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I guess scalar and vector channels have nothing to do with spatial multiplexing (SM). SM is a multiplexing technique where we sue space and time to multiplex the different signals together in one stream or in different group of streams, depending upon the strategy being used.
I would like to explain the concept of scalar and vector channels because it is used very frequently in wireless communication.
Lets talk about the single user (MS) with just one antenna and a Base Station (BS) with one antenna as well. Now the wireless channel from the MS to BS will be one complex number, let me denote it as, \[h = \alpha + j\beta\]. This type of channel is known as Scalar wireless channel where MS has single receive antenna, and only one complex number is enough to model it. But now assume that the MS has more than one receive antennas, then we can make a communication link between BS and MS through multiple streams, directing each stream toward each receive antenna at MS, I am talking about downlink in particular, u can extend this concept to uplink as well. Now each of the receive antenna channel has one complex number and when we put them together, it is modeled by a vector, and i will represent it as \[H = [h_1, \cdots, h_{n_r}]\], where I have already defined \[h\]. In nut shell we can say that if there is single receive antenna then, it is a scalar channel and if there are more than one receive antennas then it is vector channel. Mathematically i can write this whole story as \[ h \in C^{1 \times N_t} \] and \[ H \in C^{N_r \times N_t}\], scalar and vector channels, respectively. If each element of the channel, whether scalar or vector, is modeled according to Gaussian distribution, then it is called as Scalar Gaussian or Vector gaussian Channels. If its real MIMO system then foe sure its channel is modeled as Vector channel.
I hope this will make my point clear about scalar and vector Gaussian channels. I tried to make it as short as possible, I know it can be expalined in much more detailed form.
As for as latex is concerened, there is option in the message writing box while we are using edaboard. If you see at the top, there is a tab called "TeX". If you just point mouse on that tab, it explains you that you can write in latex by starting with \[ your latex code \]. Its very easy if you know how to write in latex, then just put at the begining \[ and then write as you write in LaTex, and then at the end just put \], and your formula, code will be written in LaTeX format.
You are right, SISO is the example of scalar channel. As for as MISO is concerned, when you looking channel at the MS its for sure vector channel, its just like a MAC channel, like many to one.
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