It has been some time since my last post. For a while (before many of the current members were even in the WSIL) I was one of the few posting, so I’m glad to see that the WindoWSIL has really taken off in terms of group participation and readership. Recently, my 60 GHz Wireless Communications (60G) tutorial paper appeared in IEEE Vehicular Technology Magazine, so I thought as an appropriate companion I would write an informal post for the interested reader.
What makes 60G so interesting for research?
In my opinion there are two primary reasons that 60 GHz has received so much attention recently.
- There is 7 GHz of unlicensed (free) bandwidth available in the United States alone!
Additionally, there is around 5 GHz of unlicensed bandwidth common to Europe, most of Asia, Australia, and North America. This amount of bandwidth is unparalleled at traditional frequencies such as 900 MHz, 1800 MHz, 2450 MHz, and 5000 MHz. 62 MHz of licensed spectrum around the 700 MHz carrier frequency was recently auctioned in the United States netting a total of around 20 billions of dollars. Obviously bandwidth is precious, and when 7 GHz is available, people pay attention.
- The 60G carrier frequency in fundamentally range limited and presents significant challenges in antenna design, analog circuits, digital processing, and higher (cross) layer design. For this reason the 7 GHz of bandwidth is still relatively unused even though it was opened up over 5 years ago. If operating at 60G was just a matter of ramping up the carrier frequency of current systems, there might not be so much buzz (or money) in 60G research. As communication engineers, we should be licking our chops, because it gives us some unsolved problems we can sink our teeth into. Next, I will elaborate on some of the limitations and design challenges that make 60G so interesting.
60G Challenges
The most obvious limitation of 60G to an engineer is the carrier frequency itself. Physics (via the Friis free space propagation formula) dictates that we lose 20 dB in received power every time we multiply the carrier frequency by 10. That means if I have two systems, one operating at 6 GHz and one operating at 60 GHz, I would have to transmit 20 dB more power in the 60 GHz system to achieve the same performance in a vacuum. Of course we don’t live in a vacuum, and that brings us to two more limitations at 60 GHz: reduced propagation through materials and increased Doppler effects. The ability of electromagnetic waves to penetrate solid objects is a function of the carrier frequency. Measurements have shown that propagation through objects is reduced at 60 GHz, limiting the ability of non-line-of-sight communication. Doppler frequency, which results from mobility of objects around communication devices, is proportional to the carrier frequency. Since the carrier frequency is significantly larger than traditional systems, we will experience much larger Doppler frequencies, which may complicate feedback, channel estimation, and higher layer design. 
Finally, and perhaps the limitation that encouraged national entities to remove licensing restrictions, 60 GHz wireless transmissions experience Oxygen absorption effects. It turns out that Oxygen resonates at 60 GHz, providing 10-20 dB of signal attenuation per kilometer (see image at right sourced from Marcus Spectrum Solutions).
From a design perspective, the fundamental limitations of the wireless channel are not the only difficulties. 60G antenna design is unique since the antenna dimensions are reduced. Therefore, antenna fabrication will require more expensive milling technology, especially for planar antenna arrays. RF circuits at 60 GHz may also have to discard simplifying lumped element assumptions as wavelengths approach device dimensions. Analog circuit design is complicated for many other reasons including reduced amplifier gain characteristics, reduced power output capabilities for transistors, amplification of frequency instability (phase noise). In general this leads to increased cost in engineering design or the technology implemented.
Current Activity
After the laundry list of limitations and design obstacles presented above you might be thinking to yourself “there’s no point in trying” or “it will never work.” Thankfully, that’s not the consensus of the wireless market. We have seen significant activity in industry recently to try and bring 60 GHz to the consumer in the near future. IEEE 802.16d, the precursor to WiMax, actually considered using frequencies up to 66 GHz. Unfortunately, it quickly became apparent that the above challenges were too much for mobile broadband devices that need to communicate over kilometer distances. As a consequence, all the wireless devices to appear in the near future are targeted for indoor, short range communications. IEEE 802.15.3c is currently constructing a standard for operating wireless personal area networks at 60 GHz. The 3c working group has formally accepted a proposal, an important first step towards actual standardization. 15.3c devices should be seen as a replacement for UWB, which will eventually replace Bluetooth. While, 802.15.3c is addressing a host of applications for high throughput communications, WirelessHD has a single focus. WirelessHD is a consortium of companies that have banded together to create 60G technology for high definiton wireless video streaming. Here is a nice overview of their OFDM-based standard as well as a video summary of a CES 2008 presentation. In the past wireless video streaming was subject to low performance lossy compression or high cost lossless compression. Because of the 60 GHz bandwidth available the wireless industry is hoping to provide low cost, high performance uncompressed video streaming. With 60 GHz it is only a matter of time before all peripheral devices on a personal computer are cable-less and all the wires in your home entertainment center are gone (except for power cables of course). For completeness I want to also mention that ECMA has thrown their hat into the ring and are in the process of building a 60 GHz standard. Since this is the same standardization body that brought us the WiMedia Multiband OFDM standard for UWB, I can only expect they see 60 GHz as an extension for higher rates. In that sense IEEE 802.15.3c and the ECMA standard will be directly competing; whether the two can coexist is unknown at this point.
