×(h1+h2+h3+h4)|g_{1} \times (h_{1}+h_{2}+h_{3}+h_{4})|

    2.726

    4

    [0 1]

    [0 0]

    [1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]

    g1×(h1)+g2×(h5)|g_{1} \times (h_{1})+g_{2} \times (h_{5})|

    1.371

    2

    [0 1]

    [0 1]

    [1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0]

    g1×(h1+h2)+g2×(h5+h6)|g_{1} \times (h_{1}+h_{2})+\hspace{1cm}g_{2} \times (h_{5}+h_{6})|

    2.726

    4

    [0 1]

    [1 0]

    [1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0]

    g1×(h1+h2+h3)+g2×(h5+h6+h7)|g_{1} \times (h_{1}+h_{2}+h_{3})+\hspace{3cm}g_{2} \times (h_{5}+h_{6}+h_{7})|

    4.027

    6

    [0 1]

    [1 1]

    [1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0]

    g1×(h1+h2+h3+h4)+g2×(h5+h6+h7+h8)|g_{1} \times (h_{1}+h_{2}+h_{3}+h_{4})+g_{2} \times (h_{5}+h_{6}+h_{7}+h_{8})|

    5.467

    8

    [1 0]

    [0 0]

    [1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0]

    g1×(h1)+g2×(h5)+g3×(h9)|g_{1} \times (h_{1})+g_{2} \times (h_{5})+g_{3} \times (h_{9})|

    2.013

    3

    [1 0]

    [0 1]

    [1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0]

    g1×(h1+h2)+g2×(h5+h6)+g3×(h9+h10)|g_{1} \times (h_{1}+h_{2})+g_{2} \times (h_{5}+h_{6})+g_{3} \times (h_{9}+h_{10})|

    4.027

    6

    [1 0]

    [1 0]

    [1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0]

    g1×(h1+h2+h3)+g2×(h5+h6+h7)+g3×(h9+h10+h11)|g_{1} \times (h_{1}+h_{2}+h_{3})+\hspace{1cm}g_{2} \times (h_{5}+h_{6}+h_{7})+\hspace{1cm}g_{3} \times (h_{9}+h_{10}+h_{11})|

    6.155

    9

    [1 0]

    [1 1]

    [1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0]

    g1×(h1+h2+h3+h4)+g2×(h5+h6+h7+h8)+g3×(h9+h10+h11+h12)|g_{1} \times (h_{1}+h_{2}+h_{3}+h_{4})+g_{2} \times (h_{5}+h_{6}+h_{7}+h_{8})+g_{3} \times (h_{9}+h_{10}+h_{11}+h_{12})|

    8.275

    12

    [1 1]

    [0 0]

    [1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0]

    g1×(h1)+g2×(h5)+g3×(h9)+g4×(h13)|g_{1} \times (h_{1})+g_{2} \times (h_{5})+g_{3} \times (h_{9})+g_{4} \times (h_{13})|

    2.726

    4

    [1 1]

    [0 1]

    [1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0]

    g1×(h1+h2)+g2×(h5+h6)+g3×(h9+h10)+g4×(h13+h14)|g_{1} \times (h_{1}+h_{2})+\hspace{1cm}g_{2} \times (h_{5}+h_{6})+\hspace{2cm}g_{3} \times (h_{9}+h_{10})+\hspace{1cm}g_{4} \times (h_{13}+h_{14})|

    5.467

    8

    [1 1]

    [1 0]

    [1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0]

    g1×(h1+h2+h3)+g2×(h5+h6+h7)+g3×(h9+h10+h11)+g4×(h13+h14+h15)|g_{1} \times (h_{1}+h_{2}+h_{3})+g_{2} \times (h_{5}+h_{6}+h_{7})+\hspace{1.1cm}g_{3} \times (h_{9}+h_{10}+h_{11})+g_{4} \times (h_{13}+h_{14}+h_{15})|

    8.275

    12

    [1 1]

