In LTE systems, up- and downlink are duplexed either using FDD or TDD. Why has this not been designed to utilize the same multiplexing technique as used for the downlink (OFDMA)? Resource blocks could be dynamically assigned for up- and downlink then, making everything much mor flexible. I know that for uplink sc-fdma is utilized, to minimize PAPR, is this maybe the only reason?
You are mixing two things modulation and multiple access. SC-FDMA has been chosen because it is battery-friendly modulation. SC-FDMA is used in both FDD and TDD modes.
There are several reasons why both FDD and TDD are defined.
Historically, people want to utilize efficiently the precious spectrum. FDD needs two bands while TDD needs only one.
Economically, LTE is a broadband technology, i.e. it is designed for high speed human data connection, and high speed human data connection favors downlink. For example in China, the dominant (and at the beginning of commercial LTE, the only) market of TDD LTE, Youtube video streaming takes a large part. In this case, reserving a band for UL is kind of wasteful. Moreover, LTE was commercialized in the middle of the Great Recession and operators were very skeptical in CAPEX spending.
Protocally, FDD and TDD are very different in term of multiplexing devices (UE), especially in HARQ-ACK reporting, UE scheduling etc. If you look at the procedure standards of LTE, just PHY layer for example, each mode requires very complicated scheduling. In mixing two modes in one cell, the level of complexity is huge for eNB, with no relevant benefit. However, mixing two modes between two or more cells are considerable and has been standardized since Release 11 in the Carrier Aggregation scope.
Technically, TDD supports better channel information (CSI) reporting thanks to the reciprocity of channel. Thus it is favored for beamforming, which requires accurate channel estimation, and a very good candidate for massive MIMO.
Finally, yes you can mix two modes if you want, but the efforts would not worth the benefit you get.
In the meantime, performed some research and asked some people about that problem. AlexTP is basically right. That there is the coarse and (semi-) static separation of resources for up- and downlink (known as duplex), is justified to avoid complexity.
What I meant in the original question is, that one could theoretically throw all resources (time x frequency) together, and perform scheduling in the eNodeB, using all of those resource blocks for both up- and downlink dynamically. Letting the considerations of PAPR minimization aside, then OFDMA could be used for the uplink also, and resource usage efficiency would be maximal. In case downlink traffic exceeds downlink capacity, resources from the original uplink could be used for downlink and vice versa.
However, the main source of complexity is the cross-interference between uplink and downlink transmissions. When up- and downlink use orthogonal resources (different time-spans or frequency bands) in the first place, the interference situation is reasonable. But when in a full frequency reuse network, such as LTE, a terminal in one cell may use the same resources as the eNodeB in the adjacent cell, complex interference coordination would be obligatory.
Agree with the other answer that the question is mixing up concepts. TDD/FDD has nothing to do with the multiple access provided by OFDMA. TDD/FDD is about duplexing, which is, how the traffic in the uplink and downlink are separated, and reducing interference between the traffic in the two directions.
In earlier generations of wireless cellular systems (CDMA, UMTS, ..), FDD was the very dominant choice between the two modes. Especially for voice communications, this made a lot of sense. You have bidirectional traffic that both need a narrowband channel. Separating them by frequency is a reasonable choice, where you don't need to waste time with guard intervals (for switching between uplink and downlink in the RF in TDD).
A major reason why TDD has grown in popularity in LTE versus in earlier generations of wireless cellular systems, is that the traffic patterns have vastly changed with LTE. Now, data traffic is pre-eminent, and typically asymmetric (more on the downlink than uplink). A major advantage of TDD for this kind of traffic is that the ratio of uplink to downlink is configurable in a system.