All posts by Yasir Ahmed (aka John)

About Yasir Ahmed (aka John)

More than 20 years of experience in various organizations in Pakistan, USA and Europe. Worked as Research Assistant within Mobile and Portable Radio Group (MPRG) of Virginia Tech and was one of the first researchers to propose Space Time Block Codes for eight transmit antennas. The collaboration with MPRG continued even after graduating with an MSEE degree and has resulted in 12 research publications and a book on Wireless Communications. Worked for Qualcomm USA as an Engineer with the key role of performance and conformance testing of UMTS modems. Qualcomm is the inventor of CDMA technology and owns patents critical to the 5G and 4G standards.

MSK – A Continuous Phase Modulation (CPM)

Some Background on MSK

I – In the previous post we presented the mathematical model and code for BER calculation of a popular modulation scheme called MSK. However in the code we shared, we only considered one sample per symbol, which makes MSK look like BPSK. While BPSK symbols fall on the real axis, MSK symbols alternate between real and imaginary axes, progressing by π/2 phase during each symbol period. MSK signal thus has memory and this can help in demodulation using advanced techniques such as Viterbi Algorithm. 
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Minimum Shift Keying Bit Error Rate in AWGN

I - Minimum Shift Keying (MSK) is a type of Continuous Phase Modulation (CPM) that has been used in many wireless communication systems. To be more precise it is Continuous Phase Frequency Shift Keying (CPFSK) with two frequencies f1 and f2. The frequency separation between the two tones is the minimum allowable while maintaining orthogonality and is equal to half the bit rate (or symbol rate, as both are the same). The frequency deviation is then given as Δf=Rb/4. The two tones have frequencies of fc±Δf where fc is the carrier frequency. MSK is sometimes also visualized as Offset QPSK (OQPSK) but we will not go into its details here. 
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Pulse Amplitude Modulation Symbol Error Rate in AWGN

Pulse Amplitude Modulation (PAM) is a one dimensional or in other words real modulation. Simply put it is an extension of BPSK with M amplitude levels instead of two. This can be a bit confusing because BPSK can be looked at as a phase modulation and its natural extension must be QPSK or 8-PSK modulations. To remove this ambiguity lets call M-PAM an extension of simple amplitude modulation but with M levels. In the discussion below we consider M=4 but then extend it to the general case of M=2k (k=1,2,3…).

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Beyond Massive MIMO

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.

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Wireless Channel Modeling: Back to Fundamentals

Simplified Wireless Communication Channel Model

When a wireless signal travels from a transmitter (Tx) to a receiver (Rx) it undergoes some changes. In simple terms the signal s(t) is scaled by a factor h(t) and noise n(t) is added at the receiver. Let’s take this discussion forward with a simple example. Suppose the Tx transmits one of two possible symbols, +1 or -1. In technical lingo this is called Binary Phase Shift Keying (BPSK). If the channel scaling factor is 0.1 we will either get a +0.1 or -0.1 at the Rx to which AWGN noise is added. The noise is random in nature (having a Gaussian distribution) but for simplicity we assume that it can have one of two values, +0.01 or -0.01.

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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:

  1. Unlicensed band means you do not have to pay for using the frequencies in this band.
  2. Wide bandwidth of 7 GHz allows high data rate transmissions. Remember Shannon Capacity Theorem?
  3. 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.
  4. Smaller antenna sizes allowing for multiple antennas to be put together in the form of an array providing high gain.
  5. This band is quite mature and electronic components are cheap and easily available.
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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.

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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).

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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.

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Fundamentals of a Circular Array – Mathematical Model and Code

Array Factor and Element Factor

In the previous post we discussed the case of a Square Array which is a special case of a Rectangular Array. The code we shared can handle both the cases as well as Uniform Linear Array. We did briefly talk about the response of an element vs the response of an array, but we did not put forward the mathematical relationship. So here it is:

Response of an Array = Array Factor x Element Factor

In this post as well as previous posts we have assumed the element response to be isotropic (or at least omni-directional in the plane of the array) giving us an Element Factor of 1. So the array response is nothing but equal to the Array Factor.  In this post we mostly discuss the 2D Array Factor but briefly touch upon the 3D case well at the end. Continue reading Fundamentals of a Circular Array – Mathematical Model and Code