    [1 1]

    [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]

    g1×(h1+h2+h3+h4)+g2×(h5+h6+h7+h8)+g3×(h9+h10+h11+h12)+g4×(h13+h14+h15+h16)|g_{1} \times (h_{1}+h_{2}+h_{3}+h_{4})+g_{2} \times (h_{5}+h_{6}+h_{7}+h_{8})+g_{3} \times (h_{9}+h_{10}+h_{11}+h_{12})+g_{4} \times (h_{13}+h_{14}+h_{15}+h_{16})|

    10.910

    16

    In this figure, the first column demonstrates the illustrations of the antenna blocks, transmit antennas, and their notations as B1,B2,B3,B4B_1, B_2, B_3, B_4 for transmit antenna blocks, and from T1T_1 through T16T_{16} for transmit antennas. The second, "Antenna Coefficients", column that is notated as hh is the flat fading channel coefficients for each individual antenna element. In the third, "Absolute Values of Antenna Coefficients", column the absolute values of each complex number are calculated to be able to make a proper sorting among antennas in each block under the notation of h|h|. The variable notated as gg in the forth, "Block Coefficients", column is the average values of each four adjacent antennas, which defines the flat fading channel coefficients for each block. To take the quality ranking in the block level, each value that are calculated in Block Coefficients column are considered as their absolute values in fifth, "Absolute Values of Block Coefficients", column which is notated as g|g|.

    According to this table by examining the Absolute Values of Block Coefficients column, it can be obviously detected that the quality ranking of each transmit antenna blocks is ordered as g1/4)>g1/3>g1/2>g1/1|g_{1/4}|)>|g_{1/3}|>|g_{1/2}|>|g_{1/1}|, which means that the first priority of the block selection belongs to B4B_4, then B3B_3, then B2B_2, then B1B_1. By analysing the antenna qualities in each block, it can be seen that the quantities of the h|h| values are ordered as h1/2>h1/4>h1/1>h1/3|h_{1/2}|>|h_{1/4}|>|h_{1/1}|>|h_{1/3}| in the B1B_1, which means T2T_2 offers the best channel quality, T4T_4 offers the second and T1T_1 offers the third best channel qualities, whereas T3T_3 offers the worst channel quality in B1B_1. Similarly, the channel quality orders, which also defines the antenna activation priority patterns of each transmit antenna in each antenna block can be specified from highest to lowest as T7,T5,T6,T8T_7, T_5, T_6, T_8 for B2B_2, T11,T12,T9,T10T_{11}, T_{12}, T_9, T_{10} for B3B_3, and T15,T12,T13,T16T_{15}, T_{12},T_{13},T_{16} for B4B_4.

    Within this knowledge, the given data stream 101101101011011101101101011011 is separated as Main Bits, BNM Bits, and ANM Bits to start the M-MIMO-ANM process. Transmission of the first bit in the Main Bits group, 11, three blocks that provide the best channel qualities are deployed, since the corresponding block number is 1010. In these best quality offering blocks, two highest channel quality offering antennas are activated, since the first two bits in the ANM Bits group is 0101. Thus, the transmission of the first element of the Main Bits group, 11, is operated by T15,T14T_{15}, T_{14} as the member of B4B_4, which is the highest channel quality offering antenna block, T11,T12T_{11}, T_{12} as the member of B3B_3, which is the second highest channel quality offering antenna block, and T7,T5T_7, T_5 as the member of B2B_2, which is the third highest channel quality offering antenna block. The second bit in the Main Bits group 00, is sent by four blocks, since the second couple of bits in BNM Bits group is 1111, which means the channel qualities of antenna blocks, in this case, do not matter since the all blocks are activated. However, the antenna qualities in each active block still must be taken into consideration. The second couple, 0101, in ANM Bits group is assigned, in order to decide which transmit antennas are opened in each antenna block, which indicates the activation of two transmit antennas for B1,B2,B3,B4B_1, B_2, B_3, B_4 separately. According to Fig. [5], the highest channel quality offering antennas are T15,T14,T13T_{15}, T_{14}, T_{13} for B4B_4 as the first prioritized antenna block, T11,T12,T9T_{11}, T_{12}, T_{9} for B3B_3 as the second prioritized antenna block, T7,T5,T6T_{7}, T_{5}, T_{6} for B2B_2 as the third prioritized antenna block, and T2,T4,T1T_{2}, T_{4}, T_{1} for B2B_2 as the forth prioritized antenna block. Since the last couples of BNM Bits and ANM Bits groups are 0101, and 1111 respectfully, the last bit in the Main Bits group, 00, is meant to be sent via two antenna blocks that provide the most qualified conditions with their all containing antennas. As previously stressed, the two most channel ranked blocks are B4B_4, and B3B_3 in descending order. Thus, the transmission of 00 is operated by all the containing antennas of these two blocks. All these processes are illustrated in Fig. [6].

