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Mm‐waves propagation measurements in underground mine using directional MIMO antennas

2016; Institution of Engineering and Technology; Volume: 10; Issue: 5 Linguagem: Inglês

10.1049/iet-map.2015.0408

1751-8733

Mohamad Ghaddar, Larbi Talbi, Mourad Nedil, Ismail Ben Mabrouk, Tayeb A. Denidni,

Cooperative Communication and Network Coding

IET Microwaves, Antennas & PropagationVolume 10, Issue 5 p. 517-524 Research ArticleFree Access Mm-waves propagation measurements in underground mine using directional MIMO antennas Mohamad Ghaddar, Mohamad Ghaddar Engineering School, UQAT, 675 1ère Avenue, Val d'Or, Canada, J9P 1Y3Search for more papers by this authorLarbi Talbi, Larbi Talbi Department of Computer Science and Engineering, University of Quebec – Outaouais, 101 rue St-Jean-Bosco, Case Postale 1250, succursale B, Gatineau, (Quebec), Canada, J8X 3X7Search for more papers by this authorMourad Nedil, Corresponding Author Mourad Nedil Mourad.Nedil@uqat.ca Engineering School, UQAT, 675 1ère Avenue, Val d'Or, Canada, J9P 1Y3Search for more papers by this authorIsmail Ben Mabrouk, Ismail Ben Mabrouk University of Tabuk, Tabuk, 71491 Saudi ArabiaSearch for more papers by this authorTayeb A. Denidni, Tayeb A. Denidni Wireless Communications, INRS, Place Bonaventure, 800 de la Gauchetiere, Montreal, Canada, H5A 1K6Search for more papers by this author Mohamad Ghaddar, Mohamad Ghaddar Engineering School, UQAT, 675 1ère Avenue, Val d'Or, Canada, J9P 1Y3Search for more papers by this authorLarbi Talbi, Larbi Talbi Department of Computer Science and Engineering, University of Quebec – Outaouais, 101 rue St-Jean-Bosco, Case Postale 1250, succursale B, Gatineau, (Quebec), Canada, J8X 3X7Search for more papers by this authorMourad Nedil, Corresponding Author Mourad Nedil Mourad.Nedil@uqat.ca Engineering School, UQAT, 675 1ère Avenue, Val d'Or, Canada, J9P 1Y3Search for more papers by this authorIsmail Ben Mabrouk, Ismail Ben Mabrouk University of Tabuk, Tabuk, 71491 Saudi ArabiaSearch for more papers by this authorTayeb A. Denidni, Tayeb A. Denidni Wireless Communications, INRS, Place Bonaventure, 800 de la Gauchetiere, Montreal, Canada, H5A 1K6Search for more papers by this author First published: 01 April 2016 https://doi.org/10.1049/iet-map.2015.0408Citations: 12AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study reveals the interests towards the use of directional (D)-multiple-input and multiple-output (MIMO) setup as a potential solution to overcome the severe propagation loss of inherent line of sight (LOS) mm-waves communications in underground mine. To show the advantages of the proposed D-MIMO, two separate measurement campaigns are assessed in a comparative way; the first uses a single-input single-output (SISO), while the second uses a 2 × 2 D-MIMO system. Furthermore, due to the unavoidable blockage of direct LOS in underground mines, the miner's shadowing effects (NLOS-MSE) are investigated. Thus, using both D-SISO and D-MIMO setup, the channel propagation characteristics are extracted and investigated with and without the presence of a miner completely blocking LOS. Under LOS, results show that, besides offering a reliable mm-waves link budget, D-MIMO restrains the average path loss (PL) by more than 4.7 dB, further suppresses the root mean square delay to 1.85 ns and offers an average capacity of 23.3 bits/s/Hz. As a miner completely blocks LOS, the proposed D-MIMO system has shown a greater signal ability to overcome the effects of a miner's body; NLOS-MSE compensation of about 4.3 dB and a capacity gain of 19.6 bits/s/Hz have been achieved over the conventional SISO system. 1 Introduction Millimetre (mm)-waves wireless communications have been well proven to be supporting multi-Gb/s applications [1]. This technology has been standardised by the IEEE 802.15.3c task group for indoor short-range application [2]. Another instalment of the successful 802.11 (Wi-Fi) family, namely, the IEEE 802.11ad is established to develop very high throughput WLANs in the 60 GHz band [3]. The rapid success of such technology in surface environments and the appearance of evolutional Gb/s visional applications have drawn the interest of mining industry towards the exploration of 60 GHz short-range communications within hazardous underground mine environments [4, 5]. For instance, Gb/s video applications offer instantaneous surveillance operations for maximising miners' safety and mining productivity [6]. In a previous work [4], a measurement campaign was performed using 2 × 2 multiple-input and multiple-output (MIMO) microstrip patch arrays. The downside of such a campaign is that the channel multipath effect was a major concern while the requirements for a reliable link budget was ignored. Despite the presence of heavy multipath in the channel, however, the received signal strength