Transmit diversity is antenna diversity from the transmitter side: two or more transmit antennas give a single-antenna receiver independently fading paths. It cannot be done by simply sending the same signal twice, so the antennas must be coded in time, frequency or delay, or steered with channel knowledge. The result is a steeper error curve with no extra antennas at the receiver.
This article explains the principle and the main techniques: Alamouti coding, cyclic delay diversity, transmit antenna selection and closed-loop transmission. For the wider comparison with receive diversity, see transmit and receive diversity.
The concept of transmit diversity
Transmit diversity exists because the antenna count is often lopsided. A base station or access point can carry several antennas and chains, whereas a small device may have one antenna, limited space and tight power limits. Putting the extra hardware at the transmitter delivers diversity to every receiver it serves, including simple ones.
The difficulty is that signals from two transmit antennas add in the air before the receiver can do anything. A receive diversity system has separate outputs to process, and a transmit diversity system has one.
Why repeating the signal does not work
Suppose each antenna sends s/√2, keeping total power fixed. The receiver sees (h1 + h2)s/√2. If h1 and h2 are independent complex Gaussian gains, their normalised sum is another complex Gaussian gain with the same mean power, so the channel is still one Rayleigh fader. Two antennas have achieved nothing.
Figure 1 shows this from 1 million simulated channels. The dashed curve for repeated transmission lies on top of the single-antenna curve, with 1% of the time at about 20 dB below the mean. Alamouti, with the same antennas and power, reaches 1% at 11.3 dB below the mean, an advantage of 8.7 dB.
Alamouti transmit diversity
The Alamouti code solves the problem with two antennas and two symbol periods. In period 1, antenna 1 sends s1 and antenna 2 sends s2. In period 2, antenna 1 sends -s2* and antenna 2 sends s1*. If the channel is constant across both periods, the received samples are:
r1 = h1s1 + h2s2 + n1
r2 = -h1s2* + h2s1* + n2
The receiver forms two combined outputs:
y1 = h1*r1 + h2r2* = (|h1|2 + |h2|2)s1 + noise
y2 = h2*r1 – h1r2* = (|h1|2 + |h2|2)s2 + noise
The cross terms cancel exactly, so each symbol is decoded separately with gain |h1|2 + |h2|2. That is the same sum MRC gets from two receive antennas. The code needs CSI at the receiver only, and it transmits one symbol per period, so it costs no rate. The transmitter needs no feedback.
Worked example: decoding one Alamouti block
Take h1 = 0.8 + 0.3j and h2 = -0.4 + 0.9j, with QPSK symbols s1 = (1 + j)/√2 and s2 = (1 – j)/√2. Noise samples are n1 = 0.05 – 0.02j and n2 = -0.03 + 0.04j.
- Path powers are |h1|2 = 0.73 and |h2|2 = 0.97, which sum to 1.70.
- The received samples are r1 = 0.757 + 1.677j and r2 = -0.030 + 0.181j.
- Combining gives y1 = 1.284 + 1.160j and y2 = 1.176 – 1.198j.
- Dividing by 1.70 gives 0.755 + 0.682j and 0.692 – 0.705j.
These are close to the transmitted 0.707 ± 0.707j, and the quadrants give the correct symbols. Without noise, the combining returns s1 exactly.
Diversity order and the 3 dB penalty
Alamouti delivers diversity order 2. With total power shared between two antennas, each path carries half the power, so the receiver sees the MRC result at 3.01 dB less SNR. BPSK bit error rate in Rayleigh fading with L-branch combining and branch Eb/N0 of γ is Pb = [(1-μ)/2]L Σk=0L-1 C(L-1+k, k)[(1+μ)/2]k, with μ = √(γ/(1+γ)). Alamouti uses L = 2 and γ/2.
Worked comparison: transmit diversity techniques
The table gives the Eb/N0 needed for two BER targets, from the formula above and, for antenna selection, from Pb(sel) = 2Pb(γ) – Pb(γ/2) using the L = 1 expression.
| Scheme | BER 10-3 | BER 10-4 | Saving at 10-4 | Feedback |
|---|---|---|---|---|
| SISO 1×1 | 24.0 dB | 34.0 dB | None | None |
| Alamouti 2×1 | 14.1 dB | 19.3 dB | 14.7 dB | None |
| Antenna selection 2×1 | 12.6 dB | 17.8 dB | 16.2 dB | Index only |
| Closed-loop MRT 2×1 | 11.1 dB | 16.3 dB | 17.7 dB | Full phase and gain |
| Alamouti 2×2 | 7.0 dB | 10.2 dB | 23.8 dB | None |
The savings are larger at lower error rates, which is the signature of diversity. Going from 10-3 to 10-4 costs 10.0 dB on SISO but only 5.2 dB on any of the 2×1 schemes. These are uncoded figures in ideal Rayleigh fading with perfect channel estimates, so a coded link sees smaller differences.