    Figure 6

    Simple visualization of the antenna activation process and mapping in M-MIMO-ANM-AAS scheme.

Performance Analysis of M-MIMO-ANM

Statistics of the Effective Instantaneous SNR

Because of the fact that for different number of active antenna blocks and transmit antennas in these blocks for different activation patterns, the original fading distribution parameters are not appropriate for the proposed M-MIMO-ANM. The reason why the original fading distribution channel is not appropriate for the M-MIMO-ANM can be explained by considering the data transmission process. In M-MIMO-ANM, at each channel use the antenna numbers and indices change according to BNM and ANM bits, which means the transmission slots are not always stable. That’s why the fading distribution parameters are always reconfigured by the active antenna blocks and active transmit antennas in these active blocks. This reconfiguration of fading distribution parameters is achieved by obtaining the amplitude and power of each fading channel. To obtain these parameters, a method so called numerical data fitting is used, which is explained in detail in [29].

In M-MIMO-ANM scheme, the active antenna patterns are decided by BNM bits and ANM bits, which may exhibit a random variety for the number of antenna blocks and antennas in each active block for the data transmission. Therefore, an intuitive approach is adopted to obtain a similar distribution to the original fading distribution. Acquired results prove that the intuitive distribution results from the simulations, which are named as the effective distribution, show very similar characteristics to the Rayleigh distribution with different scale factors and means, as shown in Table 3. The following formula represents the amplitude channel distribution.

fα(α)=αβ2exp(α22β2) ⁣,f_{\alpha}\left (\alpha \right)=\frac {\alpha}{\beta ^{2}} \exp \left ({-{\frac{{\alpha^{2}}}{ 2 \beta^{2}}}}\right )\!, (26)

where β\beta is th scale parameter and α=heff\alpha=h_{eff} is the Rayleigh channel distribution amplitude, ω=α2\omega = \alpha^2 is represented as the mean square of α\alpha, which is also equal to ψ\psi where ψ\psi is the mean factor as a vital parameter in the channel power calculation of the effective channel. These distribution parameters are given in Table 3 for the proposed M-MIMO-ANM.

In order to generate a power distribution function (PDF) for the γ=heff2Pσ2\gamma=\frac {|h_{eff}|^{2} P}{\sigma^{2}}, following expression is given as

fγ(γ)=fα(Ωγγˉ)1β2γˉγΩf_{\gamma}\left ({ \gamma }\right )= \dfrac {f_{\alpha}\left ({ \sqrt {\frac{\Omega \gamma }{ \bar {\gamma}}} }\right ) }{ \frac{1} {\beta^2} \sqrt {\frac{\bar {\gamma} \gamma }{ \Omega}}} (27)

By using these calculated distribution functions above, BER performance of the proposed M-MIMO-ANM can be analyzed properly.

Error Performance Analysis of M-MIMO-ANM

In the proposed M-MIMO-ANM scheme, there are three stages that operate the estimation. The first one is the estimation of the number of antenna blocks, second is the estimation of number of transmit antennas, and the third one is the transmission of estimated bits, which makes the analytical performance analysis more complicated. However, the following derived equation offers a correct performance analysis.