still appears to be very weak as the average PL exceeds 70 dB. Thus, the optimistic channel parameters extracted in [4] might become irrelevant under a helpless mm-waves link power budget. Furthermore, MSE effects on the received signal, as a miner is walking parallel to line of sight (LOS), seem to be dramatic and are expected to increase significantly as the miner blocks LOS completely. Virtually, mm-waves wireless communication links are inherently lossy; a high directivity of more than 20 dB is required to overcome the severe free space loss that limits their coverage to very few meters [7]. In the unlicensed 60 GHz band, the Federal Communications Commission (FCC) has approved a maximum effective isotropic radiated power of 43 dBm, [8]. Thus, a practical approach for increasing mm-waves links reliability is to increase either the transmitted power or the radiation directivity [7, 8]. A more recent study [5] was carried out in the mining gallery introduced in [3], but using single-input single-output (SISO) horns antennas. Such campaign has demonstrated a realistic mm-waves link budget, a further suppression of more than 43 dB in the average PL has been offered as compared with [4]. However, the major goal in [5] was to establish a LOS communication while multipath effects of the channel were ignored. Moreover, NLSO-miner's shadowing effects (NLOS-MSE) effects have not been considered. Nevertheless, increasing the radiation directivity can make it problematic when LOS is obstructed by unavoidable presence of miners in the channel. It becomes clear from the outset of the current study that, reliable underground mm-waves radios would not be achieved unless strong multipath comparable with LOS are present in the channel. In fact, MIMO gain diversity techniques [9] offer a potential solution beyond conventional SISO systems. Theoretically, under the assumption of independent and uncorrelated sub-channels, directional MIMO systems are capable of generating NT × NR copies of the LOS component superimposed by a heavy amount of multipath, then intelligently combine them at the receiver to result in a high signal-to-noise ratio (SNR) [10]. Moreover, when array elements are spaced apart sufficiently, multiple independent copies of the transmitted signal will have a low probability to experience deep fades simultaneously [11]. To the best of our literary search, the effects of D-MIMO on underground mine mm-waves wireless channel including NLOS-MSE have not been reported yet. Thus, purpose of this experimental investigation is twofold; first, to present an experimental study that reveals the priority of D-MIMO over D-SISO systems for mm-waves wireless communications in underground mines. Second, to demonstrate the proposed D-MIMO as a potential technique for mitigating NLOS-MSE. To give a clear insight towards the achieved results, two separate D-SISO and D-MIMO measurement campaigns are investigated in a comparative way, each deals with two separate scenarios that are (i) LOS: an empty static channel and then (ii) NLOS-MSE: a miner completely blocking LOS. The rest of the paper is organised as follows. Section 2 gives details about the measurement hardware setup, procedure and site description. The achieved results are then presented and analysed in Section 3 and followed by a discussion in Section 4. Finally, the conclusion is presented in Section 5. 2 Measurement setup, site description and procedure The measurements are performed using a vector network analyser (VNA). The cables that are used to feed the antennas are of type Megaphase, they suffer from a heavy attenuation of 6.723 dB/m at 60 GHz. Such undesirable attenuation is therefore compensated by connecting each port of the VNA to a 30 dB gain amplifier; the transmitter was fed by a power amplifier (PA) while the receiver was supplied with a low noise amplifier (LNA). More description details of the employed sounding equipment are provided in [4]. Under a transmitted power of 10 dBm the amplitude and phase variations of 14,001 complex tones are recorded across 57–64 GHz. The technical specifications of the used pyramidal horn elements are listed in Table 1. It is worth noting that the gains of the used horns are frequency-dependent; their variations were removed by calibrating the experimental data in an anechoic chamber with respect to 1 m reference between TX and RX. Practically, additional antenna elements to the array may further enhance the channel performance. However, due to their availability and the sounder's hardware limitation, only two elements are considered for each array. Table 1. Millitech SGH-15 pyramidal horn technical specifications polarisation Vertical beam's elevation cut 24.3° mid-band gain, dBi 23.4 frequency range, GHz 50–75 At lower frequencies, the spatial multiplexing in rich scattering environments relies upon producing spatially uncorrelated