Channel Estimation in FDD and TDD Systems

It is clear that the transmitter can only acquire the CSI indirectly, since the signal goes into the channel only after leaving the transmitter [32]. Therefore, the CSI can be obtained either by using the reciprocity principle or by using feedback from the receiver.

The reciprocity of the wireless channel implies that the channel from antenna A to antenna B can be estimated during the transmission in the opposite direction (B to A) since it is identical to the transpose of the channel fromB to A (e.g. [17, 18]) as shown in Fig. 2.6. Pilot symbols are often used for channel estimation. The reciprocity holds if both forward and reverse links are located at the same frequency, the same time, and the same antenna locations. In practical systems, however, the forward and reverse links cannot use identical frequency, time, and spatial locations. In spite of that, the reciprocity principle can still hold approximately in some situations. For example, in the temporal dimension, the reciprocity principle is held if any time lag∆_t between the forward and reverse transmission is much smaller than the channel coherence time T_c. Similarly, in the frequency dimension, any frequency offset∆f must be much smaller than the channel coherence bandwidthBc, and in the spatial dimension the antenna location differences on the two links must be much smaller than the channel coherence distanceDc [28].

Since most communication systems are bi-directional, the uplink and downlink channels must be separated into orthogonal signaling dimensions. This separation is

2.7 Channel Estimation in FDD and TDD Systems 23

H_AB

Transceiver Transceiver B

A estimates H_AB

feedback H_AB

Figure 2.7: Obtaining CSIT using Feedback.

called duplexing.

Practical channel acquisition based on reciprocity may be applicable in TDD-TDMA (Time-Division Duplex-Time-Division Multiple Access) systems [27, 32, 38, 39]. TDMA consists of dividing the frame duration Tf intoT non-overlapping subintervals, each of durationTf/T . Each user who wants to transmit has to use a particular subinterval within each frame. In TDD systems, orthogonal time slots are assigned to each user to transmit to the base station and to receive from the base station. While TDD-TDMA systems have identical forward and reverse frequency bands and antennas, there is a time lag between the forward and reverse links. As mentioned above, such time lags must be negligible compared to the channel coherence time. Even in this case, reciprocity is difficult to accomplish due to the need for very good calibration (e.g. [24]).

In Frequency-Division Multiple Access (FDMA) systems (commonly used to accommodate multiple users for voice and data), the available channel bandwidth is split into a number ofF frequency non-overlapping subchannels. Each subchannel is assigned to a user on demand. With Frequency-Division Duplex (FDD), separate frequency bands are assigned to each user for transmitting to or receiving from the base station. Therefore, FDD-FDMA systems often have identical temporal and spatial channel dimensions, but the frequency offset between the forward and reverse links is usually much larger than the channel coherence bandwidth. Therefore, reciprocity is usually not applicable in FDD systems. Instead, a feedback channel should be used to send the Channel State Information (CSI) from the transmitter to the receiver, as illustrated in Fig. 2.7.

The channel response is estimated at the receiver B during the forward link (A to B) transmission, and the information is sent to the transmitterA on the reverse-link.

The same is true in a multiuser system. The transmitter is unable to obtain the CSI during reception in FDD systems because the channels are not reciprocal. This information must be sent from the users to the transmitter by means of a feedback or reverse channel, as plotted in Fig. 2.8 for a multiuser MISO system. Such reverse channels are actually implemented in most of the standards [40–42]. In this case, calibration errors

. . .

. . .

Rx

Rx precoding

n

u

n

h

h

u

x

u

x

y

u ˆ

u ˆ

y

feedback of user k feedback of user 1

Figure 2.8: Multi-user MISO System with CSI Feedback and Precoding over Flat MISO Channels.

are estimated as part of the CSI and no special problems arise from calibration as for TDD. However, the time lag,D, between the channel measurement at the receivers and its use at the transmitter is a source of error (which will be modeled in this work by means of the feedback delay error) unless it is much smaller than the channel coherence time.

Moreover, the data rate of the feedback channel is highly limited. One drawback of feedback is the possible overhead of the reverse channel and the increasing consumption of transmit resources. Therefore, methods of reducing feedback overhead in a simple way, such as quantization or truncation of the feedback information, are crucial for practical implementations. As a consequence of the quantization, any system with limited rate CSI feedback suffers from erroneous CSI at the transmitter. Thus, the quantization operation has to be carefully designed, as done in this work.

Feedback can also be used to send channel statistics that change very slowly compared to the channel itself. In [17, 43, 44], the estimation of the statistics of the channel is discussed. As the time horizon for estimating the statistics is very large, we assume error-free knowledge of the statistics of the channel. Additionally, we assume that the channel statistics are constant and known at both the transmitter and receiver side. Nevertheless, the time lag requirement for feeding back the channel statistics is not as strong as for the feedback of the channel coefficients.