Let the three stages of the estimation process is notated by A1,A2A_1, A_2, and A3A_3 for the number of blocks estimation, the number of antenna estimation, and transmitted bit estimation, respectively. Even though the data stream grouping is the same for the BNM bits and ANM bits, it is not the same for the Main Bits. There are two bits used in each BNM and ANM bits group for the transmission of one bit in the Main Bits group. Therefore, their respective probabilities are P(A1)=2/5P(A_1)= 2/5, P(A2)=2/5P(A_2)= 2/5, P(A3)=1/5P(A_3)= 1/5. By assuming the PBNM(E)P_{BNM}(E) and PANM(E)P_{ANM}(E) are the error probabilities for A1A_1 and A2A_2, respectively. PBPSK(E)P_{BPSK}(E) is the error probability for Main bits which is modulated by BPSK, the total error probability PTotal(E)P_{Total}(E) can be formulated as

Ptot(E)=PBNM(EA1)P(A1)+PANM(EA2)P(A2)+PBPSK(EA3)P(A3)\begin{gathered} P_{{\rm tot}}(E) = P_{{\rm BNM}}(E\vert A_{1})P(A_{1})+P_{{\rm ANM}}(E\vert A_{2})P(A_{2})\\+P_{{\rm BPSK}}(E\vert A_{3})P(A_{3})\\ \end{gathered} (28)
Ptot(E)=25PBNM(E)+25PANM(E)+15PBPSK(E)P_{{\rm tot}}(E) = {2 \over 5}P_{{\rm BNM}}(E)+{2 \over 5}P_{{\rm ANM}}(E)+{1 \over 5}P_{{\rm BPSK}}(E) (29)

Average BER Performance of All Possible Antenna Number Activation Patterns

In this section, possible error calculations are represented in terms of three parameters; error caused by the BNM bits detection, error caused by the ANM bits detection, and error caused by the Main Bits detection.

As the first reason of error, the general BER formula of BNM Bits are given as follows:

BERBNMi=2TTotal×(1θi×Eb3×Bact×N0θi×Eb3×Bact×N0+1)BER_{BNM-i}=\frac{2}{T_{Total}}\times \left(1-\sqrt{\frac{\frac{\sqrt{\theta_i}\times E_b}{3 \times B_{act} \times N_0}}{\frac{\sqrt{\theta_i}\times E_b}{3 \times B_{act} \times N_0 }+1}}\right) (30)

where; ii is the iterator from 1 to B,
TTotalT_{Total} is the total number of transmit antennas in the system,
β\beta is the scale factor for the antenna activation pattern, and
θ\theta is the summation of the scale factors of the antennas in the antenna blocks.
BactB_{act} is the number of active antenna blocks among the whole antenna blocks.

After the BER results are calculated for each antenna block activation case, the average value of these results determines the BER performance of BNM bits as shown below.

BERBNM=i=1BBERBNMiB.BER_{BNM}= \frac{\sum_{i=1}^{B}BER_{BNM-i}}{B}. (31)

As the second reason of error, the general BER formula of ANM Bits are given as follows:

BERANMi=2TTotal×(1Bact×Tact×Eb2×βi×N0Bact×Tact×Eb2×βi×N0+1)BER_{ANM-i}=\frac{2}{T_{Total}}\times \left(1-\sqrt{\frac{\frac{B_{act}\times T_{act}\times E_b}{2 \times \sqrt{\beta_i} \times N_0}}{\frac{B_{act}\times T_{act}\times E_b}{2 \times \sqrt{\beta_i} \times N_0 }+1}}\right) (32)

where; ii is the iterator from 1 to TTotalT_{Total},
TactT_{act} is the number of active transmit antennas in the active antenna blocks.

After the BER results are calculated for each antenna block and transmit antenna activation case, the average value of these results determine the BER performance of ANM bits as shown below.