channels [12] where the arrays elements are spaced by the order of half-wavelengths apart from each other. However, at mm-wave frequencies, LOS component usually dominates the channel multipath due to the severe propagation mechanisms loss from the surrounding surfaces. Thus, the antenna array's geometry and positioning become critical factors for achieving an optimal spatial multiplexing over LOS channels [13, 14]. Thus, the optimum spacing between the array elements (D) is set to be 15.1 cm as reported in [14] (1)where R is the maximal link range of 10 m, λ is the 5 mm wavelength, and N is the number of array elements (N = 2). Such large spacing ensures efficient gain diversity; coherently combining four MIMO sub-channels leads to a reliable instantaneous SNR [12]. The measurements have been carried out at −40 m level of an underground mine gallery operated by the Canadian Center for Minerals and Energy Technology (CANMET). More description details about the mining gallery and its structure are provided in [4, 5]. Such persuasive choice of the measurement site ensures a reasonable referral of the achieved results to the literature. During all measurements, TX and RX arrays were maintained at a height of 1.5 m on the central line of the gallery to efficiently capture the effects of all surrounding surfaces. Two different measurement scenarios were considered, (i) LOS scenario: both TX and RX were aligned by means of separate laser beam systems mounted on each antenna to capture the strongest signal level that corresponds to LOS, (ii) NLOS-MSE scenario: only one miner is present on the midway between TX and RX while completely blocking LOS. At a maximum TX–RX range of 10 m, TX was remained in a fixed position, while the mobile RX was travelling from point A to point B along the central line of the gallery with an increment distance of 1 m (Fig. 1). In LOS case, RX initial position, point A, was set to 1 m apart from TX, however, in NLOS-MSE case, RX started its position at 2 m apart from TX to ensure a free movement of the miner between terminals. Fig. 1Open in figure viewerPowerPoint Illustrative map of CANMET underground mine gallery and TX–RX arrays locations For each location of RX along its path in the gallery, the small scale measurements are obtained by arranging the centre point of RX on a 3 × 2 (Nx × Ny) points grid. The spacing between two adjacent points on the grid was chosen to be a multiple of half wavelength (ΔX = λ; ΔY = λ/2) to obtain six independent almost uncorrelated samples of the channel. At 60 GHz the wavelength is close to 5 mm, the accurate measurement positions on the grid was realised by the use of an automated system to position RX along a linear track with an accuracy in the order of 2.5 μm, description details of the used tracking system are provided in [4]. For each RX position on the grid, the complex channel transfer function (CTF) was measured 10 times (Ns = 10) to reduce the random noise effects on the experimental data. Thus, the final measured CTF is obtained by averaging 10 × 3 × 2 (Ns × Nx × Ny) snapshots for each RX location (d) throughout the gallery (2)where Α(x, y, s, f) and θ(x, y, s, f) are the measured magnitude and phase response at of the snapshot s at frequency f and position on the grid (x, y). Following the approach in [4], the 3-D MIMO channel matrix is formed by collating CTFs of all four sub-channels (hf), where NR, NT and Nf are the number of transmit, receive array elements, and discrete frequency components. 3 Experimental analysis and results Results reported in [5] have been given a particular importance as they have demonstrated their priority for mm-waves communications compared with those microstrip patch used in [4]. Therefore, under LOS scenario, our extracted results will be fairly referred to [5] which is performed under similar measurement procedure in the considered gallery. 3.1 Distance dependent PL law The measured PL has been examined prior to other statistical parameters as it relates the received power (Pr) to the transmitted power (Pt) for each TX–RX separation distance. It is important to underline the fact that the pattern of the used antenna is frequency-dependent; a slight gain variation within about 0.2 dB is noted across the bandwidth of interest as provided by the manufacturer [15]. The unwanted effects of the sounding system hardware including feeding cables and antennas were removed from the measurements by calibrating (normalisation) all measured complex CTFs with respect to 1 m reference distance between TX and RX antennas [5, 16]. Thus, the channel multipath are examined after eliminating the effects of the sounder, antenna gains and cables losses which are considered to be 0 dB. We stress that averaging of the CTF (H) measured across 14,001 frequency tones (57–64 GHz) was done on a linear scale (not in decibels) as (3)where the