We show a way to optimize the capacity and at the same time achieve high coverage in LOS for a mmwave system indoor. We optimize MIMO with regard to maximum Shannon capacity for a pure LOS channel. We describe the general procedure in order to maximize the capacity for our considered geometry, which consists of a circular arc array at the transmitter and a uniform linear array (ULA) at the receiver. The method is based on the optimization of the interelement distances at the transmitter and the receiver. High coverage is obtained with the use of the circular geometry and beamforming. We propose an example mmwave system in the 70 GHz portion of the Eband (71–76) GHz. The results show that the proposed system is able to achieve full coverage in LOS as well as high capacity, with practical dimensions.
During the last years, there has been an increased interest in mmwave communications. The demand for fast data rate had a crucial role, and communication systems in the mmwave bands have been intensively investigated [
Our work is focused on guaranteeing two important requirements for mmwave wireless communications: provide high capacity and full LOS coverage, and we consider an indoor scenario. As mentioned before, a way to maximize the capacity in MIMO systems is to adjust the interelement distances at the transmitter and the receiver. A closedform expression for the geometry maximizing capacity was found for the case of two uniform linear arrays (ULAs) in [
The rest of the paper is organized as follows: in Section
A MIMO transmission system employs a number of transmit and receive antennas to transmit data over a channel. We denote the number of transmit antennas by
The additive noise vector contains i.i.d. circularly symmetric complex Gaussian elements with zero mean and variance
We denote the covariance matrix of the transmitted signal by
If the total average transmit power is limited to
In the following, we also assume that all receiver antennas experience the same average received power. This average received power,
For convenience, we define the variables
Here,
Equation (
It is common practice to model the channel matrix as a sum of two components, a LOS component and a NLOS component.
The mmwave system analyzed in this paper focuses only on the LOS channel because of the frequency band applied, as explained in the introduction. The entries in the LOS component matrix are discussed in more detail in the following section.
We focus on the LOS Channel, and it has previously been demonstrated that, in order to optimize the MIMO capacity, the antennas must be properly spaced [
Geometry of the proposed system.
Referring to Figure
The angles of the local spherical coordinate system at the transmitter and receiver are denoted by
In order to make
The first step is to define the vectors
The final expression was derived considering some simplifications. We consider the case where
The symbols transmitted from each antenna at the transmitter will be received at
We are going to derive the antenna separation which maximizes the Shannon capacity by considering a pure LOS channel. We Consider that trace
Now using the expression for finite geometric series, we get
This can further be expressed as
As we can see, there are different solutions, but we chose the smallest antenna distance, which is usually preferred.
Now considering that
Unless the maximum arc aperture is below 30°, a much better expression is found if we multiply this result by
From (
What comes from (
We show in Figure
LOS capacity by varying the number of transmitters (
Difference between the maximum theoretical capacity and the actual achieved capacity by varying the number of transmitters (
From a mmwave system design point of view, an obvious goal is to maximize the capacity and at the same time achieve full coverage in LOS. Our system is assumed to operate in the 70 GHz portion of the Eband (71–76 GHz) indoor (Same design procedure could be applied to all mmwave frequencies (like 60 GHz)). As described before, it is crucial at those frequencies to achieve LOS links, due to the high losses.
The system proposed is a
The system analyzed in the following sections will consider different aspects. First of all a baseline link budget is exploited; then the single element is designed. After that, the performances of the single element as well as the subarray farfield pattern will be described.
The link budget is described in Table
Example link budget parameters.
Tx Power  3  dBm 
GTx  19  dBi 
GRx  10  dBi 
Path loss [ 
−91  dB 
Background noise  −174  dBm/Hz 
Noise BW  93  dB 
Noise figure Rx  5  dB 
 


dB 
For the proposed system, we use a suspended patch antenna. Such antenna achieves improved performance compared to conventional patch antennas in terms of gain and bandwidth. A similar kind of antenna was already developed and tested at the 77 GHz automotive radar frequency [
Single element suspended patch antenna.
The substrate has a permittivity equal to 2.2, the suspended height is 200
Designed patch performances: (a) radiation pattern (b) reflection coefficient (dB).
As already explained, each transmitter is itself a subarray. Using this concept, we are able to achieve the desired coverage by smartly placing the transmitter in a room. In Figure
Referring to Figure
The performance of each subarray at the transmitter was simulated for different focusing angles in azimuth. The transmitter geometry and the radiation patterns are shown in Figure
Transmitter geometry (a) and subarray radiation patterns for different focusing angles in azimuth: broadside (b) 30° (c) and 45° (d).
The array is able to achieve a ±50° coverage in azimuth, and the gain is between 18.8 dBi and 20.4 dBi depending on the focusing angle. A taylor window is applied in order to decrease the side lobes to be at least 20 dB lower than the main lobe. This is important because in such a system they would contribute only to the multipath, which is not desired for a mmwave LOS MIMO system. With the use of a circular arc array at the transmitter, we are able to achieve full hemispherical coverage with relatively narrow beamwidths. This would not be possible in case of a linear array, since the typical maximum coverage, attainable with patch elements, is ±60° in the broadside direction.
This section will show the capacity achievable with the designed system indoor. We consider a
Coverage areas for our system.
Indoor capacity (bit/s/Hz) achievable for different scenarios: (a) SIMO (b)
The capacity attainable for the 3 scenarios is shown in Figure
In order to calculate the capacity for Figure
Indoor capacity for a moving receiver.
This paper proposed a mmwave MIMO system able to achieve highcapacity as well as fullcoverage indoor in LOS. This is possible by considering a particular geometry for the transmitter and receiver, which involves proper dimensioning of the interelement distances between each MIMO node. The geometry involves both linear and circular MIMO arrays, as well as subarrays. The proposed system considers only LOS links and highly directive beams with low side lobes. Such configuration is adopted in order to drastically reduce the multipath. Further research will be focused on evaluating the performances of the proposed system in a real scenario.