BERANM=i=1TTotalBERANMiTTotal.BER_{ANM}= \frac{\sum_{i=1}^{T_{Total}}BER_{ANM-i}}{T_{Total}}. (33)

As the third reason of error, the general BER formula of ANM Bits are given as follows:

BERMaini,j=0.4×(12×θi×βj×EbBact×Tact×N02×θi×βj×EbBact×Tact×N0+1)BER_{Main-i,j}=0.4\times \left(1-\sqrt{\frac{\frac{2\times \theta_i\times \beta_j \times E_b}{B_{act}\times T_{act} \times N_0}}{\frac{2\times \theta_i\times \beta_j \times E_b}{B_{act} \times T_{act} \times N_0 }+1}}\right) (34)

where; ii is the iterator from 1 to BB,
jj is the iterator from 1 to TTotalT_{Total}, which for each four iteration of jj, ii iterates one,

After the BER results are calculated for each antenna block activation case, the average value of these results determines the BER performance of Main bits as shown below.

BERMain=i,j=1B,TTotalBERMaini,j16.BER_{Main}= \frac{\sum_{i,j=1}^{B,T_{Total}}BER_{Main-i,j}}{16}. (35)

As a result of these BER calculations of BNM bits, ANM bits, and Main Bits the average BER of the M-MIMO-ANM system for BPSK is calculated as

BERMMIMOANM=25×BERBNM+25×BERANM+15×BERMain.\begin{gathered} BER_{M-MIMO-ANM}=\frac{2}{5}\times BER_{BNM}+\\\frac{2}{5}\times BER_{ANM}+\frac{1}{5}\times BER_{Main}.\end{gathered} (36)

Performance Demonstration

Within this section, by running the Monte-Carlo simulations for each offered scheme, Multiple MIMO-ANM, and Multiple MIMO-ANM-AAS, the performance results of each scheme are exhibited over a Rayleigh fading channel in terms of BER. In the conduction of the system number of antenna blocks and number of transmit antennas in each block are considered to be four (B=4,T=4)(B=4, T=4), which means the total number of transmit antennas in the whole system is sixteen (TTotal=16)(T_{Total}=16), whereas the number of antennas at the reception side of the system is assumed to be one (R=1)(R=1).

Even though a comparison of a less amount of transmit antenna containing Multiple MIMO-ANM scheme with the conventional MIMO-ANM scheme, which contains only four transmit antennas, would provide a better understanding in terms of the superiority of Multiple MIMO-ANM system, it would require to keep either one of those transmission antenna blocks or transmit antennas in each block singular to acquire four transmit antennas at the transmission end, which makes the purpose of the proposed Multiple MIMO-ANM scheme meaningless. Regarding this problem, Monte-Carlo simulations of the conventional MIMO-ANM are reconducted for this study, and the number of transmit antennas is changed to sixteen, to properly see the contribution of a block number sensitive transmission algorithm on the MIMO-ANM system. The parameters used in the simulations for different varieties of modulation types are given in Table [4].

TABLE 4: Simulation Parameters

Table 4

Modulation Type

BPSK (M=2)

Number of Symbols

106 per iteration

Number of Antenna Blocks

4

Number of Transmit Antennas

4

Number of Receive Antennas

1

Number of available antennas for ANM

16

Number of BNM mapping bits

2

Number of ANM mapping bits

2

Wireless channel

Block Rayleigh fading

Fig. 7 shows the numerically analyzed BER performance of the proposed M-MIMO-ANM and M-MIMO-ANM-AAS. Fig. 7 also shows the comparison of M-MIMO-ANM and conventional MIMO-ANM under different number of transmit antenna conditions (i.e. T=4T=4, T=16T=16). As the Fig. 7 indicates, even the transmit antenna number is increased to sixteen in conventional MIMO-ANM to equalize the transmit antenna number with M-MIMO-ANM, the effect of the transmit antenna blocks creates an advantage for M-MIMO-ANM, even both conventional MIMO-ANM and proposed M-MIMO-ANM are considered under the same antenna number conditions. This significant gain results in a higher data coverage rate and more effective transmit power management without sacrificing any requirements of the service operations.