location-variant PL is extracted as [14] (4)where is the averaged received power in decibels at a reference distance dO from TX, in our case dO = 1 m, n is the PL exponent and σdB denotes the location-dependent shadowing fading parameter. Scatter plots of PL against TX–RX logarithmic distances and the minimised mean squared error fitting lines are presented in Fig. 2a. Table 2 shows the average PL, n and σdB of (4). Table 2. Statistical means of the SNR, PL and PL exponent (n) System MIMO SISO Scenario LOS NLOS-MSE LOS NLOS-MSE SNR, dB 36.4 25.52 31.8 20.08 PL, dB 27.6 38.4 32.3 42.7 n 1.36 0.15 1.86 0.17 σdB 1.1 0.44 1.7 0.51 Fig. 2Open in figure viewerPowerPoint (a) Measured PL and (b) Illustrative top view of NLOS-MSE scenarioa PL against TX–RX logarithmic distance b Miner's position on the midway between TX and RX 3.1.1 LOS case During data analysis, it was found that SISO signals rely mainly on LOS ray where multipath effects are insignificant. Such fluctuation in PL around its mean is due to the technical difficulties of antennas alignment which is highly sensitive to the very short wavelength. Under SISO setup, the PL decay trend, that is, the exponent 'n' and the average PL are found to agree with (n = 1.82, PLmean ≃ 36 dB) reported in [4] which was performed using similar SISO setup. Thus, confirming the validity of our extracted results. Such exponent values (n ≤ 2) implies that mm-waves SISO signals propagate slightly better than free space, during analysis, there was no clear indications about the presence of significant multipath effects. However, the presented D-MIMO has been found to offer a considerably lower PL exponent (n = 1.36), owing to the gain diversity of D-MIMO and to the guiding effect of underground mines as the strong multipath superimposing LOS aggregate to contribute in enhancing the received signal. In contrast to SISO case, under MIMO-LOS case, the fluctuation in PL around its mean is the result of the significant variation in the amount of strong multipath. Indeed, underground mines structures are location-specific, that is, their ununiformed cross section leads to a notable variation in the amount of multipath from one location to another. As well as lowering 'n', the presented D-MIMO has shown a further suppression of about 4.7 dB in the average PL as compared with D-SISO. Furthermore, the presented D-MIMO radiation setup has shown a further reduction of more than 43 dB in the average PL as compared with the MIMO patch antennas system in [4] which is performed under a transmitted power 10 dBm, thus confirming the importance of high directive antennas for mm-waves communications. In spite the low PL exponent (n = 1.48) in [3], however, such value appears to be irrelevant under a helpless power link budget. 3.1.2 NLOS-MSE case Regardless the used setup, an abrupt fall of about 18 dB in the average received power is obvious when a miner blocks LOS (NLOS-MSE) at a TX–RX distance of 2 m, then for each increase of 1 m in distance the NLOS-MSE gap cuts down with respect to LOS. As investigated experimentally and theoretically in [17, 18], the magnitude of the diffraction coefficient (D) from a human body magnifies with TX–RX distance. Theoretically the diffracted electric field (Ed) in the shadowing zone of the miner can be expressed in terms of the incident field (Ei) as [19] (5)where k is the wavenumber and sd is the distance between the point of diffraction 'Q' and the receiving antenna as shown in Fig. 2b. The scenario illustrated in Fig. 2b has provided an interesting contribution in revealing the truth that, while the mobile RX travels farther away from TX and as the obstacle (miner) blocks LOS in the midway (d/2) between TX and RX, the diffracted ray from the obstacle experiences two propagation mechanisms simultaneously, that is, an additional diffraction ability (D) around the obstacle, encountered by an almost equal amount of decrease in the incident field (free space loss). Thus, it is not surprising that PL increases very slowly (n ≃ 0.15) throughout the channel as seen in Fig. 2a. As compared with the our conventional SISO system, the presented D-MIMO has clearly demonstrated a higher signal diffraction ability around obstacles as a result of its gain diversity effects to offer a further PL reduction of 4.3 dB (Fig. 2a). For a deeper experimental analysis, it would have been more interesting to carry measurements at larger TX–RX ranges. However, the sounding equipment were limited to a maximum range of 10 m. Apparently, following the geometrical trend of PL fitting lines in Fig. 2a two possible PL zones might be defined for underground mines mm-waves SISO communications as the distance exceeds 10 m: Zone I (point A to B): in the presence of a miner in the channel, the received power trend follows SISO-MSE (line joining A and B). Zone II (vicinity of point B): the measured PL of both