Orthogonal space-time codes beyond two antennas
Alamouti is the only complex orthogonal code that is full rate. Codes for three and four antennas exist, but with rate 3/4 at best for four antennas, so these systems trade some rate. That is one reason practical systems favour other methods when they have more than two antennas. LTE uses a space-frequency version, coding across adjacent subcarriers instead of symbol periods, which suits OFDM and tolerates channels that vary quickly in time.
Cyclic delay diversity
Cyclic delay diversity (CDD) takes a different route, one that needs no change at the receiver. Each antenna sends the same OFDM symbol, cyclically shifted by a small delay. The receiver sees a single channel, but with a delay δ between antennas the channel becomes:
H(f) = [h1 + h2e-j2πfδ]/√2
Even if the original channel is flat, H(f) now has notches every 1/δ across the band. A delay of 400 ns places a notch every 2.5 MHz, or 8 across 20 MHz, while 100 ns places one every 10 MHz, or 2. Nothing has been gained on one subcarrier, because that gain has the same Rayleigh statistics as before. The benefit appears when coding spreads data over subcarriers, so CDD turns transmit diversity into frequency diversity, which an OFDM decoder already knows how to use.
CDD also avoids unintended beamforming, where identical signals on several antennas form a pattern that nulls some directions. Wi-Fi uses a closely related method, cyclic shift diversity, for this reason. The delay must stay well inside the cyclic prefix, and it needs a coded system, so it does nothing for an uncoded narrowband link.
Closed-loop transmit diversity
With channel knowledge, the transmitter can do better than open-loop coding.
- Transmit antenna selection uses the strongest antenna, and it needs only one RF chain and an index in feedback. The gain against SISO is 16.2 dB at BER 10-4.
- Maximum ratio transmission weights each antenna by the conjugate of its channel, so signals add in phase at the receiver. It matches MRC, including the 3.01 dB of array gain that Alamouti lacks.
- Quantised feedback restricts weights to a small codebook, trading a little gain for less overhead. In time division duplex systems, the transmitter can instead infer the channel from uplink pilots, as described under channel state information.
Fast movement undoes these gains, because the channel changes before the weights are applied. Diversity techniques for SIMO and MISO shows where open-loop Alamouti overtakes feedback.
RF design considerations
Transmit diversity changes the RF budget in some useful ways. Sharing a fixed total power across two chains means each power amplifier delivers 3 dB less, so 200 mW total needs two 100 mW stages. Two smaller amplifiers can be easier to build than one large one, though they add a second chain, filtering and calibration. Regulators may limit total radiated power, so a designer cannot always count on double power.
Antenna spacing still matters. Paths must be close to uncorrelated, and the same spacing rules apply as for space diversity. Each path also needs a channel estimate, so reference signals must be sent per antenna, which adds overhead.
Frequently asked questions
What is transmit diversity?
It is a method that uses two or more transmit antennas to give a receiver independently fading paths, without needing more receive antennas. Alamouti coding, cyclic delay diversity and antenna selection are common examples. It improves reliability and does not raise peak rate.
Does transmit diversity increase data rate?
Not directly. Alamouti sends one symbol per period, the same as a single antenna. A more reliable link can support a higher modulation order on average, however, so throughput in fading can rise.
What is the difference between transmit diversity and beamforming?
Open-loop transmit diversity needs no channel knowledge at the transmitter and gives no array gain. Beamforming needs that knowledge and focuses power. Beamforming on a two-antenna link is the same as MRT, which also provides diversity.
Is antenna diversity the same as transmit diversity?
Transmit diversity is one kind of antenna diversity. Antenna diversity includes both receive and transmit forms, and the receive form is the simpler of the two because the receiver has separate signals to process.
Related topics
Transmit and receive diversity gives the fade margin view, and MIMO and multiple antenna systems sets diversity next to array gain and multiplexing. To put these gains into a design, use the RF link budget guide and the antennas hub.