Figure 7

Comparison of Different ANM Schemes Under

BPSK Conditions.

Figure 8

Simulation Results of Multiple MIMO-ANM

Under BPSK Modulation Conditions.

Fig. 8 illustrates the average error rates of each bit group in the given data stream, namely, BNM bits, which are modulated by the number of antenna blocks, ANM bits, which are modulated by the number of transmit antennas in each block, and Main bits, which are modulated by BPSK. From this figure, it can be observed that as the SNR value is increased from 0 to 30, the BER performances of each bit group are getting better results, as compared with conventional MIMO-ANM.

Since both M-MIMO-ANM and conventional MIMO-ANM schemes are capable of transmission five bits at a time in a sixteen transmit antenna case, it might be considered why the M-MIMO-ANM is more preferable than conventional MIMO-ANM. To explain this, several reasons can be offered. The first reason is obviously the superior performance of M-MIMO-ANM, that is caused by the extra channel boost by the antenna blocks as shown in Fig. 7 . The second reason is the lower complexity that the M-MIMO-ANM offers. By dividing the ANM bits in conventional MIMO-ANM as BNM bits and ANM bits for M-MIMO-ANM results in activating less number of antennas without sacrificing from BER performance.

Figure 9

Theoretical Calculation Results of Multiple

MIMO-ANM Under BPSK Modulation Conditions.

Lastly, Fig. 9 is the exhibition of the derived BER formulas for M-MIMO-ANM, where the overall average theoretical BER performance indicated in green color curve shows similar characteristics with the simulated BER performance that is shown in Fig. 8.

Conclusion

In this paper, M-MIMO-ANM scheme is proposed as a new data transmission method. The basic idea behind M-MIMO-ANM is increasing the number of transmit antennas and locating them into groups, namely the antenna blocks. By doing this, M-MIMO-ANM creates an opportunity to deploy a new dimension which is the number of antenna blocks, in addition to the number of antennas to convey extra data bits beside the transmitted bits by the antenna number modulation and conventional M-ary PSK/QAM symbols. The advantages of the M-MIMO-ANM over conventional MIMO-ANM is the lower BER performance and higher data rate in addition to the lower complexity and ability to make not only the best antenna selection, but also the best antenna block selection that is created by the best antennas.

Simulation codes

The simulation codes used to generate the results presented in this paper can be found at this link.

Authors Bio.

Muhammet Kirik is a senior electrical and electronics engineering student at Antalya International (Bilim) University, Turkey. His current research interests include orthogonal frequency-division multiplexing multiple-input multiple-output systems, multi-dimensional modulation techniques, and orthogonal/non-orthogonal multiple access schemes for future wireless systems.

Jehad M. Hamamreh is currently an Assistant Professor with the Electrical and Electronics Engineering Department, Antalya International (Bilim) University, Turkey. He received the Ph.D. degree in electrical-electronics engineering and Cyber systems from Istanbul Medipol University, Turkey, in 2018. He worked as a Researcher at the Department of Electrical and Computer Engineering in Texas A&M University. He is the inventor of 8+ Patents, and He has authored more than 55+ peer reviewed scientific papers along with several book chapters. His innovative patented works won the golden, silver and bronze medals by numerous international invention contests and fairs. His current research interests include wireless physical and MAC layers security, orthogonal frequency-division multiplexing multiple-input multiple-output systems, advanced waveforms design, multidimensional modulation techniques, and orthogonal/non-orthogonal multiple access schemes for future wireless systems. He is a regular investigator and referee for various scientific journals as well as a TPC member for several international conferences. He is an Editor at RS-OJICT and Frontiers in Communications and Networks. He can be reached at jehad.hamamreh@gmail.com.

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