scenarios, that is, NLOS-MSE and LOS coincide in the vicinity of point B, implying that SISO setups are capable to counter NLOS-MSE effects as TX–RX log-distance reaches about 15 m. Similarly, in the case of D-MIMO, MSE diminishes in the vicinity of 25 m (point C). The measured PL of both, MIMO-MSE and SISO-LOS coincide (are equal) in the vicinity of 10 m (point D) implying that D-MIMO systems are capable to counter SISO equivalent MSE as TX–RX log-distance reaches 10 m. At distances ranging from 10 m to up to 25 m the received power trend is expected to follow MIMO-MSE (line joining A and C). It is worth noting that MIMO-MSE effects remains significant for up to distance ranges that exceeds those recorded using SISO system. This is due to the gain diversity of D-MIMO that results in stronger multipath along with the high ability of diffraction around obstacles; this is not the case when using SISO systems. 3.2 Link budget SNR Given the channel setup information, the receiver noise floor in dBm across the 7 GHz channel bandwidth calculated as [20] assuming a 0 dB noise figure. (6)where K is the Boltzman constant (1.38 × 10−23J/K), T is the system temperature (279°K), and B is the frequency bandwidth under consideration in Hertz. The SNR in dB is calculated as a function of TX–RX distance along the galley as (7)where, (PT) is the transmitted power, GT and GR are the gains of TX and RX antennas (assumed 0 dB), respectively. The system was equipped by PA and LNA to compensate for the feeding cables losses, hence, the cable losses are considered to be 0 dB. The empirical cumulative distribution functions (CDF) of the channel' SNRs are shown in Fig. 3. The average power PL, 'n' and the average SNR are given in Table 2. Fig. 3Open in figure viewerPowerPoint CDFs of channel' SNR 3.3 Fading distributions and shadowing effects In the literature, the signal fading distribution of indoor environments have been extensively characterised using Rayleigh, Rice and Nakagami-m statistical distributions. For example, Ricean fading distribution is an appropriate model when a direct LOS path between TX and RX is present. However, this situation remains invalid for underground mine environments as the mean of the signal power fluctuates randomly throughout the location-specific gallery giving rise to shadow fadings that are lognormally distributed [20]. Such manifestation was obvious in Fig. 2a as the calculated PL for all RX locations deviate randomly from their regression fitting lines. The zero-mean Gaussian-distributed shadow fading parameter (σdB) which is the distance between the points of the local average power and their regression line are this estimated for both considered scenarios, as summarised in Table 2. Reasonably, the CDFs of the measured power in decibels are fitted with the lognormal distribution as presented in Fig. 4. Fig. 4Open in figure viewerPowerPoint CDFs of D-MIMO shadowing fading fit using normal distributions Indeed, each scenario contains a total of 2 × 2 × 9 = 36 MIMO sub-channels throughout the gallery. σdB of the fitted theoretical CDFs confirm the values in Table 2, using D-MIMO setup, σdB obtained under LOS is found to agree with that value reported in [4]. 3.4 Time dispersive characteristics 3.4.1 Power delay profile (PDP) Since the measurements are performed in frequency domain, PDPs are extracted using a Hamming window, that is, by applying the inverse discrete Fourier transform routine to the measured complex CTFs (Hf,d) measured at each RX location (d) throughout the gallery. Mathematically, the channel's PDP can be expressed as [20]. (8)Two PDPs measured using D-MIMO are presented in Fig. 5. At each RX location in the gallery, the strongest first perceptible paths dominating the measured PDPs are the result of the direct LOS components. Their delays range from 6.67 ns to 33.3 ns for 2 m to 10 m corresponding to the shortest TX–RX path distances, respectively. Fig. 5a gives a discernment into the D-MIMO gain diversity; coherently combining NT × NR copies of the transmitted signal superimposed by a large amount of strong channel multipath results in a higher received power level and in a further suppression in the noise power. Fig. 5Open in figure viewerPowerPoint Channel PDPs measured using D-MIMO a LOS b NLOS-MSE The magnitudes of the LOS rays along the gallery do not decrease in a monotonic trend, they fluctuates around their mean where multipath contribute constructively and destructively to LOS components. At each RX location, LOS components of the PDP are then followed by series of delayed exponentially decaying rays resulted from the propagation mechanisms such as reflection, diffraction and scattering from the surrounding irregular surfaces of the mine. In Fig. 5b, NLOS-MSE scenario does not show PDP decaying trends for the aforesaid reasons in Section 1.2. 