Design Ideas
If you’d like to know more about how to design the physical layer in view of these challenges or a look at developing technologies that may change the landscape of 60G, please refer to the aforementioned IEEE reference or its preprint here. I think there is copious room for physical layer or higher layer design suggestions that take advantage of 60 GHz with consideration of its challenges. Along with the 60G challenges, we also experience unique advantages such as reduced size constraints on antenna arrays and improved security of communication signals. I’m more than willing to hear your ideas so please contact me with any additional questions.
receivers, then a rate vector ![${\bf R} = [R_1, R_2, \ldots, R_N]$](http://windowsil.org/latexrender/pictures/bd3bc224c57f6561118b879ecc2a6301.gif "${\bf R} = [R_1, R_2, \ldots, R_N]$")
is said to be achievable on the broadcast channel if information can be transmitted reliably at rate 
from the transmitter to the receiver 
,
, simultaneously. The capacity of broadcast channel is defined as the convex hull of all achievable rate vectors. Finding the capacity of a general broadcast capacity has been a long standing open problem in information theory. In this article we will discuss the multiple input multiple output broadcast channel (MIMO-BC) whose capacity region has been found recently by Weingarten et. al.
antennas wants to transmit independent information to 
receiver is equipped with 
antennas 
. Let 
be the signal transmitted by the transmitter, then the received signal 
received by receiver ![\[{\bf y}_n = H_n{\bf x} + {\bf v}_n,\]](http://windowsil.org/latexrender/pictures/3dc6d0819d1470031d4660b271993574.gif "\[{\bf y}_n = H_n{\bf x} + {\bf v}_n,\]")
where 
is a 
channel matrix and 
is the additive white Gaussian noise (AWGN) with covariance matrix 
.
is the signal for receiver 
is transmitted by the transmitter. Dirty paper coding (DPC) is a technique developed by Costa for single input single output (SISO) AWGN channels when there is an interference signal present at the receiver together with AWGN. We assume the interference signal is known non causally at the transmitter. In this setting Costa showed that the capacity is 
which is exactly equal to the capacity of AWGN channel without any interference. Thus, DPC is shown to completely eliminate the effect of interference. Using DPC for the MIMO BC, if the signal for the first receiver is 
, then the signal 
for receiver 
is generated using 
as the interference signals and 
is transmitted from the transmitter. From now on we consider 
in this article for simplicity. With 
and 
, simultaneously achievable for receiver 
and ![\[R_1^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_1+ {\bf S}_2 + {\bf N}_1\right)}{\det\left({\bf S}_2+{\bf N}_1\right)}\]](http://windowsil.org/latexrender/pictures/d231b48745808e6900b2b7cef9bff54d.gif "\[R_1^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_1+ {\bf S}_2 + {\bf N}_1\right)}{\det\left({\bf S}_2+{\bf N}_1\right)}\]")
and ![\[R_2^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_2 + {\bf N}_2\right)} {\det\left({\bf N}_2\right)},\]](http://windowsil.org/latexrender/pictures/439320c9f3e1132578ecfaea9d24fa59.gif "\[R_2^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_2 + {\bf N}_2\right)} {\det\left({\bf N}_2\right)},\]")
where 
is the covariance matrix of ![\[R_1^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_1 + {\bf N}_1\right)}{\det\left({\bf N}_1\right)}\]](http://windowsil.org/latexrender/pictures/3bbf2faa4f6d254df3cf1b10049f875f.gif "\[R_1^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_1 + {\bf N}_1\right)}{\det\left({\bf N}_1\right)}\]")
and ![\[R_2^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_1+ {\bf S}_2 + {\bf N}_2\right)}{\det\left({\bf S}_1+{\bf N}_2\right)}.\]](http://windowsil.org/latexrender/pictures/916d11f440683b3dcc4808c18fb34666.gif "\[R_2^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_1+ {\bf S}_2 + {\bf N}_2\right)}{\det\left({\bf S}_1+{\bf N}_2\right)}.\]")
We denote the convex hull of all rate vectors achievable with DPC as 
.
