Recently Björnson and Marzetta in their publication on Antenna Arrays [1] discussed five possible future research directions. In their opinion Massive MIMO is no longer a theoretical concept and it is already being adopted in the industry. It is not uncommon to find 64 element antenna arrays being deployed in wireless communication systems. So we now need to look beyond Massive MIMO or MaMIMO as it is popularly referred to. Here are three possible future research directions that we find most interesting.

Continue reading Beyond Massive MIMO# Category Archives: 5G

# 60 GHz Millimeter Wave Band – Seems Like a Free Lunch

Let us start by first listing down the advantages of the 60 GHz Millimeter Wave Band, a band spread between 57 GHz and 64 GHz. This unlicensed band was first released in the US in 2001 but with limited allowance for transmit power (EIRP of 40 dBm). Later on, in 2013, this limit was increased to allow for greater transmit power (EIRP of 82 dBm) and larger range. The higher EIRP can be achieved with an antenna gain of 51 dBi or higher (EIRP is simply the product of transmit power and antenna gain). But first the advantages:

- Unlicensed band means you do not have to pay for using the frequencies in this band.
- Wide bandwidth of 7 GHz allows high data rate transmissions. Remember Shannon Capacity Theorem?
- High atmospheric absorption resulting in greater path loss (up to 20 dB/km) and shorter range. This means lesser co-channel interference and higher reuse factor.
- Smaller antenna sizes allowing for multiple antennas to be put together in the form of an array providing high gain.
- This band is quite mature and electronic components are cheap and easily available.

# Massive MIMO and Antenna Correlation

Some Background

In a previous post we calculated the Bit Error Rate (BER) of a Massive MIMO system using two different channel models namely deterministic and probabilistic. The deterministic channel model is derived from the geometry of the array (ULA in this case) and the distribution of users in the cell. Whereas probabilistic channel model assumes that the channel is flat fading and can be modeled, between each transmit receive pair, as a complex, circularly symmetric, Gaussian random variable with mean of zero and variance of 0.5 per dimension.

Continue reading Massive MIMO and Antenna Correlation# Path Loss at Millimeter Wave Frequencies

The mmWave Channel

It is well known that wireless signals at millimeter wave frequencies (mmWave) suffer from high path loss, which limits their range. In particular there are higher diffraction and penetration losses which makes reflected and scattered signals to be all the more important. Typical penetration losses for building materials vary from a few dBs to more than 40 dBs [1]. There is also absorption by the atmosphere which increases with frequency. But there are also some favorable bands where atmospheric losses are low (<1dB/km).

Continue reading Path Loss at Millimeter Wave Frequencies# Multicarrier Beamforming at mmWave

Some Background

We have previously discussed beamforming for single carrier signals. Now we turn our attention to multicarrier signals particularly at mmWave where the bandwidths are two orders of magnitude (100x) higher than at sub 6GHz band. We want to investigate that whether there is any distortion in the array response due to high signal bandwidths at mmWave.

But let us start with the case that we have discussed so far i.e. 1GHz single carrier case and a Uniform Linear Array (ULA). We then add two other carriers at 1.2GHz and 0.80GHz, quite an extreme case, stretching the bandwidth to 400MHz. Antenna spacing is still λ/2=0.15m corresponding to the center frequency of 1GHz.

Continue reading Multicarrier Beamforming at mmWave# BER of 64-QAM OFDM in Frequency Selective Fading-II

In the previous post we had considered a static frequency-selective channel. We now consider a time-varying frequency selective channel with 7 taps. Each tap of the time domain filter has a Gaussian distributed real component with variance 1/(2*n_tap) and a Gaussian distributed imaginary component with variance 1/(2*n_tap). The amplitude of each tap is thus Rayleigh distributed and the phase is Uniformly distributed. Since the power in each component is normalized by the filter length (n_tap) the BER performance would remain the same even if the filter length is changed (this has been verified experimentally).

```
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FUNCTION TO SIMULATE PERFORMANCE OF 64-OFDM IN TIME VARYING FREQUENCY SELECTIVE CHANNEL
% n_bits: Input, length of binary sequence
% n_fft: Input, length of FFT (Fast Fourier Transform)
% EbNodB: Input, energy per bit to noise power spectral density ratio
% ber: Output, bit error rate
% Copyright RAYmaps (www.raymaps.com)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function[ber]= M_QAM_OFDM_fading(n_bits,n_fft,EbNodB)
Eb=7;
M=64;
k=log2(M);
n_cyc=32;
EbNo=10^(EbNodB/10);
x=transpose(round(rand(1,n_bits)));
h1=modem.qammod(M);
h1.inputtype='bit';
h1.symbolorder='gray';
y=modulate(h1,x);
n_sym=length(y)/n_fft;
n_tap=7;
for n=1:n_sym;
s_ofdm=sqrt(n_fft)*ifft(y((n-1)*n_fft+1:n*n_fft),n_fft);
s_ofdm_cyc=[s_ofdm(n_fft-n_cyc+1:n_fft); s_ofdm];
ht=(1/sqrt(2))*(1/sqrt(n_tap))*(randn(1,n_tap)+j*randn(1,n_tap));
Hf=fft(ht,n_fft);
r_ofdm_cyc=conv(s_ofdm_cyc,ht);
r_ofdm_cyc=(r_ofdm_cyc(1:n_fft+n_cyc));
wn=sqrt((n_fft+n_cyc)/n_fft)*(randn(1,n_fft+n_cyc)+j*randn(1,n_fft+n_cyc));
r_ofdm_cyc=r_ofdm_cyc+sqrt(Eb/(2*EbNo))*wn.';
r_ofdm=r_ofdm_cyc(n_cyc+1:n_fft+n_cyc);
s_est((n-1)*n_fft+1:n*n_fft)=(fft(r_ofdm,n_fft)/sqrt(n_fft))./Hf.';
end
h2=modem.qamdemod(M);
h2.outputtype='bit';
h2.symbolorder='gray';
h2.decisiontype='hard decision';
z=demodulate(h2,s_est.');
ber=(n_bits-sum(x==z))/n_bits
return
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
```

As before we have used an FFT size of 128 and cyclic prefix of 32 samples. The FFT and IIFT operations are normalized to maintain the signal to noise ratio (SNR). The extra energy transmitted in the cyclic prefix is also accounted for in the SNR calibration.

It is observed that the BER performance of 64-QAM OFDM in the time-varying frequency-selective channel is quite similar to that in the static frequency-selective channel with complex filter taps. It must be noted that with 64-QAM the goal is to achieve higher bit rate, error rates can be improved using antenna diversity and channel coding schemes.

Given below is the wrapper that should be used along with the above code. The wrapper basically calls the above routine for each value of EbNodB. The length of the binary sequence and the FFT size are other inputs to the function. The bit error rate at the specific EbNodB is the output of the function.

```
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all;
close all;
k=6;
n_fft=128;
l=k*n_fft*1e3;
EbNodB=0:2:20;
for n=1:length(EbNodB);n
ber(n)=M_QAM_OFDM_fading(l,n_fft,EbNodB(n));
end;
semilogy(EbNodB,ber,'O-');
grid on
xlabel('EbNo')
ylabel('BER')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
```

In future we would use the standard LTE channel models, namely EPA, EVA and ETU in our simulation.