3.4.2 Root mean square (RMS) delay The RMS delay spread (σt) provides information about the channel dispersive characteristics and thus, the amount of inter-symbol interference to be encountered in the channel. It is computed from the measured PDP as [21]. (9)where αk and τk are the relative magnitude and the delay of kth perceptible multipath component in the profile, respectively. By considering a noise level threshold of 30 dB below the PDPs peaks, σt are extracted from the corresponding PDPs of each RX location along the gallery path. During data analysis, σt was found to increase with TX–RX range, but not in a monotonic trend as experienced in indoor environments. Such manifestation might due to the location-specific nature of underground. However, regardless of the travelled distance and the amount of multipath experienced in underground mines, smaller σt have been reported as compared with those obtained in indoor environments where their average σt reaches up to 44 ns [22]. Indeed, underground mine tunnels act as waveguides for the propagating signal [23, 24]. At large distances, the reflected, diffracted and scattered copies of the travelling signal arrive at RX with relatively small delays as compared with LOS path. Fig. 6 shows the probability of RX positions for which σt are less than a specified value (CDF). Regardless of the undertaken scenarios and the TX/RX locations, SISO horns demonstrate almost invariant σt throughout the gallery which means that the multipath effects are insignificant. Fig. 6Open in figure viewerPowerPoint CDFs of the measured RMS delay spreads As a result of the heavy multipath amount experienced using MIMO patch arrays, the average σt are 7.65 ns, 15.14 ns for LOS, LOS-MSE, respectively, as reported in [4]. For 50% of all RX locations in the gallery, the obtained values for σt are 1.85 ns, 4.68 ns, for LOS, NLOS-MSE Thus, the presented D-MIMO offers considerably short σt implying a lower design complexity for the equalisation tools required to counter the erroneous bits in the channel [11, 20]. Furthermore, the σt of D-MIMO appear to be more relevant as compared with those obtained in [4]; they are achieved under reliable power parameters of the channel. The statistics of σt are presented in Table 3. The values σt obtained using D-MIMO setup offer a middle solution between both [4, 5] in terms of dispersive characteristics of the channel, that is, D-MIMO offers a tradeoff between a single LOS path and heavy multipath. Table 3. Statistics of channel RMS delays, ns System scenario MIMO SISO LOS NLOS-MSE LOS NLOS-MSE σt mean 1.85 4.68 0.5 0.1 std. 1.35 3.2 0.3 0.05 3.5 Channel capacity estimation In practice, the channel capacity (C) depends not only on channel multipath but also on the total received power or, equivalently, the average SNR throughout the channel [12]. These two factors are usually not independent and some tradeoff should be practiced [12]. Thus, during the analysis of MIMO capacity, it is an intuitive practice to normalise the channel H-matrices of each channel frequency realisation of and at each Rx location before investigating the effects of SNR and multipath as parameters [25]. The normalised channel matrix for each channel realisation are expressed as (10)where ||||F is the Frobenius coefficients matrix. Given the channel information at RX for each frequency realisation, the channel capacity is estimated by Foshini and Gans as [23] (11)where the upper script (·)* denotes the Hermitian conjugate of the normalised channel matrix and I is the identity matrix. Equation (5) clarifies the logarithmic growth of MIMO systems capacity with respect to SNR assuming uncorrelated sub-channels and that the channel state information are perfectly known at the receiver. The maximum achievable error-free transmission (CB) over the bandwidth of interest (B) at a location d, is expressed as [26] (12)Basically, the spectral efficiency is a potential performance measure of MIMO systems radiation properties. Thus, to give a clear indication about the benefit of the diversity gain of the considered D-MIMO system, the capacity is evaluated with and without taking into account the gains of the antennas. 3.5.1 Capacity performance without the effects of antenna gains After the elimination of the antenna elements gains in (3), the capacity is calculated so that it takes into account the effects of SNR, multipath and the operating frequency. Figs. 7a and b show the dependency of the channel capacity on each TX–RX distance realisation as it is evaluated across the 7 GHz band for LOS and NLOS-MSE scenarios, respectively. Fig. 7Open in figure viewerPowerPoint Estimated capacity against TX–RX distance and frequency without the effects of the antenna gains (a) LOS, (b) NLOS-MSE a LOS b NLOS-MSE Under LOS, the location-dependent SNR leads to a decay trend in the capacity with respect to TX–RX incremental distances. In Fig. 7a, the capac