, where ![\[{\bf y}_n = {\bf H}_n{\bf x}_n + {\bf v}_n, \ n=1,2.\]](http://windowsil.org/latexrender/pictures/8357ddee5a7849d18c5943276714697d.gif "\[{\bf y}_n = {\bf H}_n{\bf x}_n + {\bf v}_n, \ n=1,2.\]")
Since we are assuming 
to be a square matrix, without loss we can multiply the received signal by 
without changing the capacity. Note that ![\[{\bf y}_n = {\bf x}_n + {\bf v}_n, \ n=1,2.\]](http://windowsil.org/latexrender/pictures/41d56e0472684582a2f72d21c7a50874.gif "\[{\bf y}_n = {\bf x}_n + {\bf v}_n, \ n=1,2.\]")
Then a transformation of AMIMO-BC is considered, called degraded and aligned MIMO BC (DAMIMO-BC), where ![\[{\bf y}_n = {\bf H}_n{\bf x}_n + {\bf v}^{*}_n, \ n=1,2.\]](http://windowsil.org/latexrender/pictures/1b4465292912001d0491981856889816.gif "\[{\bf y}_n = {\bf H}_n{\bf x}_n + {\bf v}^{*}_n, \ n=1,2.\]")
with 
, 
denotes the covariance matrix. For any two matrices, 
,by 
we mean 
is a negative semidefinite matrix. It is easy to see that DAMIMO-BC is a degraded BC channel, i.e. one receiver receives less noisy signal than the other. For the degraded BC it is known that superposition coding is optimal, however, it is not known whether Gaussian signaling is optimal or not.
For a single input single output degraded BC (SISO-DBC), where the transmitter and each receiver has a single antenna, Bergmans showed that Gaussian signaling is optimal, however, the proof of Bergmans does not extend to the DAMIMO-BC case.
be the set of all achievable rate vectors 
with Gaussian superposition coding for DAMIO-BC and let 
and 
be the input covariance matrices achieving 
and 
. To show that any rate vector which does not belong to 
is not achievable, an enhanced DAMIMO-BC is introduced, which is defined as ![\[{\bf y}_n = {\bf x}_n + {\hat {\bf v}}_n, \ n=1,2.\]](http://windowsil.org/latexrender/pictures/c87dd9d726392c3ff8868b2f862e5a20.gif "\[{\bf y}_n = {\bf x}_n + {\hat {\bf v}}_n, \ n=1,2.\]")
where ![\[cov({\hat {\bf v}}_1) \le cov({\bf v}^{*}_1), cov({\hat {\bf v}}_1) + cov({\hat {\bf v}}_2) \le cov({\bf v}^{*}_1) + cov({\bf v}^{*}_2).\]](http://windowsil.org/latexrender/pictures/db13b5f096f8748b416db46f7bbf44e4.gif "\[cov({\hat {\bf v}}_1) \le cov({\bf v}^{*}_1), cov({\hat {\bf v}}_1) + cov({\hat {\bf v}}_2) \le cov({\bf v}^{*}_1) + cov({\bf v}^{*}_2).\]")
Clearly, any rate vector achievable on DAMIMO-BC is also achievable on the enhanced DAMIMO-BC, thus the capacity region of DAMIMO-BC is contained inside the capacity region of enhanced DAMIMO-BC.
, such that ![\[\alpha_1\left(B_1 + cov({\hat {\bf v}}_1)\right) = cov({\hat {\bf v}}_{2}).\]](http://windowsil.org/latexrender/pictures/1f40c6624992a5093cb654b9216fcbb0.gif "\[\alpha_1\left(B_1 + cov({\hat {\bf v}}_1)\right) = cov({\hat {\bf v}}_{2}).\]")
achievable on enhanced DAMIMO-BC with Gaussian signaling is equal to rate vector 
obtained with Gaussian signaling for DAMIMO-BC.
which lies outside the region 
