Option #1: A new, more powerful PlayStation
The current-gen console processors are an assemblage of off-the-shelf AMD components with some level of customisation requested by Sony. In the move to 14/16nm production technology, there's a 2x increase to transistor density compared to 28nm, meaning that Sony can produce a microprocessor the same size as PS4's current Liverpool chip, but theoretically twice as powerful. Sony could also stand to benefit from AMD's advances in both CPU and GPU technology - its upcoming Zen CPU cores and Polaris GPU architecture.
However, the question of which parts are available to Sony comes down to timelines. Polaris is viable but difficulties may arise in terms of the new APU's CPU component. AMD's Zen architecture releases first as a performance desktop part towards the latter end of this year - consoles rely on low-power mobile technology, and the PC equivalents remain unclear, with no mention on AMD's roadmaps. There's a very strong possibility that a 2017 revised PlayStation could feature a relatively big jump in GPU performance, but conversely, the CPU component could remain much the same.
We know a little - but still not much - about Polaris, AMD's new GPU component, due later this year. We know that it's based on a fourth generation iteration of its GCN architecture, we know that AMD is promising a radical improvement in performance per watt (a mixture of design improvements, plus the move to 14nm FinFET fabrication technology), and we know that two processors have been designed - Polaris 10 and 11 - aimed at mainstream and higher-end markets. Think of them as today's equivalents to GCN's initial launch in 2011/2012 with the arrival of the Radeon HD 7970/7950 (codename Tahiti) and Radeon HD 7870/7850 (Pitcairn).
But here's the rub - everything we're hearing suggests that Sony is expecting this console to be paired with a UHD display. However, realistically, achieving even a 2x increase in GPU power compared to the current PS4 would be a remarkable achievement. To fit into a console-sized box, even this may be too optimistic.
Making life more difficult is the need for a bump to the surrounding memory architecture. More memory would be required to get more out of 4K resolution (higher quality textures), but more than that - faster RAM is required to service a more potent GPU. We aren't hopeful of a massive bump here, owing to cost issues. Other faster technologies - like HBM for example - exist but remain too expensive and aren't ready right now for show-time in a console.
From the media side of things, we would expect Sony to support HDMI 2.0, offering 4K video output at 60Hz along with the HDCP 2.2 content protection scheme - so Netflix at 4K on this unit would be no problem. We would not be surprised to see a next-gen 4K Blu-ray player in there either.
What we might expect:
An APU with a higher-end Polaris would push graphics on - a 2x performance boost in GPU power compared to PS4 is achievable in a console form-factor. Possibly more - we really need to see the desktop PC equivalent parts first.
By default, Polaris has support for 4K, HDMI 2.0, HDCP 2.2 and HDR.
Console would not be cheap owing to the size of the processor - conceivably on par with PS4's £359/$399 launch price.
Possibly higher depending on how much Sony pushes the boat out in terms of processor size and memory allocation.
This PS4K could co-exist with a cheaper 'PS4 Slim' based on the older APU, again using 14nm/16nm technology.
The bottom line: In 2017, production technologies on 14/16nm should be more mature, and a significantly more powerful PlayStation could be released. But the pace of technological progress in the PC space isn't as rapid as it is on mobile. It took four dramatic leaps in chip production technology to make the generation leap between PS3 and PS4 possible. By 2017, there will have only been one viable jump in fabrication technology available to console manufacturers, and expectations should be limited. Actual 4K games will be in very short supply.
But the large majority doesn't use those anymore.
